ASTM_E_2709_-_14e1.pdf

Designation:E2709141An American National StandardStandard Practice forDemonstrating Capability to Comply with an AcceptanceProcedure1This standard is issued under the fixed designation E2709;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.Asuperscript epsilon()indicates an editorial change since the last revision or reapproval.1NOTEEditorial corrections made throughout in March 2015.1.Scope1.1 This practice provides a general methodology for evalu-ating single-stage or multiple-stage acceptance procedureswhich involve a quality characteristic measured on a numericalscale.This methodology computes,at a prescribed confidencelevel,a lower bound on the probability of passing an accep-tance procedure,using estimates of the parameters of thedistribution of test results from a sampled population.1.2 For a prescribed lower probability bound,the method-ology can also generate an acceptance limit table,whichdefines a set of test method outcomes(for example,sampleaverages and standard deviations)that would pass the accep-tance procedure at a prescribed confidence level.1.3 This approach may be used for demonstrating compli-ance 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 thesafety concerns,if any,associated with its use.It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2.Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE2282 Guide for Defining the Test Result of a Test MethodE2586 Practice for Calculating and Using Basic Statistics3.Terminology3.1 DefinitionsSee Terminology E456 for a more exten-sive listing of terms in ASTM Committee E11 standards.3.1.1 characteristic,na property of items in a sample orpopulation which,when measured,counted or otherwiseobserved,helps to distinguish between the items.E22823.1.2 mean,nof a population,average or expectedvalue of a characteristic in a population,of a sampleX,sum ofthe observed values in a sample divided by the sample size.E25863.1.3 multiple-stage acceptance procedure,na procedurethat involves more than one stage of sampling and testing agiven quality characteristic and one or more acceptance criteriaper stage.3.1.4 standard deviation,nof a population,the squareroot of the average or expected value of the squared deviationof a variable from its mean of a sample,s,the square root ofthe sum of the squared deviations of the observed values in thesample divided by the sample size minus 1.E25863.1.5 test method,na definitive procedure that produces atest result.E22823.2 Definitions of Terms Specific to This Standard:3.2.1 acceptable parameter region,nthe set of values ofparameters characterizing the distribution of test results forwhich the probability of passing the acceptance procedure isgreater than a prescribed lower bound.3.2.2 acceptance region,nthe set of values of parameterestimates that will attain a prescribed lower bound on theprobability of passing an acceptance procedure at a prescribedlevel of confidence.3.2.3 acceptance limit,nthe boundary of the acceptanceregion,for example,the maximum sample standard deviationtest results for a given sample mean.4.Significance and Use4.1 This practice considers inspection procedures that mayinvolve multiple-stage sampling,where at each stage one candecide to accept or to continue sampling,and the decision toreject is deferred until the last stage.4.1.1 At each stage there are one or more acceptance criteriaon the test results;for example,limits on each individual testresult,or limits on statistics based on the sample of test results,1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved Oct.1,2014.Published October 2014.Originallyapproved in 2009.Last previous edition approved in 2012 as E2709 12.DOI:10.1520/E2709-14E01.2For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 such as the average,standard deviation,or coefficient ofvariation(relative standard deviation).4.2 The methodology in this practice defines an acceptanceregion for a set of test results from the sampled population suchthat,at a prescribed confidence level,the probability that asample from the population will pass the acceptance procedureis greater than or equal to a prespecif