E11 - Quality and Statistics

ABSTRACT
This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other. This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.
SIGNIFICANCE AND USE
4.1 Regression analysis is a procedure that uses data to study the statistical relationships between two or more variables (1, 2).3 This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.  
4.2 A regression model consists of: (1) a regression function that relates the mean values of the response variable distribution to fixed values of the predictor variable, and (2) a statistical distribution that describes the variability in the response variable values at a fixed value of the predictor variable.  
4.2.1 The regression analysis utilizes either experimental or observational data to estimate the parameters defining a regression model and their precision. Diagnostic procedures are utilized to assess the resulting model fit and can suggest other models for improved prediction performance.  
4.3 The information in this practice is arranged as follows.  
4.3.1 Section 5 gives a general outline of the steps in the regression analysis procedure. The subsequent sections cover procedures for estimation of specific regression models.  
4.3.2 Section 6 assumes a straight line relationship between the two variables. This is also known as the simple linear regression model or a first order model. This model should be used as a starting point for understanding the XY relationship and ultimately defining the best fitting model to the data.  
4.3.3 Section 7 considers a proportional relationship between the variables, where the ratio of one variable to the other is constant. The intercept is constrained to be zero. This model is useful for single point calibration, where a reference material is run periodically as a standard during routine testing to correct for drift in instrument performance over a given range of test results.  
4.3.4 Section 8 di...
SCOPE
1.1 This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other.  
1.2 The regression analysis provides graphical and calculational procedures for selecting the best statistical model that describes the relationship and for evaluation of the fit of the data to the selected model.  
1.3 The resulting regression model can be useful for developing process knowledge through description of the variable relationship, in making predictions of future values, in relating the precision of a test method to the value of the characteristic being measured, and in developing control methods for the process generating values of the variables.  
1.4 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development ...

ABSTRACT
This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards. This guide also describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates.
SIGNIFICANCE AND USE
4.1 This guide describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates. Practice E105 provides principles for designing probability sampling plans in relation to the objectives of study, costs, and practical constraints. Practice E122 aids in specifying the required sample size. Practice E141 describes conditions to ensure validity of the results of sampling. Further description of the designs and formulas in this guide, and beyond it, can be found in textbooks (1-10).3  
4.2 Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement. For bulk sampling, material is extracted into a composite.  
4.3 A sampling plan consists of instructions telling how to list addresses and how to select the addresses to be measured or extracted. A frame is a listing of addresses each of which is indexed by a single integer or by an n-tuple (several integer) number. The sampled population consists of all addresses in the frame that can actually be selected and measured. It is sometimes different from a targeted population that the user would have preferred to be covered.  
4.4 A selection scheme designates which indexes constitute the sample. If certified random numbers completely control the selection scheme the sample is called a probability sample. Certified random numbers are those generated either from a table (for example, Ref (11)) that has been tested for equal digit frequencies and for serial independence, from a computer program that was checked to have a long cycle length, or from a random physical method such as tossing of a coin or a casino-quality spinner.  
4.5 The objective of sampling is often to estimate t...
SCOPE
1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.  
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the population.  
1.3 No system of units is specified in this standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice provides a general methodology for evaluating single-stage or multiple-stage acceptance procedures which involve a quality characteristic measured on a numerical scale. This methodology computes, at a prescribed confidence level, a lower bound on the probability of passing an acceptance procedure, using estimates of the parameters of the distribution of test results from a sampled population.
SIGNIFICANCE AND USE
4.1 This practice considers inspection procedures that may involve multiple-stage sampling, where at each stage one can decide to accept or to continue sampling, and the decision to reject is deferred until the last stage.  
4.1.1 At each stage there are one or more acceptance criteria on the test results; for example, limits on each individual test result, or limits on statistics based on the sample of test results, such as the average, standard deviation, or coefficient of variation (relative standard deviation).  
4.2 The methodology in this practice defines an acceptance region for a set of test results from the sampled population such that, at a prescribed confidence level, the probability that a sample from the population will pass the acceptance procedure is greater than or equal to a prespecified lower bound.  
4.2.1 Having test results fall in the acceptance region is not equivalent to passing the acceptance procedure, but provides assurance that a sample would pass the acceptance procedure with a specified probability.  
4.2.2 This information can be used for process demonstration, validation of test methods, and qualification of instruments, processes, and materials.  
4.2.3 This information can be used for lot release (acceptance), but the lower bound may be conservative in some cases.  
4.2.4 If the results are to be applied to future test results from the same process, then it is assumed that the process is stable and predictable. If this is not the case then there can be no guarantee that the probability estimates would be valid predictions of future process performance.  
4.3 This methodology was originally developed (1-4)3 for use in two specific quality characteristics of drug products in the pharmaceutical industry but will be applicable for acceptance procedures in all industries.  
4.4 Mathematical derivations would be required that are specific to the individual criteria of each test.
SCOPE
1.1 This practice provides a general methodology for evaluating single-stage or multiple-stage acceptance procedures which involve a quality characteristic measured on a numerical scale. This methodology computes, at a prescribed confidence level, a lower bound on the probability of passing an acceptance procedure, using estimates of the parameters of the distribution of test results from a sampled population.  
1.2 For a prescribed lower probability bound, the methodology can also generate an acceptance limit table, which defines a set of test method outcomes (for example, sample averages and standard deviations) that would pass the acceptance procedure at a prescribed confidence level.  
1.3 This approach may be used for demonstrating compliance with in-process, validation, or lot-release specifications.  
1.4 The system of units for this practice is not specified.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
The purpose of this guide is to provide guidelines for identifying the elements that comprise the test result of a test method and to illustrate how these elements combine into the test result. It covers the types of measurement scales used for expressing observations and test results. This guide provides information on the construction of test results from more elemental measurements.
SIGNIFICANCE AND USE
4.1 All test methods have an output in the form of a test result. This guide provides information on the construction of test results from more elemental measurements.  
4.2 A well-defined test result is necessary before any precision statements can be made about the test method.  
4.2.1 Form and Style for ASTM Standards,2 Section A21, requires that every test method shall contain a statement regarding its precision, preferably as a result of an interlaboratory test program. Reporting of such studies is described in Practice E177, which illustrates the development of test results from observations and test determinations.  
4.2.2 Precision statements for ASTM test methods are applicable to test results. They are not applicable to test determinations or observations, unless specifically and clearly indicated otherwise.
SCOPE
1.1 This standard provides guidelines for identifying the elements that comprise the test result of a test method and to illustrate how these elements combine into the test result.  
1.2 Types of measurement scales used for expressing observations and test results are discussed.  
1.3 No system of units is specified in this standard.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice presents rules for accepting or rejecting evidence based on a sample. Statistical evidence for this practice is in the form of an estimate of a proportion, an average, a total, or other numerical characteristic of a finite population or lot. This practice is an estimate of the result which would have been obtained by investigating the entire lot or population under the same rules and with the same care as was used for the sample. One purpose of this practice is to describe straightforward sample selection and data calculation procedures so that courts, commissions, etc. will be able to verify whether such procedures have been applied.
SIGNIFICANCE AND USE
4.1 This practice is designed to permit users of sample survey data to judge the trustworthiness of results from such surveys. Practice E105 provides a statement of principles for guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material. Guide E1402 describes the principal types of sampling designs. Practice E122 aids in deciding on the required sample size.  
4.2 Section 5 gives extended definitions of the concepts basic to survey sampling and the user should verify that such concepts were indeed used and understood by those who conducted the survey. What was the frame? How large (exactly) was the quantity N? How was the parameter θ estimated and its standard error calculated? If replicate subsamples were not used, why not? Adequate answers should be given for all questions. There are many acceptable answers to the last question.  
4.3 If the sample design was relatively simple, such as simple random or stratified, then fully valid estimates of sampling variance are easily available. If a more complex design was used then methods such as discussed in Ref (1)3 or in Guide E1402 may be acceptable. Use of replicate subsamples is the most straightforward way to estimate sampling variances when the survey design is complex.  
4.4 Once the survey procedures that were used satisfy Section 5, see if any increase in sample size is needed. The calculations for making it objectively are described in Section 6.  
4.5 Refer to Section 7 to guide in the interpretation of the uncertainty in the reported value of the parameter estimate, θ^, that is, the value of its standard error, se(θ^). The quantity se(θ^) should be reviewed to verify that the risks it entails are commensurate with the size of the sample.  
4.6 When the audit subsample shows that there was reasonable conformity with prescribed procedures and when the known instances of departures from the survey plan can be shown to have no appreciable effect on the est...
SCOPE
1.1 This practice presents rules for accepting or rejecting evidence based on a sample. Statistical evidence for this practice is in the form of an estimate of a proportion, an average, a total, or other numerical characteristic of a finite population or lot. It is an estimate of the result which would have been obtained by investigating the entire lot or population under the same rules and with the same care as was used for the sample.  
1.2 One purpose of this practice is to describe straightforward sample selection and data calculation procedures so that courts, commissions, etc. will be able to verify whether such procedures have been applied. The methods may not give least uncertainty at least cost, they should however furnish a reasonable estimate with calculable uncertainty.  
1.3 This practice is primarily intended for one-of-a-kind studies. Repetitive surveys allow estimates of sampling uncertainties to be pooled; the emphasis of this practice is on estimation of sampling uncertainty from the sample itself. The parameter of interest for this practice is effectively a constant. Thus, the principal inference is a simple point estimate to be used as if it were the unknown constant, rather than, for example, a forecast or prediction interval or distribution...

ABSTRACT
This guide identifies statistical procedures for use in developing new test methods or revising or evaluating existing test methods, or both. It also cites statistical procedures especially useful in the application of test methods. This standard recommends what approaches may be taken and indicates which standards may be used to perform such assessments.
SIGNIFICANCE AND USE
4.1 The creation of a standardized test method generally follows a series of steps from inception to approval and ongoing use. In all such stages there are questions of how well the test method performs.  
4.1.1 Assessments of a new or existing test method generally involve statistical planning and analysis. This standard recommends what approaches may be taken and indicates which standards may be used to perform such assessments.  
4.2 This standard introduces a series of phases which are recommended to be considered during the life cycle of a test method as depicted in Fig. 1. These begin with a design phase where the standard is initially prepared. A development phase involves a variety of experiments that allow further refinement and understanding of how the test method performs within a laboratory. In an evaluation phase the test method is then examined by way of interlaboratory studies resulting in precision and bias statistics which are published in the standard. Finally, the test method is subject to a monitoring phase.
FIG. 1 Sequence of Steps  
4.3 All ASTM test methods are required to include statements on precision and bias.3  
4.4 Since ASTM began to require all test methods to have precision and bias statements that are based on interlaboratory studies, there has been increased concern regarding what statistical experiments and procedures to use during the development of the test methods. Although there exists a wide range of statistical procedures, there is a small group of generally accepted techniques that are beneficial to follow. This guide is designed to provide a brief overview of these procedures and to suggest an appropriate sequence of conducting these procedures.  
4.5 Statistical procedures often result in interpretations that are not absolutes. Sometimes the information obtained may be inadequate or incomplete, which may lead to additional questions and the need for further experimentation. Information outside the data is also impo...
SCOPE
1.1 This guide identifies statistical procedures for use in developing new test methods or revising or evaluating existing test methods, or both.  
1.2 This guide also cites statistical procedures especially useful in the application of test methods.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method. This practice is also concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements. ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility and knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values or between data sources.
SIGNIFICANCE AND USE
4.1 ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility. This practice may be used in obtaining the needed information as simply as possible. This information may then be used to prepare a precision statement in accordance with Practice E177. Knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values (such as specification limits) or between data sources (different laboratories, instruments, etc.).  
4.1.1 When a test method is applied to a large number of portions of a material that are as nearly alike as possible, the test results obtained will not all have the same value. A measure of the degree of agreement among these test results describes the precision of the test method for that material. Numerical measures of the variability between such test results provide inverse measures of the precision of the test method. Greater variability implies smaller (that is, poorer) precision and larger imprecision.  
4.1.2 Precision is reported as a standard deviation, coefficient of variation (relative standard deviation), variance, or a precision limit (a data range indicating no statistically significant difference between test results).  
4.1.3 This practice is designed only to estimate the precision of a test method. However, when accepted reference values are available for the property levels, the test result data obtained according to this practice may be used in estimating the bias of the test method. For a discussion of bias estimation and the relationships between precision, bias, and accuracy, see Practice E177.  
4.2 The procedures presented in this practice consist of three basic steps: planning the interlaboratory study, guiding the testing phase of the study, and analyzing the test result data.  
4.2.1 The planning phase includes forming the ILS task group, the study design, selection, and number of participating laborato...
SCOPE
1.1 This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method.  
1.2 This practice does not concern itself with the development of test methods but rather with gathering the information needed for a test method precision statement after the development stage has been successfully completed. The data obtained in the interlaboratory study may indicate, however, that further effort is needed to improve the test method.  
1.3 Since the primary purpose of this practice is the development of the information needed for a precision statement, the experimental design in this practice may not be optimum for evaluating materials, apparatus, or individual laboratories.  
1.4 Field of Application—This practice is concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements.  
1.4.1 This practice ...

ABSTRACT
This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of average outgoing quality limit, AOQL, and lot tolerance percent defective, LTPD, sampling plans for determining acceptable of lots of product. Two general types of tables are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL. For each of the types, tables are provided both for single sampling and for double sampling. Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection.
SIGNIFICANCE AND USE
4.1 Two general types of tables (Note 1) are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL. The broad conditions under which the different types have been found best adapted are indicated below.  
4.1.1 For each of the types, tables are provided both for single sampling and for double sampling. Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection. Because each line in the tables covers a range of lot sizes, the AOQL values in the LTPD tables and the LTPD values in the AOQL tables are often conservative.
Note 1: Tables in Annex A1 – Annex A4 and parts of the text are reproduced by permission of John R. Wiley and Sons. More extensive tables and discussion of the methods will be found in that text.  
4.2 The sampling tables based on lot quality protection (LTPD) (the tables in Annex A1 and Annex A2) are perhaps best adapted to conditions where interest centers on each lot separately, for example, where the individual lot tends to retain its identity either from a shipment or a service standpoint. These tables have been found particularly useful in inspections made by the ultimate consumer or a purchasing agent for lots or shipments purchased more or less intermittently.  
4.3 The sampling tables based on average quality protection (AOQL) (the tables in Annex A3 and Annex A4) are especially adapted for use where interest centers on the average quality of product after inspection rather than on the quality of each individual lot and where inspection is, therefore, intended to serve, if necessary, as a partial screen for defective pieces. The latter point of view has been found particularly helpful, for example, in consumer inspections of continuing purchases of large quantities of a product and in manufacturing process inspections of parts where the inspection lots tend to lose their identity by merger in a common storeroom from which quantities are withdraw...
SCOPE
1.1 This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of average outgoing quality limit, AOQL, and lot tolerance percent defective, LTPD, sampling plans for determining acceptable of lots of product.  
1.2 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice presents methodology for the setting of an upper confidence bound regarding an unknown fraction or quantity non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero response in a sample. Three cases are considered. In Case 1, the sample is selected from a process or a very large population of interest. In Case 2, a sample of n items is selected at random from a finite lot of N items. In Case 3, there is a process, but the output is a continuum, such as area (for example, a roll of paper or other material, a field of crop), volume (for example, a volume of liquid or gas), or time (for example, hours, days, quarterly, etc.) The sample size is defined as that portion of the �continuum� sampled, and the defined attribute may occur any number of times over the sampled portion.
SIGNIFICANCE AND USE
4.1 In Case 1, the sample is selected from a process or a very large population of interest. The population is essentially unlimited, and each item either has or has not the defined attribute. The population (process) has an unknown fraction of items p (long run average process non-conforming) having the attribute. The sample is a group of n discrete items selected at random from the process or population under consideration, and the attribute is not exhibited in the sample. The objective is to determine an upper confidence bound, pu, for the unknown fraction p whereby one can claim that p ≤ pu with some confidence coefficient (probability) C. The binomial distribution is the sampling distribution in this case.  
4.2 In Case 2, a sample of n items is selected at random from a finite lot of N items. Like Case 1, each item either has or has not the defined attribute, and the population has an unknown number, D, of items having the attribute. The sample does not exhibit the attribute. The objective is to determine an upper confidence bound, Du, for the unknown number D, whereby one can claim that D ≤ Du with some confidence coefficient (probability) C. The hypergeometric distribution is the sampling distribution in this case.  
4.3 In Case 3, there is a process, but the output is a continuum, such as area (for example, a roll of paper or other material, a field of crop), volume (for example, a volume of liquid or gas), or time (for example, hours, days, quarterly, etc.) The sample size is defined as that portion of the “continuum” sampled, and the defined attribute may occur any number of times over the sampled portion. There is an unknown average rate of occurrence, λ, for the defined attribute over the sampled interval of the continuum that is of interest. The sample does not exhibit the attribute. For a roll of paper, this might be blemishes per 100 ft2; for a volume of liquid, microbes per cubic litre; for a field of crop, spores per acre; for a time interval, ca...
SCOPE
1.1 This practice presents methodology for the setting of an upper confidence bound regarding a unknown fraction or quantity non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero response in a sample. Three cases are considered.  
1.1.1 The sample is selected from a process or a very large population of discrete items, and the number of non-conforming items in the sample is zero.  
1.1.2 A sample of items is selected at random from a finite lot of discrete items, and the number of non-conforming items in the sample is zero.  
1.1.3 The sample is a portion of a continuum (time, space, volume, area, etc.) and the number of non-conformities in the sample is zero.  
1.2 Allowance is made for misclassification error in this practice, but only when misclassification rates are well understood or known and can be approximated numerically.  
1.3 The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this standard.  
1.4 This ...

ABSTRACT
This practice establishes lot or batch sampling plans and procedures for inspection by attributes using MIL-STD-105E as a basis for sampling a steady stream of lots indexed by acceptance quality limit (AQL). It provides the sampling plans of MIL-STD-105E in ASTM format for use by ASTM committees and others and recognizes the continuing usage of MIL-STD-105E in industries supported by ASTM. This practice also establishes lot or batch sampling plans and procedures for inspection by attributes.
SIGNIFICANCE AND USE
4.1 Purpose—This publication establishes lot or batch sampling plans and procedures for inspection by attributes. This publication shall not be interpreted to supersede or conflict with any contractual requirements. The words “accept,” “acceptance,” “acceptable,” etc, refer only to the contractor’s use of the sampling plans contained in this standard and do not imply an agreement by the customer (formerly “Government” in original text) to accept any product. Determination of acceptability by the customer shall be as described in contractual documents. The sampling plans described in this standard are applicable to AQL’s of 0.01 % or higher and are therefore not suitable for applications where quality levels in the range of parts per million levels can be realized.  
4.2 Application—Sampling plans designated in this publication are applicable, but not limited, to inspection of the following: (1) end items, (2) components and raw materials, (3) operations or services, (4) materials in process, (5) supplies in storage, (6) maintenance operations, (7) data or records, (8) administrative procedures. These plans are intended primarily to be used for a continuing series of lots or batches. The plans may also be used for the inspection of isolated lots or batches, but, in this latter case, the user is cautioned to consult the operating characteristic curves to find a plan which will yield the desired protection (see 6.11).
SCOPE
1.1 This practice establishes lot or batch sampling plans and procedures for inspection by attributes using MIL-STD-105E as a basis for sampling a steady stream of lots indexed by acceptance quality limit (AQL).  
1.2 This practice provides the sampling plans of MIL-STD-105E in ASTM format for use by ASTM committees and others. It recognizes the continuing usage of MIL-STD-105E in industries supported by ASTM. Most of the original text in MIL-STD-105E is preserved in Sections 4 – 6 of this practice.  
1.3 No system of units is specified in this standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This guide presents terminology, concepts, and selected methods and formulas useful for measurement systems analysis (MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to the non-destructive measurement of the physical properties of manufactured objects. This guide presents selected concepts and methods useful for describing and understanding the measurement process. This guide is not intended to be a comprehensive survey of this topic.
SIGNIFICANCE AND USE
4.1 Many types of measurements are made routinely in research organizations, business and industry, and government and academic agencies. Typically, data are generated from experimental effort or as observational studies. From such data, management decisions are made that may have wide-reaching social, economic, and political impact. Data and decision making go hand in hand and that is why the quality of any measurement is important—for data originate from a measurement process. This guide presents selected concepts and methods useful for describing and understanding the measurement process. This guide is not intended to be a comprehensive survey of this topic.  
4.2 Any measurement result will be said to originate from a measurement process or system. The measurement process will consist of a number of input variables and general conditions that affect the final value of the measurement. The process variables, hardware and software and their properties, and the human effort required to obtain a measurement constitute the measurement process. A measurement process will have several properties that characterize the effect of the several variables and general conditions on the measurement results. It is the properties of the measurement process that are of primary interest in any such study. The term “measurement systems analysis” or MSA study is used to describe the several methods used to characterize the measurement process.
Note 1: Sample statistics discussed in this guide are as described in Practice E2586; control chart methodologies are as described in Practice E2587.
SCOPE
1.1 This guide presents terminology, concepts, and selected methods and formulas useful for measurement systems analysis (MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to the non-destructive measurement of the physical properties of manufactured objects.  
1.2 Units—The system of units for this guide is not specified. Dimensional quantities in the guide are presented only as illustrations of calculation methods and are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice covers simple methods for calculating how many units to include in a random sample in order to estimate with a specified precision, a measure of quality for all the units of a lot of material or produced by a process. It also treats the common situation where the sampling units can be considered to exhibit a single source of variability; it does not treat multi-level sources of variability.
SIGNIFICANCE AND USE
4.1 This practice is intended for use in determining the sample size required to estimate, with specified precision, a measure of quality of a lot or process. The practice applies when quality is expressed as either the lot average for a given property, or as the lot fraction not conforming to prescribed standards. The level of a characteristic may often be taken as an indication of the quality of a material. If so, an estimate of the average value of that characteristic or of the fraction of the observed values that do not conform to a specification for that characteristic becomes a measure of quality with respect to that characteristic. This practice is intended for use in determining the sample size required to estimate, with specified precision, such a measure of the quality of a lot or process either as an average value or as a fraction not conforming to a specified value.
SCOPE
1.1 This practice covers simple methods for calculating how many units to include in a random sample in order to estimate with a specified precision, a measure of quality for all the units of a lot of material, or produced by a process. This practice will clearly indicate the sample size required to estimate the average value of some property or the fraction of nonconforming items produced by a production process during the time interval covered by the random sample. If the process is not in a state of statistical control, the result will not have predictive value for immediate (future) production. The practice treats the common situation where the sampling units can be considered to exhibit a single (overall) source of variability; it does not treat multi-level sources of variability.  
1.2 The system of units for this standard is not specified. Dimensional quantities in the standard are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This standard is the general terminology standard for terms defined in the standards of Committee E11 on Quality and Statistics. A term in this standard which lists an attribution to an E11 technical standard indicates that the standard is normative for that term. Term definitions that are similar to ISO 3534 will be noted in this standard, but ISO 3534 will not be considered normative for any E11 terms.
SCOPE
1.1 This standard is the general terminology standard for terms defined in the standards of Committee E11 on Quality and Statistics.  
1.2 A term in this standard which lists an attribution to an E11 technical standard indicates that the standard is normative for that term. Any changes in the term definition in the normative standard will be editorially changed in this standard. Any terms added to an E11 standard will be editorially added to this standard with an attribution to that standard.  
1.3 Term definitions that are similar to ISO 3534 will be noted in this standard, but ISO 3534 will not be considered normative for any E11 terms.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice is intended to assist the various technical committees in the use of uniform methods of indicating the number of digits which are to be considered significant in specification limits, for example, specified maximum values and specified minimum values. This practice is also intended to be used in determining conformance with specifications when the applicable ASTM specifications or standards make a direct reference.
SCOPE
1.1 This practice is intended to assist the various technical committees in the use of uniform methods of indicating the number of digits which are to be considered significant in specification limits, for example, specified maximum values and specified minimum values. Its aim is to outline methods which should aid in clarifying the intended meaning of specification limits with which observed values or calculated test results are compared in determining conformance with specifications.  
1.2 This practice is intended to be used in determining conformance with specifications when the applicable ASTM specifications or standards make direct reference to this practice.  
1.3 Reference to this practice is valid only when a choice of method has been indicated, that is, either absolute method or rounding method.  
1.4 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice describes methods for the statistical analysis of laboratory results obtained from interlaboratory proficiency testing programs. As in accordance with Practice E1301, proficiency testing is the use of inter-laboratory comparisons for the determination of laboratory testing or measurement performance. The methods provide direction for assessing and categorizing the performance of individual laboratories based on the relative likelihood of occurrence of their test results, and for determining estimates of testing variation associated with repeatability and reproducibility. Assumptions are that a majority of the participating laboratories execute the test method properly and that samples are of sufficient homogeneity that the testing results represent results obtained from each laboratory testing essentially the same material. Each laboratory receives the same instructions or protocol.
SIGNIFICANCE AND USE
5.1 This practice is specifically designed to describe simple robust statistical methods for use in proficiency testing programs.  
5.2 Proficiency testing programs can use the methods in this practice for the purpose of comparing testing results obtained from a group of participating laboratories. The practice describes evaluation of individual laboratory results using the interquartile range and Tukey inner and outer fences.  
5.3 In addition, the data obtained in proficiency testing programs may contain information regarding repeatability (within-lab) and reproducibility (between-lab) testing variation. Repeatability information is possible only if the program uses more than one sample. See Method B. Proficiency testing programs often have a greater number of participants than might be available for conducting an interlaboratory study to determine the precision of a test method (such as described in Practice E691). Precision estimates obtained for the larger number of participants in a proficiency testing program, along with the corresponding wider variation of test conditions, can provide useful information to standards developers regarding the precision of test results that can be expected for a test method when in actual use in the general testing community.  
5.4 To estimate the precision of a test method, the participants must use the same test method to obtain their test results, and testing must be performed under the conditions required for repeatability and reproducibility. The precision estimates are applicable to the property levels and material types included in the testing program. The precision of a test method may vary considerably for different material types and at different property levels.  
5.5 This practice may be useful to proficiency testing program administrators and provides examples of statistical methods along with explanations of some of the advantages of the suggested methods of analysis. The analyses resulting from the applicatio...
SCOPE
1.1 This practice describes methods for the statistical analysis of laboratory results obtained from interlaboratory proficiency testing programs. As in accordance with Practice E1301, proficiency testing is the use of interlaboratory comparisons for the determination of laboratory testing or measurement performance. Conversely, collaborative study (or collaborative trial) is the use of interlaboratory comparisons for the determination of the precision of a test method, as covered by Practice E691.  
1.1.1 Method A covers testing programs using single test results obtained by testing a single sample (each laboratory submits a single test result).  
1.1.2 Method B covers testing programs using paired test results obtained by testing two samples (each laboratory submits one test result for each of the two samples). The two samples should be of the same material or two materials similar enough to have approximately the same degree of variation in test results.  
1.2 Methods A and B are applicable to proficiency test...

ABSTRACT
This guide covers fundamental concepts, applications, and mathematical relationships associated with reliability as used in industrial areas and as applied to simple components, processes, and systems or complex final products. This guide summarizes selected concepts, terminology, formulas, and methods associated with reliability and its application to products and processes.
SIGNIFICANCE AND USE
4.1 This practice describes the use of control charts as a tool for use in statistical process control (SPC). Control charts were developed by Shewhart (2)3 in the 1920s and are still in wide use today. SPC is a branch of statistical quality control (3, 4), which also encompasses process capability analysis and acceptance sampling inspection. Process capability analysis, as described in Practice E2281, requires the use of SPC in some of its procedures. Acceptance sampling inspection, described in Practices E1994, E2234, and E2762, requires the use of SPC to minimize rejection of product.  
4.2 Principles of SPC—A process may be defined as a set of interrelated activities that convert inputs into outputs. SPC uses various statistical methodologies to improve the quality of a process by reducing the variability of one or more of its outputs, for example, a quality characteristic of a product or service.  
4.2.1 A certain amount of variability will exist in all process outputs regardless of how well the process is designed or maintained. A process operating with only this inherent variability is said to be in a state of statistical control, with its output variability subject only to chance, or common, causes.  
4.2.2 Process upsets, said to be due to assignable, or special causes, are manifested by changes in the output level, such as a spike, shift, trend, or by changes in the variability of an output. The control chart is the basic analytical tool in SPC and is used to detect the occurrence of special causes operating on the process.  
4.2.3 When the control chart signals the presence of a special cause, other SPC tools, such as flow charts, brainstorming, cause-and-effect diagrams, or Pareto analysis, described in various references (4-8), are used to identify the special cause. Special causes, when identified, are either eliminated or controlled. When special cause variation is eliminated, process variability is reduced to its inherent variability, and control...
SCOPE
1.1 This practice provides guidance for the use of control charts in statistical process control programs, which improve process quality through reducing variation by identifying and eliminating the effect of special causes of variation.  
1.2 Control charts are used to continually monitor product or process characteristics to determine whether or not a process is in a state of statistical control. When this state is attained, the process characteristic will, at least approximately, vary within certain limits at a given probability.  
1.3 This practice applies to variables data (characteristics measured on a continuous numerical scale) and to attributes data (characteristics measured as percentages, fractions, or counts of occurrences in a defined interval of time or space).  
1.4 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations...

ABSTRACT
This standard includes those statistical items related to the area of design of experiments for which standard definitions appear desirable. It provides definitions, descriptions, discussion, and comparison of terms.
SIGNIFICANCE AND USE
3.1 This standard is a subsidiary to Terminology E456.  
3.2 It provides definitions, descriptions, discussion, and comparison of terms.
SCOPE
1.1 This standard includes those statistical items related to the area of design of experiments for which standard definitions appear desirable.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice establishes tables and procedures for applying five different types of continuous sampling plans for inspection by attributes using MIL-STD-1235B as a basis for sampling a steady stream of lots indexed by AQL. This practice represents a conversion of MIL-STD1235B to an ASTM-supported standard.
SIGNIFICANCE AND USE
4.1 The reason for preserving military sampling standards is that many organizations throughout the world still use these standards in their current form. MIL-STD-1235B is no longer supported by the U.S. Department of Defense as of the mid-1990s and is out of print, but does exist in the public domain. This practice represents a conversion of MIL-STD-1235B to an ASTM-supported standard.  
4.2 This practice provides the tables and procedures for applying five different types of continuous sampling plans for inspection by attributes. These continuous sampling plans are discussed in Sections 6 – 10 of this practice and each section includes information on:
(1) Initiation of 100 % inspection in use.
(2) Requirements on when to switch to sampling inspection.
(3) Conditions warranting a return to 100 % inspection.
(4) When a change in Code Letter, if desired, can be made.
(5) What to do when the checking inspector finds a defect that was originally found conforming by the screening inspector(s), that is, ineffective screening.
(6) Situations where a defect is found before the switch to 100 % inspection causing excessive periods of 100 % inspection so action must be taken, that is, long periods of screening.  
4.2.1 Section 6 (Section 2 in MIL-STD-1235B) describes specific procedures and applications of the CSP-1 sampling plans – a single-level continuous sampling procedure which provides for alternating between sequences of 100 % inspection and sampling inspection.  
4.2.2 Section 7 (Section 3 in MIL-STD-1235B) describes specific procedures and applications of the CSP-F sampling plans – a variation of the CSP-1 plans in that CSP-F plans are applied to a relatively short run of product, thereby permitting smaller clearance numbers to be used.  
4.2.3 Section 8 (Section 4 in MIL-STD-1235B) describes specific procedures and applications of the CSP-2 sampling plans – a modification of CSP-1 in that 100 % inspection resumes only after a prescribed number of def...
SCOPE
1.1 This practice establishes tables and procedures for applying five different types of continuous sampling plans for inspection by attributes using MIL-STD-1235B as a basis for sampling a steady stream of lots indexed by AQL.  
1.2 This practice provides the sampling plans of MIL-STD-1235B in ASTM format for use by ASTM committees and others. It recognizes the continuing usage of MIL-STD-1235B in industries supported by ASTM. Most of the original text in MIL-STD-1235B is preserved in Sections 6 – 10 of this practice.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice covers outlying observations in samples and how to test the statistical significance of outliers. The procedures in this practice were developed primarily to apply to the simplest kind of experimental data, that is, replicate measurements of some property of a given material or observations in a supposedly random sample.
SCOPE
1.1 This practice covers outlying observations in samples and how to test the statistical significance of outliers.  
1.2 The system of units for this standard is not specified. Dimensional quantities in the standard are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

SIGNIFICANCE AND USE
4.1 A ruggedness test is a special application of a statistically designed experiment that makes changes in the test method variables, called factors, and then calculates the subsequent effect of those changes upon the test results. Factors are features of the test method or of the laboratory environment that are known to vary across laboratories and are subject to control by the test method.  
4.1.1 Statistical design enables more efficient and cost-effective determination of the factor effects than would be achieved if separate experiments were carried out for each factor. The proposed designs are easy to use in developing the information needed for evaluating quantitative test methods.  
4.2 In ruggedness testing, the two levels (settings) for each factor are chosen to use moderate separations between the high and low settings. In general, if there is an underlying difference between the levels, then the size of effects will increase with increased separation between the high and low settings of the factors. A run is an execution of the test method under prescribed settings of each of the factors under study. A ruggedness test consists of a set of runs.  
4.3 A ruggedness test is usually conducted within a single laboratory on uniform material, so that the effects of changing only the factors are measured. The results may then be used to assist in determining the degree of control required of factors described in the test method.  
4.4 Ruggedness testing should precede an interlaboratory (round robin) study to correct any deficiencies in the test method and may also be part of the validation phase of developing a standard test method as described in Guide E1488.  
4.5 This standard discusses design and analysis of ruggedness testing in Section 5 and contains an example of a basic eight run design. Some caution must be used in interpretation of results, since interaction effects may be present. These effects are present when a factor effect changes with the ...
SCOPE
1.1 This practice covers conducting ruggedness tests. The purpose of a ruggedness test is to identify those factors that strongly influence the measurements provided by a specific test method and to estimate how closely those factors need to be controlled.  
1.2 This practice restricts itself to experimental designs with two levels per factor. The designs require the simultaneous change of the levels of all of the factors, thus permitting the determination of the effects of each of the factors on the measured results.  
1.3 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material. The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of some chemical. A probability sampling plan will possess an objective procedure for the selection of the sample with the use of random numbers and a definite formula for the estimate and standard error of any estimate.
SIGNIFICANCE AND USE
4.1 The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, some chemical.  
4.2 The purpose may be the rational disposition of a lot or shipment without the intermediate step of the formation of an estimate.  
4.3 The purpose may be to provide aid toward rational action concerning the production process that generated the lot, pile or shipment.  
4.4 Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncertainties, such as bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from the theory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves were carried out properly, as well. Proper sampling requires that any random numbers were generated properly, the units to be sampled from were correctly identified, located, and drawn, and the measurements were made with measurement error at a level not exceeding the required purposes.  
4.5 Determination of bias and variance and of risks can be calculated when the selection was only partially determined by random numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or require additional data which may introduce experimental error.
SCOPE
1.1 This guide is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material.  
1.2 A system of units is not specified in this standard.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources to determine if their true means or variances differ by no more than predetermined limits. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.
SIGNIFICANCE AND USE
4.1 Laboratories conducting routine testing have a continuing need to make improvements in their testing processes. In these situations it must be demonstrated that any changes will neither cause an undesirable shift in the test results from the current testing process nor substantially affect a performance characteristic of the test method. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.  
4.1.1 The equivalence limit, which represents a worst-case difference or ratio, is determined prior to the equivalence test and its value is usually set by consensus among subject-matter experts.  
4.1.2 Examples of modifications to the testing process include, but are not limited, to the following:  
(1) Changes to operating levels in the steps of the test method procedure,
(2) Installation of new instruments, apparatus, or sources of reagents and test materials,
(3) Evaluation of new personnel performing the testing, and
(4) Transfer of testing to a new location.  
4.1.3 Examples of performance characteristics directly applicable to the test method include bias, precision, sensitivity, specificity, linearity, and range. Additional characteristics are test cost and elapsed time needed to conduct the test procedure.  
4.2 Equivalence studies are performed by a designed experiment that generates test results from the modified and current testing procedures on the same types of materials that are routinely tested. The design of the experiment depends on the type of equivalence needed as discussed below. Experiment design and execution for various objectives is discussed in Section 5.  
4.2.1 Means equivalence is concerned with a potential shift in the mean test result in either direction due to a modification in the te...
SCOPE
1.1 This practice provides statistical methodology for conducting equivalence studies on numerical data from two sources of test results to determine if their true means, variances, or other parameters differ by no more than predetermined limits.  
1.2 Applications include (1) equivalence studies for bias against an accepted reference value, (2) determining means equivalence of two test methods, test apparatus, instruments, reagent sources, or operators within a laboratory or equivalence of two laboratories in a method transfer, and (3) determining non-inferiority of a modified test procedure versus a current test procedure with respect to a performance characteristic.  
1.3 The guidance in this standard applies to experiments conducted either on a single material at a given level of the test result or on multiple materials covering a selected range of test results.  
1.4 Guidance is given for determining the amount of data required for an equivalence study. The control of risks associated with the equivalence decision is discussed.  
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine t...

SIGNIFICANCE AND USE
4.1 Reliability demonstration testing is a methodology for qualifying or validating a product’s performance capability. Demonstration methods are useful for components, devices, assemblies, materials, processes, and systems. Many industries require demonstration testing either for new product development and product introduction, in validating a change to an existing product or as part of an audit. Test plans generally try to answer the questions, “How long will a product last?” or “What is its reliability?”, under stated conditions at some specific time. When time is being used as a life variable, it must be cast in some kind of “time” units. Typical time units are hours (or minutes), cycles of usage, calendar time or some variation of these. In certain cases, “time” can be accelerated in order to reduce a plan’s completion time. In the automotive industry mileage may be used as the time variable. Certain means of accelerating tests involve the use of increased power, voltage, mechanical load, humidity, vibration, or temperature (often in the form of thermal cycling).  
4.2 Two fundamental objectives in reliability test planning are: (a) demonstrating that a product meets a specific life requirement, and (b) demonstrating what a product can do – its life capability. In the first case, a requirement is specified; in the second case a series of test results are used to state a result at the present time – its current capability. Both cases share similar inputs and outputs.  
4.3 Often a life distribution model is specified such as the Weibull, the exponential, the lognormal or the normal distribution. In addition, for the specific distribution assumed, a parameter is typically assumed (or a range of values for a parameter). For example, in the Weibull case, the shape parameter, β, is assumed; in the lognormal case the scale parameter, σ, is assumed and in the normal case the standard deviation, σ, is assumed. In other cases, a non-parametric analysis can be used. N...
SCOPE
1.1 This standard covers fundamental concepts, applications and mathematical relationships associated with the planning of reliability demonstration tests as applied to components and materials testing.  
1.2 The system of units for this guide is not specified. Quantities and examples are presented only as illustrations of a method or a calculation. Any examples used are not binding on any particular product or industry.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This guide covers fundamental concepts, applications, and mathematical relationships associated with reliability as used in industrial areas and as applied to simple components, processes, and systems or complex final products. This guide summarizes selected concepts, terminology, formulas, and methods associated with reliability and its application to products and processes.
SIGNIFICANCE AND USE
4.1 The theory of reliability is used for estimating and demonstrating the probability of survival at specific times or for specific usage cycles for simple components, devices, assemblies, processes, and systems. As reliability is one key dimension of quality, it may be more generally used as a measure of quality over time or over a usage or demand sequence.  
4.1.1 Many industries require performance metrics and requirements that are reliability-centered. Reliability assessments may be needed for the determination of maintenance requirements, for spare parts allocation, for life cycle cost analysis and for warranty purposes. This guide summarizes selected concepts, terminology, formulas, and methods associated with reliability and its application to products and processes. Many mathematical relationships and methods are found in the annexes. For general statistical terms not found in Section 3, Terminology E456 and ISO 3534-1 can be used for definitional purposes and ISO Guide 73 for general terminology regarding risk analysis.  
4.2 The term “system” implies a configuration of interacting components, sub-assemblies, materials, and possibly processes all acting together to make the system work as a whole. Parts of the system may be linked in combinations of series and parallel configuration and redundancy used in some parts to improve reliability. Additional conditions of complex engineering may have to be considered.  
4.3 Process reliability concerns the assessment of any type of well-defined process. This can include manufacturing processes, business processes, and dispatch/demand type processes. Assessment typically measures the extent to which the process can continually perform its intended function without “upset” as well as process robustness.  
4.4 A number of reliability metrics are in use. For example, mean time to failure (MTTF) is a common measure of average life or average time to the first time a unit fails. For this reason it is said to apply t...
SCOPE
1.1 This guide covers fundamental concepts, applications, and mathematical relationships associated with reliability as used in industrial areas and as applied to simple components, processes, and systems or complex final products.  
1.2 The system of units for this guide is not specified. Quantities in the guide are presented only as illustrations of the method or of a calculation. Any examples used are not binding on any particular product or industry.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice presents standard sampling procedures and tables for life and reliability testing in procurement, supply, and maintenance quality control operations as well as in research and development activities. This practice describes general procedures and definitions of terms used in life test sampling and describes specific procedures and applications of the life test sampling plans for determining conformance to established reliability requirements.
SIGNIFICANCE AND USE
4.1 This practice was prepared to meet a growing need for the use of standard sampling procedures and tables for life and reliability testing in government procurement, supply, and maintenance quality control (QC) operations as well as in research and development activities where applicable.  
4.2 A characteristic feature of most life tests is that the observations are ordered in time to failure. If, for example, 20 radio tubes are placed on life test, and ti denotes the time when the ith tube fails, the data occur in such a way that t1 ≤ t2 ≤ ... ≤ tn. The same kind of ordered observations will occur whether the problem under consideration deals with the life of electric bulbs, the life of electronic components, the life of ball bearings, or the length of life of human beings after they are treated for a disease. The examples just given all involve ordering in time.  
4.3 In destructive testing involving such situations as the current needed to blow a fuse, the voltage needed to break down a condenser, or the force needed to rupture a physical material, the test can often be arranged in such a way that every item in the sample is subjected to precisely the same stimulus (current, voltage, or stress). If this is done, then clearly the weakest item will be observed to fail first, the second weakest next, and so forth. While the random variable considered mostly in this guide is time to failure, it should be emphasized, however, that the methodology provided herein can be adapted to the testing situations mentioned above when the random variable is current, voltage, stress, and so forth.  
4.4 Sections 6 and 7 describe general procedures and definitions of terms used in life test sampling. Sections 8, 9, and 10 describe specific procedures and applications of the life test sampling plans for determining conformance to established reliability requirements.  
4.5 Whenever the methodology or choice of procedures in the practice requires clarification, the user is adv...
SCOPE
1.1 This practice presents standard sampling procedures and tables for life and reliability testing in procurement, supply, and maintenance quality control operations as well as in research and development activities.  
1.2 This practice describes general procedures and definitions of terms used in life test sampling and describes specific procedures and applications of the life test sampling plans for determining conformance to established reliability requirements.  
1.3 This practice is an adaptation of the Quality Control and Reliability Handbook H-108, “Sampling Procedures and Tables for Life and Reliability Testing (Based on Exponential Distribution),” U.S. Government Printing Office, April 29, 1960.  
1.4 A system of units is not specified in this practice.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice presents a procedure and related tables of factors for adapting Practice E2234 (equivalent to MIL-STD105) sampling plans to acceptance sampling inspection when the item quality of interest is life length or reliability. Factors are provided for three alternative criteria for lot evaluation: mean life, hazard rate, and reliable life. Inspection of the sample is by attributes with testing truncated at the end of some prearranged period of time. The Weibull distribution, together with the exponential distribution as a special case, is used as the underlying statistical model. The procedure and tables presented in this practice are based on the use of the Weibull distribution in acceptance sampling inspection.
SIGNIFICANCE AND USE
4.1 The procedure and tables presented in this practice are based on the use of the Weibull distribution in acceptance sampling inspection. Details of this work, together with tables of sampling plans of other forms, have been published previously. See Refs (1-3).4 Since the basic computations required have already been made, it has been quite easy to provide these new factors. No changes in method or details of application have been made over those described in the publications referenced above. For this reason, the text portion of this report has been briefly written. Readers interested in further details are referred to these previous publications. Other sources of material on the underlying theory and approach are also available (4-7).  
4.2 The procedure to be used is essentially the same as the one normally used for attribute sampling inspection. The only difference is that sample items are tested for life or survival instead of for some other property. For single sampling, the following are the required steps:  
4.2.1 Using the tables of factors provided in Annex A1, select a suitable sampling inspection plan from those tabulated in Practice E2234.  
4.2.2 Draw at random a sample of items of the size specified by the selected Practice E2234 plan.  
4.2.3 Place the sample of items on life test for the specified period of time, t.  
4.2.4 Determine the number of sample items that failed during the test period.  
4.2.5 Compare the number of items that failed with the number allowed under the selected Practice E2234 plan.  
4.2.6 If the number that failed is equal to or less than the acceptable number, accept the lot; if the number failing exceeds the acceptable number, reject the lot.  
4.3 Both the sample sizes and the acceptance numbers used are those specified by Practice E2234 plans. It will be assumed in the section on examples that single sampling plans will be used. However, the matching double sampling and multiple sampling plans provided in MIL-...
SCOPE
1.1 This practice presents a procedure and related tables of factors for adapting Practice E2234 (equivalent to MIL-STD-105) sampling plans to acceptance sampling inspection when the item quality of interest is life length or reliability. Factors are provided for three alternative criteria for lot evaluation: mean life, hazard rate, and reliable life. Inspection of the sample is by attributes with testing truncated at the end of some prearranged period of time. The Weibull distribution, together with the exponential distribution as a special case, is used as the underlying statistical model.  
1.2 A system of units is not specified by this practice.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issue...

SIGNIFICANCE AND USE
5.1 This guide presents techniques and guidance for evaluating and assuring homogeneity of individual samples or bulk materials and can be used for either interlaboratory or intra-laboratory studies. The types of studies include, but are not limited to, studies to determine precision estimates for test methods, proficiency testing programs, and studies related to quality control of testing within a single laboratory.  
5.2 Because the test results of any laboratory study are affected by the quality of the samples tested, producing homogeneous samples and determining the degree of homogeneity is important for interpreting the results of the study.  
5.3 Five techniques are presented in this guide to evaluate sample homogeneity for a range of circumstances and degrees of rigor. The circumstances under which the studies are conducted and the degree of rigor required may differ. The user should consider the circumstances listed in each technique to determine which is appropriate for the study at hand.  
5.4 Each of the Techniques 1, 2, and 3 provides a procedure for testing and evaluating sample homogeneity when replicate testing of the samples is possible. Technique 4 provides a plan to evaluate sample homogeneity when replicate testing is not possible. Technique 5 recommends practices for producing homogeneous samples for circumstances when homogeneity testing is not possible.  
5.5 When the conditions of adequate within-sample homogeneity and between-sample homogeneity are satisfied, any differences in test results on multiple samples can reasonably be attributed to testing variation and not due to sample variation.  
5.6 When differences within or between samples are discovered and the samples are deemed insufficiently homogeneous, the sample preparation process can be improved or corrected and a new set of samples can be prepared. Or, in cases where the sample homogeneity cannot be improved or for other reasons when the samples must be used, the method of eval...
SCOPE
1.1 This guide presents techniques and guidance for evaluating and assuring homogeneity of individual samples and bulk materials used for interlaboratory and intra-laboratory studies.  
1.2 This guide is applicable to samples and reference materials used for proficiency testing programs and for interlaboratory studies to determine precision estimates for test methods. It may also be useful for activities related to quality control of testing within a single laboratory.  
1.3 Five techniques are presented for assessing sample homogeneity. The five techniques are not an exhaustive list of available techniques for assessing homogeneity of samples, but the techniques were chosen to cover a range of circumstances (and various degrees of rigor required) for laboratory studies of various types and purposes.  
1.4 Each of the first four techniques provides a scheme for testing for homogeneity and a statistical procedure for evaluating the results of the homogeneity testing. The circumstances are described for which each of the techniques is suited.  
1.5 For circumstances when homogeneity testing is not possible, the fifth technique provides guidance for producing homogeneous samples.  
1.6 The appendixes of this guide provide example spreadsheets for Techniques 1, 2, 3, and 4.  
1.7 This guide is not intended for evaluation of certified reference materials (CRMs) or materials used for calibration.  
1.8 Units—The system of units for this standard is not specified. Dimensional quantities in the standard are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.9 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to ...

ABSTRACT
The purpose of this practice is to present concepts necessary to the understanding of the terms “precision” and “bias” as used in quantitative test methods. This practice also describes methods of expressing precision and bias and, in a final section, gives examples of how statements on precision and bias may be written for ASTM test methods. A statement of precision allows potential users of a test method to assess in general terms the test method’s usefulness with respect to variability in proposed applications.
SIGNIFICANCE AND USE
4.1 Part A of the “Blue Book,” Form and Style for ASTM Standards, requires that all test methods include statements of precision and bias. This practice discusses these two concepts and provides guidance for their use in statements about test methods.  
4.2 Precision—A statement of precision allows potential users of a test method to assess in general terms the test method’s usefulness with respect to variability in proposed applications. A statement of precision is not intended to exhibit values that can be exactly duplicated in every user’s laboratory. Instead, the statement provides guidelines as to the magnitude of variability that can be expected between test results when the method is used in one, or in two or more, reasonably competent laboratories. For a discussion of precision, see 8.1.  
4.3 Bias—A statement of bias furnishes guidelines on the relationship between a set of typical test results produced by the test method under specific test conditions and a related set of accepted reference values (see 9.1).  
4.3.1 An alternative term for bias is trueness, which has a positive connotation, in that greater bias is associated with less favorable trueness. Trueness is the systematic component of accuracy.  
4.4 Accuracy—The term “accuracy,” used in earlier editions of Practice E177, embraces both precision and bias (see 9.3).
SCOPE
1.1 The purpose of this practice is to present concepts necessary to the understanding of the terms “precision” and “bias” as used in quantitative test methods. This practice also describes methods of expressing precision and bias and, in a final section, gives examples of how statements on precision and bias may be written for ASTM test methods.  
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice provides guidance for determining process capability and performance under several common scenarios of use including: normal distribution-based capability and performance indices such as Cp, Cpk, Pp, and Ppk; process capability using attribute data for non-conforming units and non-conformities per unit type variables; and additional methods in working with process capability or performance.
SIGNIFICANCE AND USE
4.1 Process Capability—Process capability can be defined as the natural or inherent behavior of a stable process that is in a state of statistical control (1).4 A “state of statistical control” is achieved when the process exhibits no detectable patterns or trends, such that the variation seen in the data is believed to be random and inherent to the process. Process capability is linked to the use of control charts and the state of statistical control. A process must be studied to evaluate its state of control before evaluating process capability.  
4.2 Process Control—There are many ways to implement control charts, but the most popular choice is to achieve a state of statistical control for the process under study. Special causes are identified by a set of rules based on probability theory. The process is investigated whenever the chart signals the occurrence of special causes. Taking appropriate actions to eliminate identified special causes and preventing their reappearance will ultimately obtain a state of statistical control. In this state, a minimum level of variation may be reached, which is referred to as common cause or inherent variation. For the purpose of this standard, this variation is a measure of the uniformity of process output, typically a product characteristic.  
4.3 Process Capability Indices—The behavior of a process (as related to inherent variability) in the state of statistical control is used to describe its capability. To compare a process with customer requirements (or specifications), it is common practice to think of capability in terms of the proportion of the process output that is within product specifications or tolerances. The metric of this proportion is the percentage of the process spread used up by the specification. This comparison becomes the essence of all process capability measures. The manner in which these measures are calculated defines the different types of capability indices and their use. Two process capability i...
SCOPE
1.1 This practice provides guidance for determining process capability and performance under several common scenarios of use including: (a) normal distribution based capability and performance indices such as Cp, Cpk, Pp, and Ppk; (b) process capability using attribute data for non-conforming units and non-conformities per unit type variables, and (c) additional methods in working with process capability or performance.  
1.2 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This guide covers key elements of an evaluation of a laboratory’s measurement practices and the statistical analysis of the resulting data, as well as addresses an evaluation that covers a broad range of in-house quality measurements, some of which may be directly related to accreditation requirements. It provides an overview of the documentation needed for verification and monitoring of the practices used in the laboratory for measurement. In addition, it guides the user in verifying that the extent of documentation and the quality of statistical evaluations performed on the data being generated is sufficient. This guide is also intended to provide guidance for laboratory quality managers, accrediting bodies and assessors in evaluating the measurement practices of a laboratory and statistically analyzing the resulting data from these practices.
SIGNIFICANCE AND USE
4.1 This guide is intended to provide guidance for laboratory quality managers, accrediting bodies and assessors in evaluating the measurement practices of a laboratory, the protocol for statistically analyzing the resulting data from these practices, and the statistical results from these practices.  
4.2 This guide is generic in the sense that it covers the entire range of in-house quality measurement practices found in a testing laboratory, and the results of the described evaluation may be used by accrediting agencies for assessment purposes to determine whether their requirements can be satisfied through the laboratory’s existing quality data program.  
4.3 It is not the intent of this guide to serve as sole criterion for evaluating and accrediting laboratories. Evaluation of measurement practices is only one aspect in a comprehensive quality program.
SCOPE
1.1 This guide covers key elements of an evaluation of a laboratory’s measurement practices and the statistical analysis of the resulting data. This guide addresses an evaluation that covers a broad range of in-house quality measurements, some of which may be directly related to accreditation requirements.  
1.2 This guide provides an overview of the documentation needed for verification and monitoring of the practices used in the laboratory for measurement. In addition, it guides the user in verifying that the extent of documentation and the quality of statistical evaluations performed on the data being generated is sufficient. The user is advised to fully document all work covered by the scope of this guide as a general principle of laboratory practice and for audit purposes, whether internal or external.  
1.3 This guide is not designed to be exhaustive for all aspects of work realized under its scope. The user is encouraged to thoroughly realize (achieve in practice) the principles set forth in this guide, consulting other relevant standards and industry documents when appropriate.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This guide provides concepts necessary for understanding the term “uncertainty” when applied to a quantitative test result. Several measures of uncertainty can be applied to a given measurement result; the interpretation of some of the common forms is described. This guide describes methods for expressing test result uncertainty and relates these to standard statistical methodology. Relationships between uncertainty and concepts of precision and bias are described. This guide also presents concepts needed for a laboratory to identify and characterize components of method performance. Elements that an ASTM method can include to provide guidance to the user on estimating uncertainty for the method are described. This guide describes some of the types of data that the laboratory can use as the basis for reporting uncertainty.
SIGNIFICANCE AND USE
4.1 Part A of the “Blue Book,” Form and Style for ASTM Standards, introduces the statement of measurement uncertainty as an optional part of the report given for the result of applying a particular test method to a particular material.  
4.2 Preparation of uncertainty estimates is a requirement for laboratory accreditation under ISO/IEC 17025. This guide describes some of the types of data that the laboratory can use as the basis for reporting uncertainty.
SCOPE
1.1 This guide provides concepts necessary for understanding the term “uncertainty” when applied to a quantitative test result. Several measures of uncertainty can be applied to a given measurement result; the interpretation of some of the common forms is described.  
1.2 This guide describes methods for expressing test result uncertainty and relates these to standard statistical methodology. Relationships between uncertainty and concepts of precision and bias are described.  
1.3 This guide also presents concepts needed for a laboratory to identify and characterize components of method performance. Elements that an ASTM method can include to provide guidance to the user on estimating uncertainty for the method are described.  
1.4 The system of units for this guide is not specified. Dimensional quantities in the guide are presented only as illustrations of calculation methods and are not binding on products or test methods treated.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice establishes lot or batch sampling plans and procedures for inspection by variables using MIL-STD-414 as a basis for sampling a steady stream of lots indexed by AQL. This practice was prepared to meet a growing need for the use of standard sampling plans for inspection by variables in customer procurement, supply and storage, and maintenance inspection operations. The variables sampling plans apply to a single quality characteristic which can be measured on a continuous scale, and for which quality is expressed in terms of percent defective. The theory underlying the development of the variables sampling plans, including the operating characteristic curves, assumes that measurements of the quality characteristic are independent, identically distributed normal random variables.
SIGNIFICANCE AND USE
5.1 This practice was prepared to meet a growing need for the use of standard sampling plans for inspection by variables in customer procurement, supply and storage, and maintenance inspection operations. The variables sampling plans apply to a single quality characteristic which can be measured on a continuous scale, and for which quality is expressed in terms of percent defective. The theory underlying the development of the variables sampling plans, including the operating characteristic curves, assumes that measurements of the quality characteristic are independent, identically distributed normal random variables.  
5.2 In comparison with attributes sampling plans, variables sampling plans have the advantage of usually resulting in considerable savings in sample size for comparable assurance as to the correctness of decisions in judging a single quality characteristic, or for the same sample size, greater assurance is obtained using variables plans. Attributes sampling plans have the advantage of greater simplicity, of being applicable to either single or multiple quality characteristics, and of requiring no knowledge about the distribution of the continuous measurements of any of the quality characteristics.  
5.3 It is important to note that variables sampling plans are not to be used indiscriminately, simply because it is possible to obtain variables measurement data. In considering applications where the normality or independence assumptions may be questioned, the user is advised to consult his technical agency to determine the feasibility of application.  
5.4 Application—Sampling plans designated in this publication are applicable, but not limited, to inspection of the following: (1) end items, (2) components and raw materials, (3) operations or services, (4) materials in process, (5) supplies in storage, (6) maintenance operations, (7) data or records, and (8) administrative procedures.
SCOPE
1.1 Purpose—This practice establishes lot or batch sampling plans and procedures for inspection by variables using MIL-STD-414 as a basis for sampling a steady stream of lots indexed by AQL.  
1.2 This practice provides the sampling plans of MIL-STD-414 in ASTM format for use by ASTM committees and others. It recognizes the continuing usage of MIL-STD-414 in industries supported by ASTM. Most of the original text in MIL-STD-414 is preserved in Sections 6 – 9 of this practice.  
1.3 The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Tech...

ABSTRACT
This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.
This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.
SIGNIFICANCE AND USE
4.1 This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.  
4.1.1 A data set containing a single variable usually consists of a column of numbers. Each row is a separate observation or instance of measurement of the variable. The numbers themselves are the result of applying the measurement process to the variable being studied or observed. We may refer to each observation of a variable as an item in the data set. In many situations, there may be several variables defined for study.  
4.1.2 The sample is selected from a larger set called the population. The population can be a finite set of items, a very large or essentially unlimited set of items, or a process. In a process, the items originate over time and the population is dynamic, continuing to emerge and possibly change over time. Sample data serve as representatives of the population from which the sample originates. It is the population that is of primary interest in any particular study.  
4.2 The data (measurements and observations) may be of the variable type or the simple attribute type. In the case of attributes, the data may be either binary trials or a count of a defined event over some interval (time, space, volume, weight, or area). Binary trials consist of a sequence of 0s and 1s in which a “1” indicates that the inspected item exhibited the attribute being studied and a “0” indicates the item did not exhibit the attribute. Each inspection item is assigned either a “0” or a “1.” Such data are often governed by the binomial distribution. For a count of events over some interval, the number of times the event is observed on the inspection interval ...
SCOPE
1.1 This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.  
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice describes techniques for a laboratory to estimate the uncertainty of a test result using data from test results on a control sample. This practice provides one method for a laboratory to estimate Measurement Uncertainty in accordance with Section A22.3 in Form and Style for ASTM Standards. This practice describes the use of control charts to evaluate the data obtained and presents a special type of control chart to monitor the estimate of uncertainty.
This practice provides one way for a laboratory to develop data-based Type A estimates of uncertainty as referred to in Section A22 in Form and Style for ASTM Standards.
SIGNIFICANCE AND USE
4.1 This practice provides one way for a laboratory to develop data-based Type A estimates of uncertainty as referred to in Section A22 in Form and Style for ASTM Standards.  
4.2 Laboratories accredited under ISO/IEC 17025 are required to present uncertainty estimates for their test results. This practice provides procedures that use test results to develop uncertainty estimates for an individual laboratory.  
4.3 Generally, these test results will be from a single sample of stable and homogeneous material known as a control or check sample.  
4.4 The true value of the characteristic(s) of the control sample being measured will ordinarily be unknown. However, this methodology may also be used if the control sample is a reference material, in which case the test method bias may also be estimated and incorporated into the uncertainty estimate. Many test methods do not have true reference materials available to provide traceable chains of uncertainty estimation.  
4.5 This practice also allows for ongoing monitoring of the laboratory uncertainty. As estimates of the level of uncertainty change, possibly as contributions to uncertainty are identified and minimized, revision to the laboratory uncertainty will be possible.
SCOPE
1.1 This practice describes techniques for a laboratory to estimate the uncertainty of a test result using data from test results on a control sample. This practice provides one method for a laboratory to estimate Measurement Uncertainty in accordance with Section A22.3 in Form and Style for ASTM Standards.  
1.2 Uncertainty as defined by this practice applies to the capabilities of a single laboratory. Any estimate of uncertainty determined through the use of this practice applies only to the individual laboratory for which the data are presented.  
1.3 The laboratory uses a well defined and established test method in determining a series of test results. The uncertainty estimated using this practice only applies when the same test method is followed. The uncertainty only applies for the material types represented by the control samples, and multiple control samples may be needed, especially if the method has different precision for different sample types or response levels.  
1.4 The uncertainty estimate determined by this practice represents the intermediate precision of test results. This estimate seeks to quantify the total variation expected within a single laboratory using a single established test method while incorporating as many known sources of variation as possible.  
1.5 This practice does not establish error estimates (error budget) attributed to individual factors that could influence uncertainty.  
1.6 This practice describes the use of control charts to evaluate the data obtained and presents a special type of control chart to monitor the estimate of uncertainty.  
1.7 The system of units for this standard is not specified. Dimensional quantities in the standard are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.8 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmenta...

ABSTRACT
This guide establishes lot or batch and continuous sampling plans using MIL-STD-1916 as a basis. It represents an alternative sampling approach to attributes sampling (MILSTD-105E, same as Practice E2234), variables sampling (MILSTD-414, Practice E2762), and continuous sampling (MILSTD-1235B, Practice E2819). This standard provides a set of sampling plans and procedures for planning and conducting inspections to assess quality and conformance to contract requirements. This standard eliminates acceptable quality levels (AQL’s) and associated practices within specifications.
SIGNIFICANCE AND USE
5.1 Procurement practices encourage industry innovation and provide flexibility to achieve the benefits of continuous improvement.  
5.2 There is an evolving industrial product quality philosophy that recognizes the need for quality policy changes that will provide producers with opportunities and incentives toward improvement of product quality and cooperative relationships between the producer and the consumer.  
5.3 Process controls and statistical control methods are the preferable means of preventing nonconformances, controlling quality, and generating information for improvement. An effective process control system may also be used to provide information to assess the quality of deliverables submitted for acceptance. Producers are encouraged to use process control and statistical control procedures for their internal control and to submit effective process control procedures in lieu of prescribed sampling requirements to the consumer for approval.  
5.4 Sampling inspection by itself is an inefficient industrial practice for demonstrating conformance to the requirements of a contract and its technical data package. The application of sampling plans for acceptance involves both consumer and producer risks; and increased sampling is one way of reducing these risks, but it also increases costs. Producers can reduce risks by employing efficient processes with appropriate process controls. To the extent that such practices are employed and are effective, risk is controlled and, consequently, inspection and testing can be reduced.  
5.5 The following points provide the basis for this standard:  
5.5.1 Producers are required to submit deliverables that conform to requirements and to generate and maintain sufficient evidence of conformance.  
5.5.2 Producers are responsible for establishing their own manufacturing and process controls to produce results in accordance with requirements.  
5.5.3 Producers are expected to use recognized prevention practices such as...
SCOPE
1.1 This guide establishes lot or batch and continuous sampling plans using MIL-STD-1916 as a basis. It represents an alternative sampling approach to attributes sampling (MIL-STD-105E, same as Practice E2234), variables sampling (MIL-STD-414, Practice E2762), and continuous sampling (MIL-STD-1235B, Practice E2819).  
1.2 This guide provides the sampling plans of MIL-STD-1916 in ASTM format for use by ASTM committees and others. It recognizes the continuing usage of MIL-STD-1916 in industries supported by ASTM. Most of the original text in MIL-STD-1916 is preserved in Sections 4 – 6 of this guide. The original wording of “Government” in MIL-STD-1916 has been changed to “consumer”, and “contractor” has been changed to “producer” to make this standard more generic.  
1.3 Purpose—To encourage producers supplying goods and services to its consumers to submit efficient and effective process control (prevention) procedures in place of prescribed sampling requirements. The goal is to support the movement away from an AQL-based inspection (detection) strategy to implementation of an effective prevention-based strategy including a comprehensive quality system, continuous improvement and a partnership with the consumer. The underlying theme is a partnership between consumer and the producer, with the requisite competence of both parties, and a cle...

ABSTRACT
The purpose of this guide is to provide guidelines for identifying the elements that comprise the test result of a test method and to illustrate how these elements combine into the test result. It covers the types of measurement scales used for expressing observations and test results. This guide provides information on the construction of test results from more elemental measurements.
SIGNIFICANCE AND USE
4.1 All test methods have an output in the form of a test result. This guide provides information on the construction of test results from more elemental measurements.  
4.2 A well defined test result is necessary before any precision statements can be made about the test method.  
4.2.1 Form and Style for ASTM Standards,2 Section A21, requires that every test method shall contain a statement regarding its precision, preferably as a result of an interlaboratory test program. Reporting of such studies is described in Practice E177, which illustrates the development of test results from observations and test determinations.  
4.2.2 Precision statements for ASTM test methods are applicable to test results. They are not applicable to test determinations or observations, unless specifically and clearly indicated otherwise.
SCOPE
1.1 The purpose of this guide is to provide guidelines for identifying the elements that comprise the test result of a test method and to illustrate how these elements combine into the test result.  
1.2 Types of measurement scales used for expressing observations and test results are discussed.  
1.3 No system of units is specified in this standard.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice provides a general methodology for evaluating single-stage or multiple-stage acceptance procedures which involve a quality characteristic measured on a numerical scale. This methodology computes, at a prescribed confidence level, a lower bound on the probability of passing an acceptance procedure, using estimates of the parameters of the distribution of test results from a sampled population.
SIGNIFICANCE AND USE
4.1 This practice considers inspection procedures that may involve multiple-stage sampling, where at each stage one can decide to accept or to continue sampling, and the decision to reject is deferred until the last stage.  
4.1.1 At each stage there are one or more acceptance criteria on the test results; for example, limits on each individual test result, or limits on statistics based on the sample of test results, such as the average, standard deviation, or coefficient of variation (relative standard deviation).  
4.2 The methodology in this practice defines an acceptance region for a set of test results from the sampled population such that, at a prescribed confidence level, the probability that a sample from the population will pass the acceptance procedure is greater than or equal to a prespecified lower bound.  
4.2.1 Having test results fall in the acceptance region is not equivalent to passing the acceptance procedure, but provides assurance that a sample would pass the acceptance procedure with a specified probability.  
4.2.2 This information can be used for process demonstration, validation of test methods, and qualification of instruments, processes, and materials.  
4.2.3 This information can be used for lot release (acceptance), but the lower bound may be conservative in some cases.  
4.2.4 If the results are to be applied to future test results from the same process, then it is assumed that the process is stable and predictable. If this is not the case then there can be no guarantee that the probability estimates would be valid predictions of future process performance.  
4.3 This methodology was originally developed (1-4)3 for use in two specific quality characteristics of drug products in the pharmaceutical industry but will be applicable for acceptance procedures in all industries.  
4.4 Mathematical derivations would be required that are specific to the individual criteria of each test.
SCOPE
1.1 This practice provides a general methodology for evaluating single-stage or multiple-stage acceptance procedures which involve a quality characteristic measured on a numerical scale. This methodology computes, at a prescribed confidence level, a lower bound on the probability of passing an acceptance procedure, using estimates of the parameters of the distribution of test results from a sampled population.  
1.2 For a prescribed lower probability bound, the methodology can also generate an acceptance limit table, which defines a set of test method outcomes (for example, sample averages and standard deviations) that would pass the acceptance procedure at a prescribed confidence level.  
1.3 This approach may be used for demonstrating compliance with in-process, validation, or lot-release specifications.  
1.4 The system of units for this practice is not specified.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This guide identifies statistical procedures for use in developing new test methods or revising or evaluating existing test methods, or both. It also cites statistical procedures especially useful in the application of test methods. This standard recommends what approaches may be taken and indicates which standards may be used to perform such assessments.
SIGNIFICANCE AND USE
4.1 The creation of a standardized test method generally follows a series of steps from inception to approval and ongoing use. In all such stages there are questions of how well the test method performs.  
4.1.1 Assessments of a new or existing test method generally involve statistical planning and analysis. This standard recommends what approaches may be taken and indicates which standards may be used to perform such assessments.  
4.2 This standard introduces a series of phases which are recommended to be considered during the life cycle of a test method as depicted in Fig. 1. These begin with a design phase where the standard is initially prepared. A development phase involves a variety of experiments that allow further refinement and understanding of how the test method performs within a laboratory. In an evaluation phase the test method is then examined by way of interlaboratory studies resulting in precision and bias statistics which are published in the standard. Finally, the test method is subject to a monitoring phase.
FIG. 1 Sequence of Steps  
4.3 All ASTM test methods are required to include statements on precision and bias.3  
4.4 Since ASTM began to require all test methods to have precision and bias statements that are based on interlaboratory test methods, there has been increased concern regarding what statistical experiments and procedures to use during the development of the test methods. Although there exists a wide range of statistical procedures, there is a small group of generally accepted techniques that are beneficial to follow. This guide is designed to provide a brief overview of these procedures and to suggest an appropriate sequence of carrying out these procedures.  
4.5 Statistical procedures often result in interpretations that are not absolutes. Sometimes the information obtained may be inadequate or incomplete, which may lead to additional questions and the need for further experimentation. Information outside the data is al...
SCOPE
1.1 This guide identifies statistical procedures for use in developing new test methods or revising or evaluating existing test methods, or both.  
1.2 This guide also cites statistical procedures especially useful in the application of test methods.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method. This practice is also concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements. ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility and knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values or between data sources.
SIGNIFICANCE AND USE
4.1 ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility. This practice may be used in obtaining the needed information as simply as possible. This information may then be used to prepare a precision statement in accordance with Practice E177. Knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values (such as specification limits) or between data sources (different laboratories, instruments, etc.).  
4.1.1 When a test method is applied to a large number of portions of a material that are as nearly alike as possible, the test results obtained will not all have the same value. A measure of the degree of agreement among these test results describes the precision of the test method for that material. Numerical measures of the variability between such test results provide inverse measures of the precision of the test method. Greater variability implies smaller (that is, poorer) precision and larger imprecision.  
4.1.2 Precision is reported as a standard deviation, coefficient of variation (relative standard deviation), variance, or a precision limit (a data range indicating no statistically significant difference between test results).  
4.1.3 This practice is designed only to estimate the precision of a test method. However, when accepted reference values are available for the property levels, the test result data obtained according to this practice may be used in estimating the bias of the test method. For a discussion of bias estimation and the relationships between precision, bias, and accuracy, see Practice E177.  
4.2 The procedures presented in this practice consist of three basic steps: planning the interlaboratory study, guiding the testing phase of the study, and analyzing the test result data.  
4.2.1 The planning phase includes forming the ILS task group, the study design, selection, and number of participating laborato...
SCOPE
1.1 This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method.  
1.2 This practice does not concern itself with the development of test methods but rather with gathering the information needed for a test method precision statement after the development stage has been successfully completed. The data obtained in the interlaboratory study may indicate, however, that further effort is needed to improve the test method.  
1.3 Since the primary purpose of this practice is the development of the information needed for a precision statement, the experimental design in this practice may not be optimum for evaluating materials, apparatus, or individual laboratories.  
1.4 Field of Application—This practice is concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements.  
1.4.1 This practice ...

ABSTRACT
This guide presents terminology, concepts, and selected methods and formulas useful for measurement systems analysis (MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to the non-destructive measurement of the physical properties of manufactured objects. This guide presents selected concepts and methods useful for describing and understanding the measurement process. This guide is not intended to be a comprehensive survey of this topic.
SIGNIFICANCE AND USE
4.1 Many types of measurements are made routinely in research organizations, business and industry, and government and academic agencies. Typically, data are generated from experimental effort or as observational studies. From such data, management decisions are made that may have wide-reaching social, economic, and political impact. Data and decision making go hand in hand and that is why the quality of any measurement is important—for data originate from a measurement process. This guide presents selected concepts and methods useful for describing and understanding the measurement process. This guide is not intended to be a comprehensive survey of this topic.  
4.2 Any measurement result will be said to originate from a measurement process or system. The measurement process will consist of a number of input variables and general conditions that affect the final value of the measurement. The process variables, hardware and software and their properties, and the human effort required to obtain a measurement constitute the measurement process. A measurement process will have several properties that characterize the effect of the several variables and general conditions on the measurement results. It is the properties of the measurement process that are of primary interest in any such study. The term “measurement systems analysis” or MSA study is used to describe the several methods used to characterize the measurement process.
Note 1: Sample statistics discussed in this guide are as described in Practice E2586; control chart methodologies are as described in Practice E2587.
SCOPE
1.1 This guide presents terminology, concepts, and selected methods and formulas useful for measurement systems analysis (MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to the non-destructive measurement of the physical properties of manufactured objects.  
1.2 Units—The system of units for this guide is not specified. Dimensional quantities in the guide are presented only as illustrations of calculation methods and are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This standard is the general terminology standard for terms defined in the standards of Committee E11 on Quality and Statistics. A term in this standard which lists an attribution to an E11 technical standard indicates that the standard is normative for that term. Term definitions that are similar to ISO 3534 will be noted in this standard, but ISO 3534 will not be considered normative for any E11 terms.
SCOPE
1.1 This standard is the general terminology standard for terms defined in the standards of Committee E11 on Quality and Statistics.  
1.2 A term in this standard which lists an attribution to an E11 technical standard indicates that the standard is normative for that term. Any changes in the term definition in the normative standard will be editorially changed in this standard. Any terms added to an E11 standard will be editorially added to this standard with an attribution to that standard.  
1.3 Term definitions that are similar to ISO 3534 will be noted in this standard, but ISO 3534 will not be considered normative for any E11 terms.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method. This practice is also concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements. ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility and knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values or between data sources.
SIGNIFICANCE AND USE
4.1 ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility. This practice may be used in obtaining the needed information as simply as possible. This information may then be used to prepare a precision statement in accordance with Practice E177. Knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values (such as specification limits) or between data sources (different laboratories, instruments, etc.).  
4.1.1 When a test method is applied to a large number of portions of a material that are as nearly alike as possible, the test results obtained will not all have the same value. A measure of the degree of agreement among these test results describes the precision of the test method for that material. Numerical measures of the variability between such test results provide inverse measures of the precision of the test method. Greater variability implies smaller (that is, poorer) precision and larger imprecision.  
4.1.2 Precision is reported as a standard deviation, coefficient of variation (relative standard deviation), variance, or a precision limit (a data range indicating no statistically significant difference between test results).  
4.1.3 This practice is designed only to estimate the precision of a test method. However, when accepted reference values are available for the property levels, the test result data obtained according to this practice may be used in estimating the bias of the test method. For a discussion of bias estimation and the relationships between precision, bias, and accuracy, see Practice E177.  
4.2 The procedures presented in this practice consist of three basic steps: planning the interlaboratory study, guiding the testing phase of the study, and analyzing the test result data.  
4.2.1 The planning phase includes forming the ILS task group, the study design, selection, and number of participating laborato...
SCOPE
1.1 This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method.  
1.2 This practice does not concern itself with the development of test methods but rather with gathering the information needed for a test method precision statement after the development stage has been successfully completed. The data obtained in the interlaboratory study may indicate, however, that further effort is needed to improve the test method.  
1.3 Since the primary purpose of this practice is the development of the information needed for a precision statement, the experimental design in this practice may not be optimum for evaluating materials, apparatus, or individual laboratories.  
1.4 Field of Application—This practice is concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements.  
1.4.1 This practice ...

ABSTRACT
This practice presents a procedure and related tables of factors for adapting Practice E2234 (equivalent to MIL-STD105) sampling plans to acceptance sampling inspection when the item quality of interest is life length or reliability. Factors are provided for three alternative criteria for lot evaluation: mean life, hazard rate, and reliable life. Inspection of the sample is by attributes with testing truncated at the end of some prearranged period of time. The Weibull distribution, together with the exponential distribution as a special case, is used as the underlying statistical model. The procedure and tables presented in this practice are based on the use of the Weibull distribution in acceptance sampling inspection.
SIGNIFICANCE AND USE
4.1 The procedure and tables presented in this practice are based on the use of the Weibull distribution in acceptance sampling inspection. Details of this work, together with tables of sampling plans of other forms, have been published previously. See Refs (1-3).4 Since the basic computations required have already been made, it has been quite easy to provide these new factors. No changes in method or details of application have been made over those described in the publications referenced above. For this reason, the text portion of this report has been briefly written. Readers interested in further details are referred to these previous publications. Other sources of material on the underlying theory and approach are also available (4-7).  
4.2 The procedure to be used is essentially the same as the one normally used for attribute sampling inspection. The only difference is that sample items are tested for life or survival instead of for some other property. For single sampling, the following are the required steps:  
4.2.1 Using the tables of factors provided in Annex A1, select a suitable sampling inspection plan from those tabulated in Practice E2234.  
4.2.2 Draw at random a sample of items of the size specified by the selected Practice E2234 plan.  
4.2.3 Place the sample of items on life test for the specified period of time, t.  
4.2.4 Determine the number of sample items that failed during the test period.  
4.2.5 Compare the number of items that failed with the number allowed under the selected Practice E2234 plan.  
4.2.6 If the number that failed is equal to or less than the acceptable number, accept the lot; if the number failing exceeds the acceptable number, reject the lot.  
4.3 Both the sample sizes and the acceptance numbers used are those specified by Practice E2234 plans. It will be assumed in the section on examples that single sampling plans will be used. However, the matching double sampling and multiple sampling plans provided in MIL-...
SCOPE
1.1 This practice presents a procedure and related tables of factors for adapting Practice E2234 (equivalent to MIL-STD-105) sampling plans to acceptance sampling inspection when the item quality of interest is life length or reliability. Factors are provided for three alternative criteria for lot evaluation: mean life, hazard rate, and reliable life. Inspection of the sample is by attributes with testing truncated at the end of some prearranged period of time. The Weibull distribution, together with the exponential distribution as a special case, is used as the underlying statistical model.  
1.2 A system of units is not specified by this practice.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issue...

ABSTRACT
This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method. This practice is also concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements. ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility and knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values or between data sources.
SIGNIFICANCE AND USE
4.1 ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility. This practice may be used in obtaining the needed information as simply as possible. This information may then be used to prepare a precision statement in accordance with Practice E177. Knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values (such as specification limits) or between data sources (different laboratories, instruments, etc.).  
4.1.1 When a test method is applied to a large number of portions of a material that are as nearly alike as possible, the test results obtained will not all have the same value. A measure of the degree of agreement among these test results describes the precision of the test method for that material. Numerical measures of the variability between such test results provide inverse measures of the precision of the test method. Greater variability implies smaller (that is, poorer) precision and larger imprecision.  
4.1.2 Precision is reported as a standard deviation, coefficient of variation (relative standard deviation), variance, or a precision limit (a data range indicating no statistically significant difference between test results).  
4.1.3 This practice is designed only to estimate the precision of a test method. However, when accepted reference values are available for the property levels, the test result data obtained according to this practice may be used in estimating the bias of the test method. For a discussion of bias estimation and the relationships between precision, bias, and accuracy, see Practice E177.  
4.2 The procedures presented in this practice consist of three basic steps: planning the interlaboratory study, guiding the testing phase of the study, and analyzing the test result data.  
4.2.1 The planning phase includes forming the ILS task group, the study design, selection, and number of participating laborato...
SCOPE
1.1 This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method.  
1.2 This practice does not concern itself with the development of test methods but rather with gathering the information needed for a test method precision statement after the development stage has been successfully completed. The data obtained in the interlaboratory study may indicate, however, that further effort is needed to improve the test method.  
1.3 Since the primary purpose of this practice is the development of the information needed for a precision statement, the experimental design in this practice may not be optimum for evaluating materials, apparatus, or individual laboratories.  
1.4 Field of Application—This practice is concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements.  
1.4.1 This practice ...

ABSTRACT
This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources to determine if their true means or variances differ by no more than predetermined limits. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.
SIGNIFICANCE AND USE
4.1 Laboratories conducting routine testing have a continuing need to make improvements in their testing processes. In these situations it must be demonstrated that any changes will neither cause an undesirable shift in the test results from the current testing process nor substantially affect a performance characteristic of the test method. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.  
4.1.1 The equivalence limit, which represents a worst-case difference or ratio, is determined prior to the equivalence test and its value is usually set by consensus among subject-matter experts.  
4.1.2 Examples of modifications to the testing process include, but are not limited, to the following:  
(1) Changes to operating levels in the steps of the test method procedure,
(2) Installation of new instruments, apparatus, or sources of reagents and test materials,
(3) Evaluation of new personnel performing the testing, and
(4) Transfer of testing to a new location.  
4.1.3 Examples of performance characteristics directly applicable to the test method include bias, precision, sensitivity, specificity, linearity, and range. Additional characteristics are test cost and elapsed time needed to conduct the test procedure.  
4.2 Equivalence testing is performed by a designed experiment that generates test results from the modified and current testing procedures on the same types of materials that are routinely tested. The design of the experiment depends on the type of equivalence needed as discussed below. Experiment design and execution for various objectives is discussed in Section 5.  
4.2.1 Means equivalence is concerned with a potential shift in the mean test result in either direction due to a modification in the tes...
SCOPE
1.1 This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources of test results to determine if their true means, variances, or other parameters differ by no more than predetermined limits.  
1.2 Applications include (1) equivalence testing for bias against an accepted reference value, (2) determining means equivalence of two test methods, test apparatus, instruments, reagent sources, or operators within a laboratory or equivalence of two laboratories in a method transfer, and (3) determining non-inferiority of a modified test procedure versus a current test procedure with respect to a performance characteristic.  
1.3 The guidance in this standard applies to experiments conducted either on a single material at a given level of the test result or on multiple materials covering a selected range of test results.  
1.4 Guidance is given for determining the amount of data required for an equivalence trial. The control of risks associated with the equivalence decision is discussed.  
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine t...

ABSTRACT
This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources to determine if their true means or variances differ by no more than predetermined limits. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.
SIGNIFICANCE AND USE
4.1 Laboratories conducting routine testing have a continuing need to make improvements in their testing processes. In these situations it must be demonstrated that any changes will neither cause an undesirable shift in the test results from the current testing process nor substantially affect a performance characteristic of the test method. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.  
4.1.1 The equivalence limit, which represents a worst-case difference or ratio, is determined prior to the equivalence test and its value is usually set by consensus among subject-matter experts.  
4.1.2 Examples of modifications to the testing process include, but are not limited, to the following:  
(1) Changes to operating levels in the steps of the test method procedure,
(2) Installation of new instruments, apparatus, or sources of reagents and test materials,
(3) Evaluation of new personnel performing the testing, and
(4) Transfer of testing to a new location.  
4.1.3 Examples of performance characteristics directly applicable to the test method include bias, precision, sensitivity, specificity, linearity, and range. Additional characteristics are test cost and elapsed time needed to conduct the test procedure.  
4.2 Equivalence testing is performed by a designed experiment that generates test results from the modified and current testing procedures on the same types of materials that are routinely tested. The design of the experiment depends on the type of equivalence needed as discussed below. Experiment design and execution for various objectives is discussed in Section 5.  
4.2.1 Means equivalence is concerned with a potential shift in the mean test result in either direction due to a modification in the tes...
SCOPE
1.1 This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources of test results to determine if their true means, variances, or other parameters differ by no more than predetermined limits.  
1.2 Applications include (1) equivalence testing for bias against an accepted reference value, (2) determining means equivalence of two test methods, test apparatus, instruments, reagent sources, or operators within a laboratory or equivalence of two laboratories in a method transfer, and (3) determining non-inferiority of a modified test procedure versus a current test procedure with respect to a performance characteristic.  
1.3 The guidance in this standard applies to experiments conducted either on a single material at a given level of the test result or on multiple materials covering a selected range of test results.  
1.4 Guidance is given for determining the amount of data required for an equivalence trial. The control of risks associated with the equivalence decision is discussed.  
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine t...

SIGNIFICANCE AND USE
4.1 A ruggedness test is a special application of a statistically designed experiment that makes changes in the test method variables, called factors, and then calculates the subsequent effect of those changes upon the test results. Factors are features of the test method or of the laboratory environment that are known to vary across laboratories and are subject to control by the test method.  
4.1.1 Statistical design enables more efficient and cost-effective determination of the factor effects than would be achieved if separate experiments were carried out for each factor. The proposed designs are easy to use in developing the information needed for evaluating quantitative test methods.  
4.2 In ruggedness testing, the two levels (settings) for each factor are chosen to use moderate separations between the high and low settings. In general, if there is an underlying difference between the levels, then the size of effects will increase with increased separation between the high and low settings of the factors. A run is an execution of the test method under prescribed settings of each of the factors under study. A ruggedness test consists of a set of runs.  
4.3 A ruggedness test is usually conducted within a single laboratory on uniform material, so that the effects of changing only the factors are measured. The results may then be used to assist in determining the degree of control required of factors described in the test method.  
4.4 Ruggedness testing should precede an interlaboratory (round robin) study to correct any deficiencies in the test method and may also be part of the validation phase of developing a standard test method as described in Guide E1488.  
4.5 This standard discusses design and analysis of ruggedness testing in Section 5 and contains an example of a basic eight run design. Some caution must be used in interpretation of results, since interaction effects may be present. These effects are present when a factor effect changes with the ...
SCOPE
1.1 This practice covers conducting ruggedness tests. The purpose of a ruggedness test is to identify those factors that strongly influence the measurements provided by a specific test method and to estimate how closely those factors need to be controlled.  
1.2 This practice restricts itself to experimental designs with two levels per factor. The designs require the simultaneous change of the levels of all of the factors, thus permitting the determination of the effects of each of the factors on the measured results.  
1.3 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
The purpose of this practice is to present concepts necessary to the understanding of the terms “precision” and “bias” as used in quantitative test methods. This practice also describes methods of expressing precision and bias and, in a final section, gives examples of how statements on precision and bias may be written for ASTM test methods. A statement of precision allows potential users of a test method to assess in general terms the test method’s usefulness with respect to variability in proposed applications.
In this practice only quantitative test methods that produce numerical results are considered. Also, the word “material” is used to mean material, product, system or service; the word “property” is used herein to mean that a quantitative test result can be obtained that describes a characteristic or a quality, or some other aspect of the material; and “test method” refers to both the document and the procedure described therein for obtaining a quantitative test result for one property.
SIGNIFICANCE AND USE
4.1 Part A of the “Blue Book,” Form and Style for ASTM Standards, requires that all test methods include statements of precision and bias. This practice discusses these two concepts and provides guidance for their use in statements about test methods.  
4.2 Precision—A statement of precision allows potential users of a test method to assess in general terms the test method’s usefulness with respect to variability in proposed applications. A statement of precision is not intended to exhibit values that can be exactly duplicated in every user’s laboratory. Instead, the statement provides guidelines as to the magnitude of variability that can be expected between test results when the method is used in one, or in two or more, reasonably competent laboratories. For a discussion of precision, see 8.1.  
4.3 Bias—A statement of bias furnishes guidelines on the relationship between a set of typical test results produced by the test method under specific test conditions and a related set of accepted reference values (see 9.1).  
4.3.1 An alternative term for bias is trueness, which has a positive connotation, in that greater bias is associated with less favorable trueness. Trueness is the systematic component of accuracy.  
4.4 Accuracy—The term “accuracy,” used in earlier editions of Practice E177, embraces both precision and bias (see 9.3).
SCOPE
1.1 The purpose of this practice is to present concepts necessary to the understanding of the terms “precision” and “bias” as used in quantitative test methods. This practice also describes methods of expressing precision and bias and, in a final section, gives examples of how statements on precision and bias may be written for ASTM test methods.  
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other. This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.
SIGNIFICANCE AND USE
4.1 Regression analysis is a procedure that uses data to study the statistical relationships between two or more variables (1, 2).3 This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.  
4.2 A regression model consists of: (1) a regression function that relates the mean values of the response variable distribution to fixed values of the predictor variable, and (2) a statistical distribution that describes the variability in the response variable values at a fixed value of the predictor variable.  
4.2.1 The regression analysis utilizes either experimental or observational data to estimate the parameters defining a regression model and their precision. Diagnostic procedures are utilized to assess the resulting model fit and can suggest other models for improved prediction performance.  
4.3 The information in this practice is arranged as follows.  
4.3.1 Section 5 gives a general outline of the steps in the regression analysis procedure. The subsequent sections cover procedures for estimation of specific regression models.  
4.3.2 Section 6 assumes a straight line relationship between the two variables. This is also known as the simple linear regression model or a first order model. This model should be used as a starting point for understanding the XY relationship and ultimately defining the best fitting model to the data.  
4.3.3 Section 7 considers a proportional relationship between the variables, where the ratio of one variable to the other is constant. The intercept is constrained to be zero. This model is useful for single point calibration, where a reference material is run periodically as a standard during routine testing to correct for drift in instrument performance over a given range of test results.  
4.3.4 Section 8 di...
SCOPE
1.1 This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other.  
1.2 The regression analysis provides graphical and calculational procedures for selecting the best statistical model that describes the relationship and for evaluation of the fit of the data to the selected model.  
1.3 The resulting regression model can be useful for developing process knowledge through description of the variable relationship, in making predictions of future values, in relating the precision of a test method to the value of the characteristic being measured, and in developing control methods for the process generating values of the variables.  
1.4 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development ...

ABSTRACT
This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method. This practice is also concerned exclusively with test methods which yield a single numerical figure as the test result, although the single figure may be the outcome of a calculation from a set of measurements. ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility and knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values or between data sources.
The procedures presented in this practice consist of three basic steps: planning the interlaboratory study, guiding the testing phase of the study, and analyzing the test result data.
SIGNIFICANCE AND USE
4.1 ASTM regulations require precision statements in all test methods in terms of repeatability and reproducibility. This practice may be used in obtaining the needed information as simply as possible. This information may then be used to prepare a precision statement in accordance with Practice E177. Knowledge of the test method precision is useful in commerce and in technical work when comparing test results against standard values (such as specification limits) or between data sources (different laboratories, instruments, etc.).  
4.1.1 When a test method is applied to a large number of portions of a material that are as nearly alike as possible, the test results obtained will not all have the same value. A measure of the degree of agreement among these test results describes the precision of the test method for that material. Numerical measures of the variability between such test results provide inverse measures of the precision of the test method. Greater variability implies smaller (that is, poorer) precision and larger imprecision.  
4.1.2 Precision is reported as a standard deviation, coefficient of variation (relative standard deviation), variance, or a precision limit (a data range indicating no statistically significant difference between test results).  
4.1.3 This practice is designed only to estimate the precision of a test method. However, when accepted reference values are available for the property levels, the test result data obtained according to this practice may be used in estimating the bias of the test method. For a discussion of bias estimation and the relationships between precision, bias, and accuracy, see Practice E177.  
4.2 The procedures presented in this practice consist of three basic steps: planning the interlaboratory study, guiding the testing phase of the study, and analyzing the test result data.  
4.2.1 The planning phase includes forming the ILS task group, the study design, selection and number of participating laborator...
SCOPE
1.1 This practice describes the techniques for planning, conducting, analyzing, and treating the results of an interlaboratory study (ILS) of a test method. The statistical techniques described in this practice provide adequate information for formulating the precision statement of a test method.  
1.2 This practice does not concern itself with the development of test methods but rather with gathering the information needed for a test method precision statement after the development stage has been successfully completed. The data obtained in the interlaboratory study may indicate, however, that further effort is needed to improve the test method.  
1.3 Since the primary purpose of this practice is the development of the information needed for a precision statement, the experimental design in this practice may not be optimum for evaluating materials, apparatus, or individual laboratories.  
1.4 Field of Application—This practice is concerned exclusively with ...