1、Designation:E12217An American National StandardStandard Practice forCalculating Sample Size to Estimate,With SpecifiedPrecision,the Average for a Characteristic of a Lot orProcess1This standard is issued under the fixed designation E122;the number immediately following the designation indicates the
2、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.This standard has been approved for use by agencies of the U.S.Departm
3、ent of Defense.1.Scope1.1 This practice covers simple methods for calculating howmany units to include in a random sample in order to estimatewith a specified precision,a measure of quality for all the unitsof a lot of material,or produced by a process.This practice willclearly indicate the sample s
4、ize required to estimate theaverage value of some property or the fraction of nonconform-ing items produced by a production process during the timeinterval covered by the random sample.If the process is not ina state of statistical control,the result will not have predictivevalue for immediate(futur
5、e)production.The practice treats thecommon situation where the sampling units can be consideredto exhibit a single(overall)source of variability;it does nottreat multi-level sources of variability.1.2 The system of units for this standard is not specified.Dimensional quantities in the standard are p
6、resented only asillustrations of calculation methods.The examples are notbinding on products or test methods treated.1.3 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopmen
7、t of International Standards,Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade(TBT)Committee.2.Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and Statistics3.Terminology3.1 DefinitionsUnless otherwise noted,all statistical ter
8、msare defined in Terminology E456.3.1.1 pooled standard deviation,sp,nthe estimate of astandard deviation derived by combining sample standarddeviations of several samples,weighting squared standarddeviations by their degrees of freedom.3.2 SymbolsSymbols used in all equations are defined asfollows:
9、E=the maximum acceptable difference between the trueaverage and the sample average.e=E/,maximum acceptable difference expressed as afraction of.f=degrees of freedom for a standard deviation estimate(7.5).k=the total number of samples available from the same orsimilar lots.=lot or process mean or exp
10、ected value of X,the resultof measuring all the units in the lot or process.0=an advance estimate of.N=size of the lot.n=size of the sample taken from a lot or process.nj=size of sample j.nL=size of the sample from a finite lot(7.4).p=fraction of a lot or process whose units have thenonconforming ch
11、aracteristic under investigation.p0=an advance estimate of p.p=fraction nonconforming in the sample.R=range of a set of sampling values.The largest minus thesmallest observation.Rj=range of sample j.R=(j51kRj/k,average of the range of k samples,all of thesame size(8.2.2).=lot or process standard dev
12、iation of X,the result ofmeasuring all of the units of a finite lot or process.0=an advance estimate of.s=F(i51nXi2XH!2/n 2 1!G12,an estimate of the standarddeviation from n observation,Xi,i=1 to n.1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the dire
13、ct responsibility of Subcommittee E11.10 on Sampling/Statistics.Current edition approved April 1,2017.Published April 2017.Originallyapproved in 1958.Last previous edition approved in 2009 as E122 091.DOI:10.1520/E0122-17.2For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact A
14、STM 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 StatesThis international standard was deve
15、loped in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade(TBT)Committee.1 s=(j51kSj/k,average
16、s from k samples all of the same size(8.2.1).sp=pooled(weighted average)s from k samples,not all ofthe same size(8.2).sj=standard deviation of sample j.Vo=an advance estimate of V,equal to o/o.v=s/X,the coefficient of variation estimated from thesample.vp=pooled(weighted average)of v from k samples(8.3).vj=coefficient of variation from sample j.X=numerical value of the characteristic of an individualunit being measured.X=(i51nXi/niaverage of n observations,Xi,i=1 to n.4.Significance and Use4.1 T