ASTM D4854-95(2001)
(Guide)Standard Guide for Estimating the Magnitude of Variability from Expected Sources in Sampling Plans (Withdrawn 2009)
Standard Guide for Estimating the Magnitude of Variability from Expected Sources in Sampling Plans (Withdrawn 2009)
SIGNIFICANCE AND USE
This guide is useful in estimating the variation due to lot sampling units, laboratory sampling units, and specimen selection and testing during the sampling and testing of a lot of material.
Estimates of variation from the several sources will make it possible to write sampling plans which balance the cost of sampling and testing with the desired precision of the plan.
This guide is useful in: (1) designing process controls and (2) developing sampling plans as parts of product specifications.
This guide can be used for designing new sampling plans or for improving old plans.
This guide is concerned with the process of sampling. This is unlike Practice D 2904 or Practice D 4467 which are concerned with the process of testing.
Studies based on this guide are applicable only to the material(s) on which the studies are made. If the conclusions are to be used for a specification, then separate studies should be made on three or more kinds of materials of the type on which the test method may be used and which produce test results covering the range of interest.
SCOPE
1.1 This guide serves as an aid to subcommittees in writing specifications and sampling procedures.
1.2 The guide explains how to estimate the contributions of the variability of lot sampling units, laboratory sampling units, and specimens to the variation of the test result of a sampling plan.
1.3 The guide explains how to combine the estimates of the variability from the three sources to obtain an estimate of the variability of the sampling plan results.
1.4 The guide is applicable to all sampling plans that produce variables data (Note 1). It is not applicable to plans that produce attribute data, since such plans do not take specimens in stages, but require that specimens be taken at random from all of the individual items in the lot. Note 0This guide is applicable to all sampling plans that produce variables data regardless of the kind of frequency distribution of these data, 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 Results6Keywords 7Analysis of Data Using ANOVAAnnex A1A Numerical ExampleAnnex A2
WITHDRAWN RATIONALE
This guide serves as an aid to subcommittees in writing specifications and sampling procedures.
Formerly under the jurisdiction of Committee D13 on Textiles, this guide was withdrawn in March 2009 because D13 no longer has the expertise to maintain and statistical standards are being maintained by committee E11.
General Information
Relations
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
Designation: D 4854 – 95 (Reapproved 2001)
Standard Guide for
Estimating the Magnitude of Variability from Expected
Sources in Sampling Plans
This standard is issued under the fixed designation D4854; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope D4271 PracticeforWritingStatementsonSamplinginTest
Methods for Textiles
1.1 This guide serves as an aid to subcommittees in writing
D4467 Practice for InterlaboratoryTesting of aTextileTest
specifications and sampling procedures.
Method that Produces Non-Normally Distributed Data
1.2 The guide explains how to estimate the contributions of
E456 Terminology Relating to Quality and Statistics
the variability of lot sampling units, laboratory sampling units,
2.2 ASTM Adjuncts:
and specimens to the variation of the test result of a sampling
TEX-PAC
plan.
1.3 The guide explains how to combine the estimates of the
NOTE 2—Tex-Pac is a group of PC programs on floppy disks, available
variability from the three sources to obtain an estimate of the throughASTM Headquarters, 100 Barr Harbor Drive, Conshohocken, PA
19428, USA. The calculations described in the annexes of this guide,
variability of the sampling plan results.
including the cost comparisons of various sampling plans, can be
1.4 The guide is applicable to all sampling plans that
conducted using one of these programs.
produce variables data (Note 1). It is not applicable to plans
that produce attribute data, since such plans do not take
3. Terminology
specimens in stages, but require that specimens be taken at
3.1 Definitions:
random from all of the individual items in the lot.
3.1.1 analysis of variance (ANOVA), n—a procedure for
NOTE 1—This guide is applicable to all sampling plans that produce
dividing the total variation of a set of data into two or more
variables data regardless of the kind of frequency distribution of these
parts, one of which estimates the error due to selecting and
data, because no estimates are made of any probabilities.
testing specimens and the other part(s) possible sources of
1.5 This guide includes the following topics:
additional variation.
Section 3.1.2 attribute data, n—observed values or determinations
Topic Title
Number
which indicate the presence or absence of specific character-
Scope 1
istics.
Referenced Documents 2
Terminology 3 3.1.3 component of variance, n—a part of a total variance
Significance and Use 4
identified with a specific source of variability.
Sampling Plans Producing Variables Data 5
3.1.4 degrees of freedom, n—for a set,thenumberofvalues
Reducing Variability of Sampling Results 6
Keywords 7 that can be assigned arbitrarily and still get the same value for
Analysis of Data Using ANOVA Annex A1
each of one or more statistics calculated from the set of data.
A Numerical Example Annex A2
3.1.4.1 Discussion— For example, if only an average is
2. Referenced Documents specifiedforasetoffiveobservations,therearefourdegreesof
freedom since the same average can be obtained with any
2.1 ASTM Standards:
values substituted for four of the observations as long as the
D123 Terminology Relating to Textiles
fifth value is set to give the correct total. If both the average
D2904 Practice for InterlaboratoryTesting of aTextileTest
andstandarddeviationhavebeenspecified,thereareonlythree
Method that Produces Normally Distributed Data
degrees of freedom left.
This guide is under the jurisdiction of ASTM Committee D13 on Textiles and
is the direct responsibility of Subcommittee D13.93 on Statistics. Annual Book of ASTM Standards, Vol 07.02.
Current edition approved May 15, 1995. Published July 1995. Originally Annual Book of ASTM Standards, Vol 14.02.
published as D4854–88. Last previous edition D4854–91. PC programs on floppy disks are available throughASTM. For a 3 ⁄2 inch disk
Annual Book of ASTM Standards, Vol 07.01. request PCN:12-429040-18, for a 5 ⁄4 inch disk request PCN:12-429041-18.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 4854
3.1.5 determination value, n—the numerical quantity calcu- 3.1.20 variance, s , n—of a population, a measure of the
lated by means of the test method equation from the measure- dispersion of members of the population expressed as a
ment values obtained as directed in a test method. (Syn. function of the sum of the squared deviations from the
determination) (See also observation.) population mean.
3.1.21 variance, s , n—of a sample, a measure of the
3.1.6 laboratory sample, n—a portion of material taken to
represent the lot sample, or the original material, and used in dispersion of variates observed in a sample expressed as a
function of the squared deviations from the sample average.
the laboratory as a source of test specimens.
3.1.22 For definitions of textile terms, refer to Terminology
3.1.7 lot sample, n—one or more shipping units taken to
represent an acceptance sampling lot and used as a source of D123.Fordefinitionsofstatisticalterms,refertoTerminology
D123 or Terminology E456, or appropriate textbooks on
laboratory samples.
statistics.
3.1.8 mean square—in analysis of variance,acontractionof
the expression “mean of the squared deviations from the
4. Significance and Use
appropriate average(s)” where the divisor of each sum of
squares is the appropriate degrees of freedom.
4.1 Thisguideisusefulinestimatingthevariationduetolot
3.1.9 observation, n—(1) the process of determining the
sampling units, laboratory sampling units, and specimen selec-
presence or absence of attributes or making measurements of a
tion and testing during the sampling and testing of a lot of
variable,(2)aresultoftheprocessofdeterminingthepresence
material.
or absence of an attribute or making a measurement of a
4.2 Estimates of variation from the several sources will
variable. (Compare measurement value, determination value,
makeitpossibletowritesamplingplanswhichbalancethecost
and test result.)
of sampling and testing with the desired precision of the plan.
3.1.10 precision, n—thedegreeofagreementwithinasetof
4.3 This guide is useful in: (1) designing process controls
observations or test results obtained as directed in a method.
and (2) developing sampling plans as parts of product specifi-
3.1.10.1 Discussion—The term “precision,” delimited in
cations.
various ways, is used to describe different aspects of precision.
4.4 This guide can be used for designing new sampling
This usage was chosen in preference to the use of “repeatabil-
plans or for improving old plans.
ity” and “reproducibility” which have been assigned conflict-
4.5 This guide is concerned with the process of sampling.
ing meanings by various authors and standardizing bodies.
This is unlike Practice D2904 or Practice D4467 which are
3.1.11 random sampling, n—the process of selecting units
concerned with the process of testing.
for a sample of size n in such a manner that all combinations
4.6 Studies based on this guide are applicable only to the
of n units under consideration have an equal or ascertainable
material(s) on which the studies are made. If the conclusions
chance of being selected as the sample. (Syn. simple random
are to be used for a specification, then separate studies should
sampling and sampling at random.)
be made on three or more kinds of materials of the type on
3.1.12 sample, n—(1) a portion of a lot of material which is
which the test method may be used and which produce test
taken for testing or record purposes; (2) a group of specimens results covering the range of interest.
used, or observations made, which provide information that
can be used for making statistical inferences about the popu- 5. Sampling Plans Producing Variables Data
lation(s) from which they were drawn. (See also lot sample,
5.1 Fortheresultsofusingthisguidetobecompletelyvalid,
laboratory sample, and specimen.)
it is necessary that all of the sampling units at every stage be
3.1.13 sampling plan, n—a procedure for obtaining a
taken randomly. It is not always practical to achieve complete
sample.
randomness, but every reasonable effort should be made to do
3.1.14 sampling plan result, n—thenumberobtainedforuse
so.
in judging the acceptability of a lot when applying a sampling
5.2 In sampling plans which produce variables data, there
plan.
are three stages in which variation can occur. For a schematic
3.1.15 sampling unit, n—an identifiable, discrete unit or
representationofthesethreestagesseeFig.1(seealsoPractice
subunit of material that could be taken as part of a sample.
D4271):
3.1.16 specimen, n—a specific portion of a material or
5.2.1 Lot Sample—Variation among the averages of the
laboratory sample upon which a test is performed or which is
sampling units within a lot sample is due to differences
taken for that purpose. (Syn. test specimen.)
between such items as cases, cartons, and bolts, variation
3.1.17 sum of squares—in analysis of variance, a contrac-
among laboratory samples plus test method error and differ-
tion of the expression “sum of the squared deviations from the
ences among specimens. To estimate variation due to lot
appropriateaverage(s)”wheretheaverage(s)ofinterestmaybe
sampling units alone, proceed as directed in 5.3 and 5.4.
the average(s) of a specific subset(s) of data or of the entire set
5.2.2 Laboratory Sample—Within the lot sampling units,
of data.
variation among the averages of the laboratory sampling units
3.1.18 test result, n—a value obtained by applying a test is due to differences among such items as cones within cases,
method, expressed either as a single determination or a
garments within cartons, and swatches within bolts, plus test
specified combination of a number of determinations.
method error and differences among specimens. To estimate
3.1.19 variables data, n—measurements which vary and variation due to laboratory sampling units alone, proceed as
may take any of a specified set of numerical values. directed in 5.3 and 5.4.
D 4854
stable, that is, until the estimates of the mean squares change
very little with additional use of the sampling plan.
5.4 After the estimates of the mean squares have stabilized,
do any desired pooling of sums of squares and degrees of
freedom(seeNote3).Calculatethecomponentsofvariancefor
each of the stages, using the equations for mean squares
composition in Table A1.1 or Table A1.2. Details of how to
make these calculations are shown in Annex A1.
NOTE 3—There is disagreement among statisticians on if and when to
pool sums of squares and degrees of freedom. This guide recommends
pooling under certain circumstances. When and how to pool is discussed
in A1.2.1, A1.2.2, A1.2.3, and A1.3.1.
6. Reducing Variability of Sampling Results
6.1 Variability of Sampling Results—Calculate the esti-
mated variance of the sampling plan result (average of all
specimen determinations), v, for several sampling plans, using
Eq 1:
v 5 L/n 1 T/mn 1 E/mnk (1)
where:
v = estimated variance of sampling plan results,
L = mean squared deviation due to variation among lot
sampling units,
FIG. 1 Sampling Plan—Three Stages
n = number of sampling units in the lot samples,
T = mean squared deviation due to laboratory samples,
m = number of laboratory sampling units from one lot
5.2.3 Specimens—Variation among determination values on
sampling unit,
specimens is due to the test method error and the differences
E = mean squared deviation due to testing specimens, and
among specimens within laboratory sampling units such as
k = number of specimens per laboratory sampling unit.
cones, garments, and swatches. Usually it is not feasible to
6.1.1 The values of L, T, and E are obtained by the use of
separate these two errors. To estimate the variation among
analysis of variance and estimation of the components of
specimens proceed as directed in 5.3 and 5.4.
variance as directed in 5.3 and 5.4, and explained in the
5.3 If a sampling plan has already been put into operation,
annexes.
or if a new plan is proposed, put it into operation, and collect
6.2 Sampling Plan Choice—Other things being equal, from
the resulting data. In the case of either an old plan or a new
those sampling plans examined as directed in 6.1, choose the
plan, obtain at least two sampling units at each of the stages of
plan which has an acceptable variability with an acceptable
sampling. Sample at least two lots and make an ANOVA for
cost. Once the sizes of L, T, and E have been determined, both
each lot as directed inAnnexA1. Continue collecting data for
the anticipated variability and cost of obtaining a sampling
successive lots and make a new ANOVA of the data for each
result for any desired combination of m, n, and k may be
lot.Tabulatetheresultingsumsofsquares,degreesoffreedom,
calculated. See Annex A2 and Table A2.4.
andmeansquaresinaformatlikethatofTableA2.3.Calculate
the totals for the sums of squares and for the degrees of
7. Keywords
freedom to date and calculate the combined mean squares for
the lots sampled to date. Continue until the results become 7.1 sampling plans; statistics; variability
D 4854
ANNEXES
(Mandatory Information)
A1. ANALYSIS OF DATA USING ANOVA
sampling units within the lot sample, laboratory sampling units within the
A1.1 Sampling Stages—Data taken as directed in 5.3 will
laboratory samples within lot samples, and specimens within the labora-
be in three, two, or one stage as follows:
tory sampling units within laboratory samples within lot samples.
A1.1.1 Three-Stage Sampling—For a sampling plan having
A1.2.1 If the estimate of the mean square for lot samples is
distinct sampling units in the lot sample, laboratory samples,
less than or equal to that for laboratory samples, it means that
and specimens, the ANOVA takes the form of lot sampling
all of the variation in lot samples may be explained by the
units with two stages of subsampling (laboratory sampling
variation in laboratory samples. In this case, set L =0, and
units within lot samples and specimens within laboratory
pool the mean squares for lot and laboratory samples to give a
sampling units). See A1.2.
new estimate of the mean square for laboratory samples:
A1.1.2 Two-Stage Sampling—For a sampling plan having
[(2)–(4)]/(mn − 1). Rewrite theANOVAtable, omitting the lot
distinct sampling units in the lot sample, but the laboratory
sample line, replacing the sum of squares for laboratory
sampling units serve as test specimens, the ANOVA takes the
...
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