ASTM_E_122_-_09e1.pdf

Designation:E122091An 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 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.Department of Defense.1NOTEEditorial corrections were made to 8.4.1.2 in November 2011.1.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 size 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(future)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.2.Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and Statistics3.Terminology3.1 DefinitionsUnless otherwise noted,all statistical termsare defined in Terminology E456.3.2 SymbolsSymbols used in all equations are defined asfollows: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 expected 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 characteristic 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 deviation of X,the result ofmeasuring all of the units of a finite lot or process.0=an advance estimate of.s=F(i51nXi2XH!2/n21!12G,an estimate of the standarddeviation from n observation,Xi,i=1 to n.s=(j51kSj/k,average 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).1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.10 on Sampling/Statistics.Current edition approved Aug.1,2009.Published September 2009.Originallyapproved in 1958.Last previous edition approved in 2007 as E122 07.DOI:10.1520/E0122-09E01.2For 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 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 This practice is intended for use in determining thesample size required to estimate,with specified precision,ameasure of quality of a lot or process.The practice applieswhen quality is expressed as either the lot average for a givenproperty,or as the lot fraction not conforming to prescribedstandards.The level of a characteristic may often be taken as anindication of the quality of a material.If so,an estimate of theaverage value of that characteristic or of the fraction of theobserved values that do not conform to a specification for thatcharacteristic becomes a measure of quality with respect to thatcharacteristic.This practice is intended for use in determiningthe sample size required to estimate,with specified precision,such a measure of the quality of a lot or process either as anaverage value or as a fraction not conforming to a specifiedvalue.5.Empirical Knowledge Needed5.1 Some empirical knowledge of the problem is desirablein advance.5.1.1 We may have some idea abou