iTeh StandardsiTeh Standards
EURUSD
Your shopping cart is empty.
ASTM

ASTM E2709-14e1

(Practice)

Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure

Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure

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 and health practices and determine the applicability of regulatory limitations prior to use.

General Information

Status
Historical
Publication Date
30-Sep-2014
ICS
03.120.30 - Application of statistical methods
Technical Committee
E11 - Quality and Statistics
Drafting Committee
E11.20 - Test Method Evaluation and Quality Control
Current Stage
Ref Project

Relations

Replaces
ASTM E2709-14 - Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure
Effective Date
01-Oct-2014
Referred By
ASTM E2810-19 - Standard Practice for Demonstrating Capability to Comply with the Test for Uniformity of Dosage Units
Effective Date
01-Oct-2014
Referred By
ASTM E456-13a(2022) - Standard Terminology Relating to Quality and Statistics
Effective Date
01-Oct-2014

Buy Standard

ASTM E2709-14e1 - Standard Practice for Demonstrating Capability to Comply with an Acceptance ProcedureASTM E2709-14e1 - Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure
PreviousNext
Standard
ASTM E2709-14e1 - Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure
English language
7 pages
sale 15% off
Preview
sale 15% off
Preview
REDLINE ASTM E2709-14e1 - Standard Practice for Demonstrating Capability to Comply with an Acceptance ProcedureREDLINE ASTM E2709-14e1 - Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure
PreviousNext
Standard
REDLINE ASTM E2709-14e1 - Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure
English language
7 pages
sale 15% off
Preview
sale 15% off
Preview

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
´1
Designation: E2709 − 14 An American National Standard
Standard Practice for
Demonstrating Capability to Comply with an Acceptance
1
Procedure
This standard is issued under the fixed designation E2709; 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 made throughout in March 2015.
1. Scope E2282 Guide for Defining the Test Result of a Test Method
E2586 Practice for Calculating and Using Basic Statistics
1.1 This practice provides a general methodology for evalu-
ating single-stage or multiple-stage acceptance procedures
3. Terminology
which involve a quality characteristic measured on a numerical
scale. This methodology computes, at a prescribed confidence
3.1 Definitions—See Terminology E456 for a more exten-
level, a lower bound on the probability of passing an accep-
sive listing of terms in ASTM Committee E11 standards.
tance procedure, using estimates of the parameters of the
3.1.1 characteristic, n—a property of items in a sample or
distribution of test results from a sampled population.
population which, when measured, counted or otherwise
1.2 For a prescribed lower probability bound, the method-
observed, helps to distinguish between the items. E2282
ology can also generate an acceptance limit table, which
3.1.2 mean, n—of a population, µ, average or expected
defines a set of test method outcomes (for example, sample
¯
value of a characteristic in a population, of a sample X, sum of
averages and standard deviations) that would pass the accep-
the observed values in a sample divided by the sample size.
tance procedure at a prescribed confidence level.
E2586
1.3 This approach may be used for demonstrating compli-
ance with in-process, validation, or lot-release specifications.
3.1.3 multiple-stage acceptance procedure, n—a procedure
that involves more than one stage of sampling and testing a
1.4 The system of units for this practice is not specified.
givenqualitycharacteristicandoneormoreacceptancecriteria
1.5 This standard does not purport to address all of the
per stage.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
3.1.4 standard deviation, n—of a population, σ, the square
priate safety and health practices and determine the applica-
root of the average or expected value of the squared deviation
bility of regulatory limitations prior to use.
of a variable from its mean – of a sample, s, the square root of
1.6 This international standard was developed in accor-
the sum of the squared deviations of the observed values in the
dance with internationally recognized principles on standard-
sample divided by the sample size minus 1. E2586
ization established in the Decision on Principles for the
3.1.5 test method, n—a definitive procedure that produces a
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical test result. E2282
Barriers to Trade (TBT) Committee.
3.2 Definitions of Terms Specific to This Standard:
2. Referenced Documents
3.2.1 acceptable parameter region, n—the set of values of
2
parameters characterizing the distribution of test results for
2.1 ASTM Standards:
which the probability of passing the acceptance procedure is
E456 Terminology Relating to Quality and Statistics
greater than a prescribed lower bound.
1
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
3.2.2 acceptance region, n—the set of values of parameter
Statistics and is the direct responsibility of Subcommittee E11.20 on Test Method
estimates that will attain a prescribed lower bound on the
Evaluation and Quality Control.
Current edition approved Oct. 1, 2014. Published October 2014. Originally
probability of passing an acceptance procedure at a prescribed
approved in 2009. Last previous edition approved in 2012 as E2709 – 12. DOI:
level of confidence.
10.1520/E2709-14E01.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3.2.3 acceptance limit, n—the boundary of the acceptance
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
region, for example, the maximum sample standard deviation
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. test results for a given sample mean.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
´1
E2709 − 14
4. Significance and Use ability of that stage as a function of the probabilities o
...

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: E2709 − 14 E2709 − 14 An American National Standard
Standard Practice for
Demonstrating Capability to Comply with an Acceptance
1
Procedure
This standard is issued under the fixed designation E2709; 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 made throughout in March 2015.
1. 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 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
E2282 Guide for Defining the Test Result of a Test Method
E2586 Practice for Calculating and Using Basic Statistics
3. Terminology
3.1 Definitions—See Terminology E456 for a more extensive listing of terms in ASTM Committee E11 standards.
3.1.1 characteristic, n—a property of items in a sample or population which, when measured, counted or otherwise observed,
helps to distinguish between the items. E2282
¯
3.1.2 mean, n—of a population, μ, average or expected value of a characteristic in a population, of a sampleX , sum of the
observed values in a sample divided by the sample size. E2586
3.1.3 multiple-stage acceptance procedure, n—a procedure that involves more than one stage of sampling and testing a given
quality characteristic and one or more acceptance criteria per stage.
3.1.4 standard deviation, n—of a population, σ, the square root of the average or expected value of the squared deviation of a
variable from its mean – of a sample, s, the square root of the sum of the squared deviations of the observed values in the sample
divided by the sample size minus 1. E2586
3.1.5 test method, n—a definitive procedure that produces a test result. E2282
3.2 Definitions of Terms Specific to This Standard:
1
This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.20 on Test Method
Evaluation and Quality Control.
Current edition approved Oct. 1, 2014. Published October 2014. Originally approved in 2009. Last previous edition approved in 2012 as E2709 – 12. DOI:
10.1520/E2709-14.10.1520/E2709-14E01.
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’sstandard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
´1
E2709 − 14
3.2.1 acceptable parameter region, n—the set of values of parameters characterizing the distribution of test results for which
the probability of passing the acceptance procedure is greater than a prescribed lower bound.
3.2.2 acceptance region, n—the set of values of parameter estimates that will attain a prescribed lower bound on the probability
of passing an acceptance procedure at a prescribed level of confidence.
3.2.3 acceptance limit, n—the boundary of the acceptance region, for example, the maximum sample standard deviation test
results for a given sample mean.
4. Significance and Use
4.1 This practice considers inspection procedures that may involve multiple-s
...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.

This May Also Interest You

ASTM
ASTM E141-10(2023)(Practice)
Standard Practice for Acceptance of Evidence Based on the Results of Probability Sampling

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...

  • Standard
    6 pages
    English language
    sale 15% off
ASTM
ASTM E2709-23(Practice)
Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure

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.

  • Standard
    8 pages
    English language
    sale 15% off
  • Standard
    8 pages
    English language
    sale 15% off
ASTM
ASTM E3080-23(Practice)
Standard Practice for Regression Analysis with a Single Predictor Variable

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 ...

  • Standard
    23 pages
    English language
    sale 15% off
  • Standard
    23 pages
    English language
    sale 15% off
ASTM
ASTM E1994-09(2023)(Practice)
Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans

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.

  • Standard
    23 pages
    English language
    sale 15% off
ASTM
ASTM E2334-09(2023)(Practice)
Standard Practice for Setting an Upper Confidence Bound for a Fraction or Number of Non-Conforming items, or a Rate of Occurrence for Non-Conformities, Using Attribute Data, When There is a Zero Response in the Sample

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 ...

  • Standard
    10 pages
    English language
    sale 15% off
ASTM
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.

  • Standard
    5 pages
    English language
    sale 15% off
ASTM
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...

  • Standard
    29 pages
    English language
    sale 15% off
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.

  • Standard
    26 pages
    English language
    sale 15% off
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.

  • Standard
    11 pages
    English language
    sale 15% off
  • Standard
    11 pages
    English language
    sale 15% off
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...

  • Standard
    24 pages
    English language
    sale 15% off
  • Standard
    24 pages
    English language
    sale 15% off