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ASTM E2587-15

(Practice)

Standard Practice for Use of Control Charts in Statistical Process Control

Standard Practice for Use of Control Charts in Statistical Process Control

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) 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 so as 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 co...
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 and health practices and determine the applicability of regulatory limitations prior to use.

General Information

Status
Historical
Publication Date
31-Mar-2015
ICS
03.120.30 - Application of statistical methods
Technical Committee
E11 - Quality and Statistics
Drafting Committee
E11.30 - Statistical Quality Control
Current Stage
Ref Project

Relations

Replaces
ASTM E2587-14e1 - Standard Practice for Use of Control Charts in Statistical Process Control
Effective Date
01-Apr-2015
Referred By
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ASTM E177-20 - Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods
Effective Date
01-Apr-2015
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ASTM E1323-15(2020) - Standard Guide for Evaluating Laboratory Measurement Practices and the Statistical Analysis of the Resulting Data
Effective Date
01-Apr-2015
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ASTM E2782-17(2022)e1 - Standard Guide for Measurement Systems Analysis (MSA)
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ASTM E2554-18e1 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
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ASTM E456-13a(2022) - Standard Terminology Relating to Quality and Statistics
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Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2587 − 15 AnAmerican National Standard
Standard Practice for
1
Use of Control Charts in Statistical Process Control
This standard is issued under the fixed designation E2587; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope E2762 Practice for Sampling a Stream of Product by Vari-
ables Indexed by AQL
1.1 This practice provides guidance for the use of control
charts in statistical process control programs, which improve
3. Terminology
process quality through reducing variation by identifying and
eliminating the effect of special causes of variation. 3.1 Definitions:
3.1.1 See Terminology E456 for a more extensive listing of
1.2 Control charts are used to continually monitor product
statistical terms.
orprocesscharacteristicstodeterminewhetherornotaprocess
isinastateofstatisticalcontrol.Whenthisstateisattained,the 3.1.2 assignable cause, n—factor that contributes to varia-
tion in a process or product output that is feasible to detect and
process characteristic will, at least approximately, vary within
certain limits at a given probability. identify (see special cause).
3.1.2.1 Discussion—Many factors will contribute to
1.3 This practice applies to variables data (characteristics
variation, but it may not be feasible (economically or other-
measured on a continuous numerical scale) and to attributes
wise) to identify some of them.
data (characteristics measured as percentages, fractions, or
counts of occurrences in a defined interval of time or space).
3.1.3 attributes data, n—observed values or test results that
indicate the presence or absence of specific characteristics or
1.4 The system of units for this practice is not specified.
counts of occurrences of events in time or space.
Dimensional quantities in the practice are presented only as
illustrations of calculation methods. The examples are not
3.1.4 average run length (ARL), n—the average number of
binding on products or test methods treated.
times that a process will have been sampled and evaluated
before a shift in process level is signaled.
1.5 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the 3.1.4.1 Discussion—A long ARL is desirable for a process
responsibility of the user of this standard to establish appro- located at its specified level (so as to minimize calling for
priate safety and health practices and determine the applica- unneededinvestigationorcorrectiveaction)andashortARLis
bility of regulatory limitations prior to use.
desirable for a process shifted to some undesirable level (so
that corrective action will be called for promptly).ARLcurves
2. Referenced Documents
are used to describe the relative quickness in detecting level
2
shifts of various control chart systems (see 5.1.4). The average
2.1 ASTM Standards:
number of units that will have been produced before a shift in
E456 Terminology Relating to Quality and Statistics
level is signaled may also be of interest from an economic
E1994 Practice for Use of Process Oriented AOQL and
standpoint.
LTPD Sampling Plans
E2234 Practice for Sampling a Stream of Product by Attri-
3.1.5 c chart, n—control chart that monitors the count of
butes Indexed by AQL
occurrences of an event in a defined increment of time or
E2281 Practice for Process and Measurement Capability
space.
Indices
3.1.6 center line, n—line on a control chart depicting the
average level of the statistic being monitored.
1
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
3.1.7 chance cause, n—source of inherent random variation
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
Quality Control. in a process which is predictable within statistical limits (see
Current edition approved April 1, 2015. Published April 2015. Originally
common cause).
ε1
approved in 2007. Last previous edition approved in 2014 as E2587 – 14 . DOI:
3.1.7.1 Discussion—Chance causes may be unidentifiable,
10.1520/E2587-15.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or or may have known origins that are not easily controllable or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
cost effective to eliminate.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. 3.1.8 common cause, n—(see chance cause).
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E2587 − 15
3.1.9 control chart, n—chart on w
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: E2587 − 14 E2587 − 15 An American National Standard
Standard Practice for
1
Use of Control Charts in Statistical Process Control
This standard is issued under the fixed designation E2587; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1
ε NOTE—Editorial corrections were made to Section 3 in February 2015.
1. 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 and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2
2.1 ASTM Standards:
E456 Terminology Relating to Quality and Statistics
E1994 Practice for Use of Process Oriented AOQL and LTPD Sampling Plans
E2234 Practice for Sampling a Stream of Product by Attributes Indexed by AQL
E2281 Practice for Process and Measurement Capability Indices
E2762 Practice for Sampling a Stream of Product by Variables Indexed by AQL
3. Terminology
3.1 Definitions:
3.1.1 See Terminology E456 for a more extensive listing of statistical terms.
3.1.2 assignable cause, n—factor that contributes to variation in a process or product output that is feasible to detect and identify
(see special cause).
1
This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical Quality
Control.
Current edition approved Oct. 1, 2014April 1, 2015. Published November 2014April 2015. Originally approved in 2007. Last previous edition approved in 20122014 as
ε1
E2587 – 12.E2587 – 14 . DOI: 10.1520/E2587-14E01.10.1520/E2587-15.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
3.1.2.1 Discussion—
Many factors will contribute to variation, but it may not be feasible (economically or otherwise) to identify some of them.
3.1.3 attributes data, n—observed values or test results that indicate the presence or absence of specific characteristics or counts
of occurrences of events in time or space.
3.1.4 average run length (ARL), n—the average number of times that a process will have been sampled and evaluated before
a shift in process level is signaled.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E2587 − 15
3.1.4.1 Discussion—
A long ARL is desirable for a process located at its specified level (so as to minimize calling for unneeded investigation or
corrective action) and a short ARL is desirable for a process shifted to some undesirable level (so that corrective action will be
called for promptly). ARL curves are used to describe the relative quickness in detecting level shifts of various control chart
systems (see 5.1.4). The average number of units that will have been produced before a shift in level is signaled may also be of
interest from an economic standpoint.
3.1.5 c chart, n—control chart that monitors the count of occurrences of an event in a defined increment of time or space.
3.1.6 center line
...

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ASTM E141-10(2023)(Practice)
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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
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ABSTRACT
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SIGNIFICANCE AND USE
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ABSTRACT
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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 ...

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ASTM E122-17(2022)(Practice)
Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process

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.

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ASTM E2587-16(2021)e1(Practice)
Standard Practice for Use of Control Charts in Statistical Process Control

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...

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ASTM E2819-11(2021)(Practice)
Standard Practice for Single- and Multi-Level Continuous Sampling of a Stream of Product by Attributes Indexed by AQL

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.

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ASTM E178-21(Practice)
Standard Practice for Dealing With Outlying Observations

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.

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ASTM E2935-21(Practice)
Standard Practice for Evaluating Equivalence of Two Testing Processes

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...

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