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ASTM E122-09e1

(Practice)

Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process

Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process

SIGNIFICANCE AND USE
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.

General Information

Status
Historical
Publication Date
31-Jul-2011
ICS
03.120.30 - Application of statistical methods
Technical Committee
E11 - Quality and Statistics
Drafting Committee
E11.10 - Sampling / Statistics
Current Stage
Ref Project

Relations

Replaces
ASTM E122-09 - Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process
Effective Date
01-Aug-2011
Referred By
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Effective Date
01-Aug-2011
Referred By
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Effective Date
01-Aug-2011
Referred By
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Effective Date
01-Aug-2011
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ASTM D6804-19 - Standard Guide for Hand Hole Design in Corrugated Boxes
Effective Date
01-Aug-2011
Referred By
ASTM D3652/D3652M-01(2020) - Standard Test Method for Thickness of Pressure-Sensitive Tapes
Effective Date
01-Aug-2011
Referred By
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Effective Date
01-Aug-2011
Referred By
ASTM D3654/D3654M-06(2019) - Standard Test Methods for Shear Adhesion of Pressure-Sensitive Tapes
Effective Date
01-Aug-2011
Referred By
ASTM D3833/D3833M-96(2019) - Standard Test Method for Water Vapor Transmission of Pressure-Sensitive Tapes
Effective Date
01-Aug-2011
Referred By
ASTM D7956/D7956M-16 - Standard Practice for Compressive Testing of Thin Damaged Laminates Using a Sandwich Long Beam Flexure Specimen
Effective Date
01-Aug-2011
Referred By
ASTM C393/C393M-20 - Standard Test Method for Core Shear Properties of Sandwich Constructions by Beam Flexure
Effective Date
01-Aug-2011
Referred By
ASTM D4506-21 - Standard Test Method for Determining In Situ Modulus of Deformation of a Rock Mass Using the Radial Jacking Test
Effective Date
01-Aug-2011
Referred By
ASTM D5607-16 - Standard Test Method for Performing Laboratory Direct Shear Strength Tests of Rock Specimens Under Constant Normal Force
Effective Date
01-Aug-2011
Referred By
ASTM D6415/D6415M-22 - Standard Test Method for Measuring the Curved Beam Strength of a Fiber-Reinforced Polymer-Matrix Composite
Effective Date
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Referred By
ASTM D6115-97(2019) - Standard Test Method for Mode I Fatigue Delamination Growth Onset of Unidirectional Fiber-Reinforced Polymer Matrix Composites
Effective Date
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ASTM E122-09e1 - Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or ProcessASTM E122-09e1 - Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process
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ASTM E122-09e1 - Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process
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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
´1
Designation:E122 −09 An American National Standard
Standard Practice for
Calculating Sample Size to Estimate, With Specified
Precision, the Average for a Characteristic of a Lot or
1
Process
This standard is issued under the fixed designation E122; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1
ε NOTE—Editorial corrections were made to 8.4.1.2 in November 2011.
1. Scope
e = E/µ, maximum acceptable difference expressed as a
fraction of µ.
1.1 Thispracticecoverssimplemethodsforcalculatinghow
f = degrees of freedom for a standard deviation estimate
many units to include in a random sample in order to estimate
(7.5).
with a specified precision, a measure of quality for all the units
k = thetotalnumberofsamplesavailablefromthesameor
ofalotofmaterial,orproducedbyaprocess.Thispracticewill
similar lots.
clearly indicate the sample size required to estimate the
µ = lot or process mean or expected value of X, the result
average value of some property or the fraction of nonconform-
of measuring all the units in the lot or process.
ing items produced by a production process during the time
µ = an advance estimate of µ.
0
interval covered by the random sample. If the process is not in
N = size of the lot.
a state of statistical control, the result will not have predictive
n = size of the sample taken from a lot or process.
valueforimmediate(future)production.Thepracticetreatsthe
n = size of sample j.
j
common situation where the sampling units can be considered
n = size of the sample from a finite lot (7.4).
L
to exhibit a single (overall) source of variability; it does not
p' = fraction of a lot or process whose units have the
treat multi-level sources of variability.
nonconforming characteristic under investigation.
p = an advance estimate of p'.
0
2. Referenced Documents
p = fraction nonconforming in the sample.
2
R = rangeofasetofsamplingvalues.Thelargestminusthe
2.1 ASTM Standards:
smallest observation.
E456Terminology Relating to Quality and Statistics
R = range of sample j.
j
k
¯
R =
3. Terminology
R /k , average of the range of k samples, all of the
(
j
j51
3.1 Definitions—Unlessotherwisenoted,allstatisticalterms
same size (8.2.2).
are defined in Terminology E456.
σ = lot or process standard deviation of X, the result of
3.2 Symbols—Symbols used in all equations are defined as
measuring all of the units of a finite lot or process.
follows:
σ = an advance estimate of σ.
0
n
2
s =
H 1⁄2
~X 2X! / n21 , an estimate of the standard
E = the maximum acceptable difference between the true F ~ ! G
( i
i51
average and the sample average.
deviation σ from n observation, X, i=1 to n.
i
k
s¯ =
S /k , average s from k samples all of the same size
( j
j51
1
(8.2.1).
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
s = pooled (weighted average) s from k samples, not all of
p
Statistics.
the same size (8.2).
Current edition approved Aug. 1, 2009. Published September 2009. Originally
s = standard deviation of sample j.
j
approved in 1958. Last previous edition approved in 2007 as E122–07. DOI:
V = an advance estimate of V, equal to δ /µ .
10.1520/E0122-09E01. o o o
2 ¯
v = s/X, the coefficient of variation estimated from the
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
sample.
Standards volume information, refer to the standard’s Document Summary page on
v = pooled (weighted average) of v from k samples (8.3).
p
the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
´1
E122−09
6. Precision Desired
v = coefficient of variation from sample j.
j
X = numerical value of the characteristic of an individual
6.1 Theapproximateprecisiondesiredfortheestimatemust
unit being measured.
be prescribed. That is, it must be decided what maximum
n
¯
X =
X /n average of n observations, X,i=1to n. deviation, E, can be tolerated between the estimate to be made
( i i i
i51
from the sample and the result that would be obtained by
measuring every unit in the lot or process.
4. Significance and Use
6.2 Insomecases,themaximumallowablesamplingerroris
4.1 This practice is intended for use in determining the
expressed as a proportion, e, or a percentage, 100 e. For
sample size required to estimate, with specified precision, a
e
...

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SCOPE
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SCOPE
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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
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
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
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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