ASTM_D_4854_-_95_2001.pdf

Designation:D 4854 95(Reapproved 2001)Standard Guide forEstimating the Magnitude of Variability from ExpectedSources in Sampling Plans1This standard is issued under the fixed designation D 4854;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(e)indicates an editorial change since the last revision or reapproval.1.Scope1.1 This guide serves as an aid to subcommittees in writingspecifications and sampling procedures.1.2 The guide explains how to estimate the contributions ofthe variability of lot sampling units,laboratory sampling units,and specimens to the variation of the test result of a samplingplan.1.3 The guide explains how to combine the estimates of thevariability from the three sources to obtain an estimate of thevariability of the sampling plan results.1.4 The guide is applicable to all sampling plans thatproduce variables data(Note 1).It is not applicable to plansthat produce attribute data,since such plans do not takespecimens in stages,but require that specimens be taken atrandom from all of the individual items in the lot.NOTE1This guide is applicable to all sampling plans that producevariables data regardless of the kind of frequency distribution of thesedata,because no estimates are made of any probabilities.1.5 This guide includes the following topics:Topic TitleSectionNumberScope1Referenced Documents2Terminology3Significance and Use4Sampling Plans Producing Variables Data5Reducing Variability of Sampling Results6Keywords7Analysis of Data Using ANOVAAnnex A1A Numerical ExampleAnnex A22.Referenced Documents2.1 ASTM Standards:D 123 Terminology Relating to Textiles2D 2904 Practice for Interlaboratory Testing of a Textile TestMethod that Produces Normally Distributed Data2D 4271 Practice for Writing Statements on Sampling in TestMethods for Textiles3D 4467 Practice for Interlaboratory Testing of a Textile TestMethod that Produces Non-Normally Distributed Data3E 456 Terminology Relating to Quality and Statistics42.2 ASTM Adjuncts:TEX-PAC5NOTE2Tex-Pac is a group of PC programs on floppy disks,availablethrough ASTM Headquarters,100 Barr Harbor Drive,Conshohocken,PA19428,USA.The calculations described in the annexes of this guide,including the cost comparisons of various sampling plans,can beconducted using one of these programs.3.Terminology3.1 Definitions:3.1.1 analysis of variance(ANOVA),na procedure fordividing the total variation of a set of data into two or moreparts,one of which estimates the error due to selecting andtesting specimens and the other part(s)possible sources ofadditional variation.3.1.2 attribute data,nobserved values or determinationswhich indicate the presence or absence of specific character-istics.3.1.3 component of variance,na part of a total varianceidentified with a specific source of variability.3.1.4 degrees of freedom,nfor a set,the number of valuesthat can be assigned arbitrarily and still get the same value foreach of one or more statistics calculated from the set of data.3.1.4.1 Discussion For example,if only an average isspecified for a set of five observations,there are four degrees offreedom since the same average can be obtained with anyvalues substituted for four of the observations as long as thefifth value is set to give the correct total.If both the averageand standard deviation have been specified,there are only threedegrees of freedom left.3.1.5 determination value,nthe numerical quantity calcu-lated by means of the test method equation from the measure-ment values obtained as directed in a test method.(Syn.determination)(See also observation.)3.1.6 laboratory sample,na portion of material taken torepresent the lot sample,or the original material,and used inthe laboratory as a source of test specimens.3.1.7 lot sample,none or more shipping units taken torepresent an acceptance sampling lot and used as a source oflaboratory samples.1This guide is under the jurisdiction of ASTM Committee D13 on Textiles andis the direct responsibility of Subcommittee D13.93 on Statistics.Current edition approved May 15,1995.Published July 1995.Originallypublished as D 4854 88.Last previous edition D 4854 91.2Annual Book of ASTM Standards,Vol 07.01.3Annual Book of ASTM Standards,Vol 07.02.4Annual Book of ASTM Standards,Vol 14.02.5PC programs on floppy disks are available through ASTM.For a 312inch diskrequest PCN:12-429040-18,for a 514inch disk request PCN:12-429041-18.1Copyright ASTM,100 Barr Harbor Drive,West Conshohocken,PA 19428-2959,United States.3.1.8 mean squarein analysis of variance,a contraction ofthe expression“mean of the squared deviations from theappropriate average(s)”where the divisor of each sum ofsquares is the appropriate degrees of freedom.3.1.9 observation,n(1)the process of determining thepresence or absence of attributes or making measurements of avariable,(2)a result of the proces