1、Designation: E 177 06bAn American National StandardStandard Practice forUse of the Terms Precision and Bias in ASTM Test Methods1This standard is issued under the fixed designation E 177; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revis
2、ion, 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.This standard has been approved for use by agencies of the Department of Defense.1. Scope1.1 The purpose of this
3、 practice is to present conceptsnecessary to the understanding of the terms “precision” and“bias” as used in quantitative test methods. This practice alsodescribes methods of expressing precision and bias and, in afinal section, gives examples of how statements on precisionand bias may be written fo
4、r ASTM test methods.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory requirements prior t
5、o use.2. Referenced Documents2.1 ASTM Standards:2E 178 Practice for Dealing With Outlying ObservationsE 456 Terminology Relating to Quality and StatisticsE 691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE 2282 Guide for Defining the Test Result of a Te
6、st Method3. Terminology3.1 Definitions:3.1.1 accepted reference value, na value that serves as anagreed-upon reference for comparison, and which is derivedas: (1) a theoretical or established value, based on scientificprinciples, (2) an assigned or certified value, based on experi-mental work of som
7、e national or international organization, or(3) a consensus or certified value, based on collaborativeexperimental work under the auspices of a scientific orengineering group.3.1.1.1 DiscussionA national or international organiza-tion, referred to in (2), generally maintains measurementstandards to
8、which the reference values obtained are traceable.3.1.2 accuracy, nthe closeness of agreement between atest result and an accepted reference value.3.1.2.1 DiscussionThe term accuracy, when applied to aset of test results, involves a combination of a randomcomponent and of a common systematic error o
9、r bias compo-nent.3.1.3 bias, nthe difference between the expectation of thetest results and an accepted reference value.3.1.3.1 DiscussionBias is the total systematic error ascontrasted to random error. There may be one or moresystematic error components contributing to the bias. A largersystematic
10、 difference from the accepted reference value isreflected by a larger bias value.3.1.4 intermediate precision, nthe closeness of agreementbetween test results obtained under specified intermediateprecision conditions.3.1.4.1 DiscussionThe specific measure and the specificconditions must be specified
11、 for each intermediate measure ofprecision; thus, “standard deviation of test results amongoperators in a laboratory,” or “day-to-day standard deviationwithin a laboratory for the same operator.”3.1.4.2 DiscussionBecause the training of operators, theagreement of different pieces of equipment in the
12、 samelaboratory and the variation of environmental conditions withlonger time intervals all depend on the degree of within-laboratory control, the intermediate measures of precision arelikely to vary appreciably from laboratory to laboratory. Thus,intermediate precisions may be more characteristic o
13、f indi-vidual laboratories than of the test method.3.1.5 intermediate precision conditions, nconditions un-der which test results are obtained with the same test methodusing test units or test specimens taken at random from a singlequantity of material that is as nearly homogeneous as possible,and w
14、ith changing conditions such as operator, measuringequipment, location within the laboratory, and time.3.1.6 precision, nthe closeness of agreement betweenindependent test results obtained under stipulated conditions.3.1.6.1 DiscussionPrecision depends on random errorsand does not relate to the acce
15、pted reference value.3.1.6.2 DiscussionThe measure of precision usually isexpressed in terms of imprecision and computed as a standarddeviation of the test results. Less precision is reflected by alarger standard deviation.1This practice is under the jurisdiction of ASTM Committee E11 on Quality and
16、Statistics and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved Nov. 15, 2006. Published January 2007. Originallyapproved in 1961. Last previous edition approved in 2006 as E 177 06a.2For referenced ASTM standards, visit the AS
17、TM 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.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, Unit
18、ed States.3.1.6.3 Discussion“Independent test results” means re-sults obtained in a manner not influenced by any previousresult on the same or similar test object. Quantitative measuresof precision depend critically on the stipulated conditions.Repeatability and reproducibility conditions are partic
19、ular setsof extreme stipulated conditions.3.1.7 repeatability, nprecision under repeatability condi-tions.3.1.7.1 DiscussionRepeatability is one of the concepts orcategories of the precision of a test method.3.1.7.2 DiscussionMeasures of repeatability defined inthis compilation are repeatability sta
20、ndard deviation and re-peatability limit.3.1.8 repeatability conditions, nconditions where inde-pendent test results are obtained with the same method onidentical test items in the same laboratory by the same operatorusing the same equipment within short intervals of time.3.1.8.1 DiscussionSee preci
21、sion, 3.1.6.3. The “same op-erator, same equipment” requirement means that for a particu-lar step in the measurement process, the same combination ofoperator and equipment is used for every test result. Thus, oneoperator may prepare the test specimens, a second measure thedimensions and a third meas
22、ure the mass in a test method fordetermining density.3.1.8.2 DiscussionBy “in the shortest practical period oftime” is meant that the test results, at least for one material, areobtained in a time period not less than in normal testing and notso long as to permit significant change in test material,
23、equipment or environment.3.1.9 repeatability limit (r), nthe value below which theabsolute difference between two individual test results obtainedunder repeatability conditions may be expected to occur with aprobability of approximately 0.95 (95 %).3.1.9.1 DiscussionThe repeatability limit is 2.8 (
24、1.96=2 ) times the repeatability standard deviation. This multi-plier is independent of the size of the interlaboratory study.3.1.9.2 DiscussionThe approximation to 0.95 is reason-ably good (say 0.90 to 0.98) when many laboratories (30 ormore) are involved, but is likely to be poor when fewer thanei
25、ght laboratories are studied.3.1.10 repeatability standard deviation (sr), nthe standarddeviation of test results obtained under repeatability condi-tions.3.1.10.1 DiscussionIt is a measure of the dispersion of thedistribution of test results under repeatability conditions.3.1.10.2 DiscussionSimilar
26、ly, “repeatability variance”and “repeatability coefficient of variation” could be defined andused as measures of the dispersion of test results underrepeatability conditions.In an interlaboratory study, this isthe pooled standard deviation of test results obtained underrepeatability conditions.3.1.1
27、0.3 DiscussionThe repeatability standard deviation,usually considered a property of the test method, will generallybe smaller than the within-laboratory standard deviation. (Seewithin-laboratory standard deviation.)3.1.11 reproducibility, nprecision under reproducibilityconditions.3.1.12 reproducibi
28、lity conditions, nconditions where testresults are obtained with the same method on identical testitems in different laboratories with different operators usingdifferent equipment.3.1.12.1 DiscussionIdentical material means either thesame test units or test specimens are tested by all thelaboratorie
29、s as for a nondestructive test or test units or testspecimens are taken at random from a single quantity ofmaterial that is as nearly homogeneous as possible.A different laboratory of necessity means a different operator,different equipment, and different location and under different super-visory co
30、ntrol.3.1.13 reproducibility limit (R), nthe value below whichthe absolute difference between two test results obtained underreproducibility conditions may be expected to occur with aprobability of approximately 0.95 (95 %).3.1.13.1 DiscussionThe reproducibility limit is 2.8 (1.96=2 ) times the repr
31、oducibility standard deviation. Themultiplier is independent of the size of the interlaboratorystudy (that is, of the number of laboratories participating).3.1.13.2 DiscussionThe approximation to 0.95 is reason-ably good (say 0.90 to 0.98) when many laboratories (30 ormore) are involved but is likel
32、y to be poor when fewer thaneight laboratories are studied.3.1.14 reproducibility standard deviation (sR), nthe stan-dard deviation of test results obtained under reproducibilityconditions.3.1.14.1 DiscussionOther measures of the dispersion oftest results obtained under reproducibility conditions ar
33、e the“reproducibility variance” and the “reproducibility coefficientof variation.”3.1.14.2 DiscussionThe reproducibility standard devia-tion includes, in addition to between-laboratory variability, therepeatability standard deviation and a contribution from theinteraction of laboratory factors (that
34、 is, differences betweenoperators, equipment and environments) with material factors(that is, the differences between properties of the materialsother than that property of interest).3.1.15 trueness, nthe closeness of agreement between thepopulation mean of the measurements or test results and theac
35、cepted reference value.3.1.15.1 Discussion“Population mean” is, conceptually,the average value of an indefinitely large number of test results3.1.16 within-laboratory standard deviation, nthe stan-dard deviation of test results obtained within a laboratory for asingle material under conditions that
36、may include such ele-ments as different operators, equipment, and longer timeintervals.3.1.16.1 DiscussionBecause the training of operators, theagreement of different pieces of equipment in the samelaboratory and the variation of environmental conditions withlonger time intervals depend on the degre
37、e of within-laboratorycontrol, the within-laboratory standard deviation is likely tovary appreciably from laboratory to laboratory.4. Significance and Use4.1 Part A of the “Blue Book,” Form and Style for ASTMStandards, requires that all test methods include statements ofE 177 06b2precision and bias.
38、 This practice discusses these two conceptsand provides guidance for their use in statements about testmethods.4.2 PrecisionA statement of precision allows potentialusers of a test method to assess in general terms the testmethods usefulness with respect to variability in proposedapplications. A sta
39、tement of precision is not intended to exhibitvalues that can be exactly duplicated in every users laboratory.Instead, the statement provides guidelines as to the magnitudeof variability that can be expected between test results whenthe method is used in one, or in two or more, reasonablycompetent l
40、aboratories. For a discussion of precision, seeSection 15.4.3 BiasA statement of bias furnishes guidelines on therelationship between a set of typical test results produced bythe test method under specific test conditions and a related setof accepted reference values (see Section 16).4.3.1 An altern
41、ative term for bias is trueness, which has apositive connotation, in that greater bias is associated with lessfavorable trueness. Trueness is the systematic component ofaccuracy.4.4 AccuracyThe term “accuracy,” used in earlier editionsof Practice E 177, embraces both precision and bias (seeSection 1
42、7 and Note 3).4.5 ATable of Contents is shown below, listing the conceptsin this standard.TABLE OF CONTENTS Sec-tionGENERAL CONCEPTSTest Method 5Measurement Terminology 6SOURCES OF VARIABILITYExperimental Realization of a Test Method 7Operator 8Apparatus 9Environment 10Sample 11Time 12STATISTICAL CO
43、NCEPTSAccepted Reference Value 13Statistical Control 14Precision 15Bias 16Accuracy 17Variation of Precision and Bias with Material 18Variation of Precision and Bias with Sources of Variability 19COMBINATIONS OF SOURCES OF VARIABILITYRepeatability and Laboratory Bias 20Other Within-a-Single Laborator
44、y Precisions 21Reproducibility and Bias of the Test Method 22Range of Materials 23METHODS OF EXPRESSING PRECISION AND BIASIndexes of Precision 24Preferred Indexes of Precision for ASTM Test Methods 25Preferred Statements of Bias for ASTM Test Methods 26Elements of a Statement of Precision and Bias 2
45、7STATEMENTS OF PRECISION AND BIASExamples of Statements of Precision and Bias 28GENERAL CONCEPTS5. Test Method5.1 Section 2 of the ASTM Regulations describes a testmethod as “a definitive procedure for the identification, mea-surement, and evaluation of one or more qualities, character-istics, or pr
46、operties of a material, product, system or servicethat produces a test result.”5.2 In this practice only quantitative test methods thatproduce numerical results are considered. Also, the word“material” is used to mean material, product, system or service;the word “property” is used herein to mean th
47、at a quantitativetest result can be obtained that describes a characteristic or aquality, or some other aspect of the material; and “test method”refers to both the document and the procedure describedtherein for obtaining a quantitative test result for one property.For a discussion of test result, s
48、ee Section .5.3 A well-written test method specifies control over suchfactors as the test equipment, the test environment, the quali-fications of the operator (explicitly or implicitly), the prepara-tion of test specimens, and the operating procedure for usingthe equipment in the test environment to
49、 measure someproperty of the test specimens. The test method will alsospecify the number of test specimens required and howmeasurements on them are to be combined to provide a testresult (Section ), and might also reference a sampling proce-dure appropriate for the intended use of the method.5.4 It is necessary that the writers of the test method provideinstructions or requirements for every known outside influence.6. Measurement Terminology6.1 A test result is the value obtained by carrying out thecomplete protocol of the test method o
