Standard Practice for Establishing Consistent Test Method Tolerances (Withdrawn 2007)

SIGNIFICANCE AND USE
In any test method, every direction to measure a property of a material should be accompanied by a measurement tolerance. Likewise, determination and test result tolerances should be specified. This practice provides a method for evaluating the consistency of the test method tolerances specified.
This practice should be used both in the development of new test methods and in evaluating old test methods which are being revised.
The test result tolerance obtained using this practice is not a substitute for a precision statement based on interlaboratory testing. However, the measurement tolerances selected by means of this practice will be an important part of the test method conditions affecting the precision of the test method. MATHEMATICAL RELATIONSHIPS   Top
SCOPE
1.1 This practice should be used in the development of any test method in which the determination value is calculated from measurement values by means of an equation. The practice is not applicable to such determination values as those calculated from counts of nonconformities, ratios of successes to failures, gradings, or ratings.
1.2 The purpose of this practice is to provide guidance in the specifying of realistic and consistent tolerances for making measurements and for reporting the results of testing.
1.3 This practice can be used as a guide for obtaining the minimum test result tolerance that should be specified with a particular set of specified measurement tolerances, the maximum permissible measurement tolerances which should be specified to achieve a specified test result tolerance, and more consistent specified measurement tolerances.
1.4 These measurement and test result tolerances are not statistically determined tolerances that are obtained by using the test method but are the tolerances specified in the test method.
1.5 In the process of selecting test method tolerances, the task group developing or revising a test method must evaluate not only the consistency of the selected tolerances but also the technical and economical feasibility of the measurement tolerances and the suitability of the test result tolerance for the purposes for which the test method will be used. This practice provides guidance only for establishing the consistency of the test method tolerances.
1.6 This practice is presented in the following sections:NumberScope 1Referenced Documents2TERMINOLOGYDefinitions3Discussion of Terms4Expressing Test Method Tolerances5Tolerance Symbols6SUMMARY AND USESSummary of Practice 7 Uses and Significance8MATHEMATICAL RELATIONSHIPSPropagation Equations9Tolerance Terms10Determination Tolerances11Consistency Criteria12APPLICATION OF PRINCIPLESProcedure 13 Mass per Unit Area Example14ANNEXESGeneral Propagation Equation Annex A1 Specific Propagation EquationsAnnex A2
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
WITHDRAWN RATIONALE
This practice is being withdrawn because the scope of the standard, precision of recording measurements, is partly covered in E29. Propagation of errors methodology presented in the standard is also available from other sources.
Formerly under the jurisdiction of ASTM Committee E11 on Quality and Statistics, this practice was withdrawn in October 2007.

General Information

Status
Withdrawn
Publication Date
29-Mar-1984
Withdrawal Date
30-Sep-2007
Current Stage
Ref Project

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ASTM D4356-84(2002) - Standard Practice for Establishing Consistent Test Method Tolerances (Withdrawn 2007)
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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
An American National Standard
Designation:D4356–84(Reapproved2002)
Standard Practice for
Establishing Consistent Test Method Tolerances
This standard is issued under the fixed designation D4356; 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
Propagation Equations 9
Tolerance Terms 10
1.1 This practice should be used in the development of any
Determination Tolerances 11
testmethodinwhichthedeterminationvalueiscalculatedfrom
Consistency Criteria 12
APPLICATION OF PRINCIPLES
measurement values by means of an equation. The practice is
Procedure 13
not applicable to such determination values as those calculated
Mass per Unit Area Example 14
from counts of nonconformities, ratios of successes to failures,
ANNEXES
General Propagation Equation Annex A1
gradings, or ratings.
Specific Propagation Equations Annex A2
1.2 Thepurposeofthispracticeistoprovideguidanceinthe
1.7 This standard does not purport to address all of the
specifying of realistic and consistent tolerances for making
safety concerns, if any, associated with its use. It is the
measurements and for reporting the results of testing.
responsibility of the user of this standard to establish appro-
1.3 This practice can be used as a guide for obtaining the
priate safety and health practices and determine the applica-
minimum test result tolerance that should be specified with a
bility of regulatory limitations prior to use.
particular set of specified measurement tolerances, the maxi-
mum permissible measurement tolerances which should be
2. Referenced Documents
specified to achieve a specified test result tolerance, and more
2.1 ASTM Standards:
consistent specified measurement tolerances.
D123 Terminology Relating to Textiles
1.4 These measurement and test result tolerances are not
D2905 Practice for Statements on Number of Specimens
statistically determined tolerances that are obtained by using
for Textiles
the test method but are the tolerances specified in the test
E29 Practice for Using Significant Digits in Test Data to
method.
Determine Conformance with Specifications
1.5 In the process of selecting test method tolerances, the
E456 Terminology Relating to Quality and Statistics
task group developing or revising a test method must evaluate
not only the consistency of the selected tolerances but also the
3. Terminology
technical and economical feasibility of the measurement toler-
3.1 Definitions:
ances and the suitability of the test result tolerance for the
3.1.1 determination process, n—the act of carrying out the
purposes for which the test method will be used. This practice
series of operations specified in the test method whereby a
provides guidance only for establishing the consistency of the
single value is obtained. (Syn. determination. See Section 4.)
test method tolerances.
3.1.1.1 Discussion—A determination process may involve
1.6 This practice is presented in the following sections:
several measurements of the same type or different types, as
Number well as an equation by which the determination value is
Scope 1
calculated from the measurement values observed.
Referenced Documents 2
3.1.2 determination tolerance, n—as specified in a test
TERMINOLOGY
Definitions 3 method, the exactness with which a determination value is to
Discussion of Terms 4
be calculated and recorded.
Expressing Test Method Tolerances 5
3.1.2.1 Discussion—In this practice, the determination tol-
Tolerance Symbols 6
SUMMARYAND USES erance also serves as the bridge between the test result
Summary of Practice 7
tolerance and the measurement tolerances. The value of the
Uses and Significance 8
determinationtolerancecalculatedfromthespecifiedtestresult
MATHEMATICAL RELATIONSHIPS
tolerance is compared with the value calculated from the
specified measurement tolerances.
ThispracticeisunderthejurisdictionofASTMCommitteeE11onQualityand
Statistics and is the direct responsibility of Subcommittee E11.20 on Test Method
Evaluation and Quality Control. Annual Book of ASTM Standards, Vol 07.01.
Current edition approved March 30, 1984. Published August 1984. Annual Book of ASTM Standards, Vol 14.02.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D4356–84 (2002)
3.1.3 determination value, n—thenumericalquantitycalcu- lengthandmass.Twodifferentlengthmeasurementsaremade,
lated by means of the test method equation from the measure- the length and the width of the specimen. One determination
ment values obtained as directed in a test method. (Syn. value of the mass per unit area is calculated by dividing the
determination. See Section 4.) massmeasurementvaluebytheproductofthelengthmeasure-
3.1.4 measurement process, n—the act of quantifying a ment value and the width measurement value from one
property or dimension. (Syn. measurement. See Section 4.) specimen.
3.1.4.1 Discussion—One test method determination may 4.1.3 If the test method directs that mass per unit area
involve several different kinds of measurement. determinations are to be made on three test specimens, the test
3.1.5 measurement tolerance, n—as specified in a test result is the average of the three determination values, each
method,theexactnesswithwhichameasurementistobemade obtained as directed in 4.1.2.
and recorded. 4.2 Test Method Tolerances:
3.1.6 measurement tolerance propagation equation, n—the 4.2.1 Thespecifiedmeasurementtolerancestelltheoperator
mathematical formula, derived from the test method equation, howcloselyobservationsaretobemadeandrecorded.“Weigh
whichshowsthedependenceofthedeterminationtoleranceon thespecimentothenearest0.01g”and“Measurethelengthof
the measurement tolerances. (Syn. propagation equation.) the specimen to the nearest 0.02 in.” are examples of typical
3.1.6.1 Discussion—Propagation equations and the propa- measurement tolerance specifications in a test method.
gation of errors are discussed in Annex A1. 4.2.2 The specified determination and test result tolerances
3.1.7 measurement value, n—the numerical result of quan- tell the operator how many significant digits should be re-
tifying a particular property or dimension. (Syn. measurement. corded in the determination value and in the test result,
See Section 4.) respectively.
3.1.7.1 Discussion—Measurement values in test methods
5. Expressing Test Method Tolerances
areoftwogeneraltypes:thosewhosemagnitudeisspecifiedin
5.1 Tolerances in test methods are commonly specified in
the test method, such as the dimensions of a specimen, and
one of four ways which are combinations of two general
those whose magnitude is found by testing, such as the
distinctions. A test method tolerance may be absolute or
measured mass of a specimen.
relativeandmaybeexpressedeitherasarangehavinganupper
3.1.8 propagation equation, n—Synonym of measurement
and a lower limit or as the result of rounding-off. These
tolerance propagation equation.
distinctions are illustrated by the following equivalent instruc-
3.1.9 test method equation, n—the mathematical formula
tions that are possible in weighing a 5.00 g test specimen:
specified in a test method, whereby the determination value is
Absolute Relative
calculated from measurement values.
Upper and Lower Limit within 60.005 g within 60.1 %
3.1.10 test method tolerances, n—as specified in a test
Rounding-off to the nearest 0.01 g to the nearest 0.2 %
method, the measurement tolerances, the determination toler-
5.2 Within one method, state all test method tolerances in
ance, and the test result tolerance.
either the rounding-off mode or the upper and lower limit
3.1.11 test result, n—a value obtained by applying a given
mode.The rounding-off mode is preferred for all test methods.
test method, expressed either as a single determination or a
Use a series of absolute tolerances for successive levels of a
specified combination of a number of determinations.
measurement or determination in preference to a relative
3.1.11.1 Discussion—In this practice the test result is the
tolerance.
average of the number of determination values specified in the
5.3 Thenumericalvalueofatoleranceexpressedintermsof
test method.
rounding-off is twice that for the same tolerance expressed as
3.1.12 testresulttolerance,n—asspecifiedinatestmethod,
an upper and lower limit.Adiscussion of rounding-off appears
the exactness with which a test result is to be recorded and
in Section 3 of Practice E29 and in Chapter 4 of Ref (1) .
reported.
Numbers are usually rounded-off to the nearest 1, 2, or 5 units
3.1.13 tolerance terms, n—the individual members of a
in the last place.
measurement tolerance propagation equation in which each
member contains only one test method tolerance.
6. Tolerance Symbols
3.1.14 For the definitions of other terms used in this
6.1 An absolute tolerance is symbolized by a capital delta,
practice, refer to Terminology D123 and Terminology E456.
D, followed by a capital letter designating a measurement
4. Discussion of Terms
value, a determination value or a test result. Thus, DA.
6.2 A relative tolerance is symbolized by the absolute
4.1 Test Results, Determinations, and Measurements:
tolerance, D A, divided by the corresponding measurement
4.1.1 A test result is always a value (numerical quantity),
value, determination value, or test result, A. Thus, DA/A.
but measurement and determination are often used as referring
6.3 Relative tolerances are expressed as percentages by
to general concepts, processes or values—the context indicat-
100DA/A.Allrelativetolerancesforaspecifictestmethodmust
ing which meaning is intended. In this practice it is necessary
beexpressedinthesamewaythroughout,eitherasfractionsor
tomakethesedistinctionsexplicitbymeansofthetermsgiven
as percentages.
in Section 3.
4.1.2 The necessary distinctions can be illustrated by a test
method for obtaining the mass per unit area of a fabric. Two
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
kinds of measurement are required for each test specimen, this standard.
D4356–84 (2002)
SUMMARYAND USES
E = the specimen length.
9.2.2 The corresponding propagation equation is Eq 2,
7. Summary of Practice
derived in A2.4.1.
7.1 Aspecific measurement tolerance propagation equation
2 2 2 2
~DW/W! /2 5 ~DM/M! 1 ~DD/D! 1 ~DE/E! (2)
relating the determination tolerance to the measurement toler-
ances is derived by applying an adaptation of the law of error
where:
propagation to the test method equation. In this measurement
(DW/W) /2 = the mass per unit area determination toler-
tolerance propagation equation, the determination tolerance
ance term,
termshouldequalthesumofindividualmeasurementtolerance
(DM/M) = the mass measurement tolerance term,
terms.
(DD/D) = the width measurement tolerance term, and
7.2 Tentativemeasurementanddeterminationtoleranceval- (DE/E) = the length measurement tolerance term.
ues are substituted in the propagation equation terms, and the
10. Tolerance Terms
consistency of the selected test method tolerances is judged by
the relative magnitudes of the tolerance terms.
10.1 As shown in Annex A2, every propagation equation
7.3 Successive adjustments in the selected test method
can be expressed in the form of r=a+b+c . . ., in which
tolerance values are made until a consistent set of test method
eachofthetermsofthisequationcontainsonlyonetestmethod
tolerances is established.
tolerance.Thertermcontainsthedeterminationtolerance, DR,
and the other terms contain such measurement tolerances as
8. Significance and Use
DA, DB, and DC. The terms r, a, b, and c are tolerance terms.
8.1 In any test method, every direction to measure a
10.1.1 For the mass per unit area example r=(DW/W) /2,
2 2 2
property of a material should be accompanied by a measure-
a=(DM/M) , b=(DD/D) , and c=(DE/E) , as can be seen
ment tolerance. Likewise, determination and test result toler-
from Eq 2.
ances should be specified. This practice provides a method for
NOTE 1—The number of measurement tolerance terms is not restricted
evaluating the consistency of the test method tolerances
to 3, of course, but matches the number of measurements, q, for which
specified.
tolerances are specified.
8.2 Thispracticeshouldbeusedbothinthedevelopmentof
10.2 Thekeytothispracticeistherecognitionthatthereare
new test methods and in evaluating old test methods which are
two ways of calculating the determination tolerance term:
being revised.
10.2.1 The determination tolerance term, r, can be calcu-
8.3 The test result tolerance obtained using this practice is
lated from a specified value of DR using the expression for r
not a substitute for a precision statement based on interlabo-
given in the propagation equation. For example, in Eq 2
ratory testing. However, the measurement tolerances selected
r=(DW/W) /2. By substituting a typical value for W and a
by means of this practice will be an important part of the test
specified value for DW, a value of r is obtained.
method conditions affecting the precision of the test method.
10.2.2 The determination tolerance term can also be calcu-
lated as the sum of the measurement tolerance terms a, b, c,
MATHEMATICAL RELATIONSHIPS
etc., which have been calculated from specified values of DA,
9. Propagation Equations
DB, DC, etc. For the mass per unit area example, an estimate
of the value of r may be obtained from values of a, b, and c
9.1 The test method equations by which determination
found by substituting values of DM, M, DD, D, DE, and E in
values are calculated from measurement values in textile
2 2 2
thetolerancetermexpressions(DM/M) ,(DD/D) and(DE/E) .
testing usually involve simple sums or differences, products or
10.3 These two ways of calculating the determination tol-
ratios,orcombinationsofthese.Measurementtolerancepropa-
erance term usually produce different results, often radically
gation equations for each of these types of relationships are
derived in Annex A2 by applying the general measurement different. In order to deal with this inconsistency, the second
way of calculating the determination tolerance term is labelled
tolerance propagation equation, developed in Annex A1,to
each of the typical test method equations. Propagation equa- u, which equalsa+b+c+. .
10.3.1 Therefore, in the following sections, r is the deter-
tionsforanumberoftextiletestmethodequationsaregivenin
Table A2.1. mination tolerance term value calculated from the specified
determination tolerance by means of the expression for r
9.2 In the following discussion, the determi
...

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