1、Designation: E 177 08An 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 revisi
2、on, 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 Department of Defense.1. Scope1.1 The purpose of this p
3、ractice 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 for
4、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 to
5、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 Test
6、 Method3. Terminology3.1 Definitions: Terminology E 456 provides a more exten-sive list of terms in E11 standards.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 scientificprincip
7、les, (2) an assigned or certified value, based on experi-mental work of some 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 orga
8、niza-tion, referred to in (2), generally maintains measurementstandards to 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, inv
9、olves a combination of a randomcomponent and of a common systematic error or 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 m
10、oresystematic error components contributing to the bias. A largersystematic difference from the accepted reference value isreflected by a larger bias value.3.1.4 characteristic, na property of items in a sample orpopulation which, when measured, counted or otherwise ob-served, helps to distinguish b
11、etween the items. E 22823.1.5 intermediate precision, nthe closeness of agreementbetween test results obtained under specified intermediateprecision conditions.3.1.5.1 DiscussionThe specific measure and the specificconditions must be specified for each intermediate measure ofprecision; thus, “standa
12、rd deviation of test results amongoperators in a laboratory,” or “day-to-day standard deviationwithin a laboratory for the same operator.”3.1.5.2 DiscussionBecause the training of operators, theagreement of different pieces of equipment in the samelaboratory and the variation of environmental condit
13、ions 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 of indi-vidual laboratories than of the test method.3.1.6
14、intermediate precision conditions, n conditions 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 with changing conditions such as operator, measuringequip
15、ment, location within the laboratory, and time.1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved Oct. 1, 2008. Published October 2008. O
16、riginallyapproved in 1961. Last previous edition approved in 2006 as E 177 06b.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 o
17、nthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.7 observation, nthe process of obtaining informationregarding the presence or absence of an attribute of a testspecimen, or of making a reading on a characteristic
18、 ordimension of a test specimen. E 22823.1.8 observed value, nthe value obtained by making anobservation. E 22823.1.9 precision, nthe closeness of agreement betweenindependent test results obtained under stipulated conditions.3.1.9.1 DiscussionPrecision depends on random errorsand does not relate to
19、 the accepted reference value.3.1.9.2 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.3.1.9.3 Discussion“Independent test results” means re-sults obtained
20、 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 particular setsof extreme stipulated conditions.3.1.10 repeatability, nprecision und
21、er repeatability con-ditions.3.1.10.1 DiscussionRepeatability is one of the conceptsor categories of the precision of a test method.3.1.10.2 DiscussionMeasures of repeatability defined inthis compilation are repeatability standard deviation and re-peatability limit.3.1.11 repeatability conditions, n
22、conditions 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.3.1.11.1 DiscussionSee precision, The “same operator,same equipment” requirement means that for a par
23、ticular stepin the measurement process, the same combination of operatorand equipment is used for every test result. Thus, one operatormay prepare the test specimens, a second measure the dimen-sions and a third measure the mass in a test method fordetermining density.3.1.11.2 DiscussionBy “in the s
24、hortest 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,equipment or environment.3.1.12 repeatability limit (r), nthe value below which the
25、absolute difference between two individual test results obtainedunder repeatability conditions may be expected to occur with aprobability of approximately 0.95 (95 %).3.1.12.1 DiscussionThe repeatability limit is 2.8 ( 1.96=2 ) times the repeatability standard deviation. This multi-plier is independ
26、ent of the size of the interlaboratory study.3.1.12.2 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 thaneight laboratories are studied.3.1.13 repeatability standard deviation (sr), nthe
27、standarddeviation of test results obtained under repeatability condi-tions.3.1.13.1 DiscussionIt is a measure of the dispersion of thedistribution of test results under repeatability conditions.3.1.13.2 DiscussionSimilarly, “repeatability variance”and “repeatability coefficient of variation” could b
28、e 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.3.1.13.3 DiscussionThe repeatability standard deviation,usually considered a property
29、 of the test method, will generallybe smaller than the within-laboratory standard deviation. (Seewithin-laboratory standard deviation.)3.1.14 reproducibility, nprecision under reproducibilityconditions.3.1.15 reproducibility conditions, nconditions where testresults are obtained with the same method
30、 on identical testitems in different laboratories with different operators usingdifferent equipment.3.1.15.1 DiscussionIdentical material means either thesame test units or test specimens are tested by all thelaboratories as for a nondestructive test or test units or testspecimens are taken at rando
31、m 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 control.3.1.16 reproducibility limit (R), nthe value below whichthe absolute diffe
32、rence between two test results obtained underreproducibility conditions may be expected to occur with aprobability of approximately 0.95 (95 %).3.1.16.1 DiscussionThe reproducibility limit is 2.8 (1.96=2 ) times the reproducibility standard deviation. Themultiplier is independent of the size of the
33、interlaboratorystudy (that is, of the number of laboratories participating).3.1.16.2 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 thaneight laboratories are studied.3.1.17 reproducibilit
34、y standard deviation (sR), nthe stan-dard deviation of test results obtained under reproducibilityconditions.3.1.17.1 DiscussionOther measures of the dispersion oftest results obtained under reproducibility conditions are the“reproducibility variance” and the “reproducibility coefficientof variation
35、.”3.1.17.2 DiscussionThe reproducibility standard devia-tion includes, in addition to between-laboratory variability, therepeatability standard deviation and a contribution from theinteraction of laboratory factors (that is, differences betweenoperators, equipment and environments) with material fac
36、tors(that is, the differences between properties of the materialsother than that property of interest).3.1.18 test determination, nthe value of a characteristic ordimension of a single test specimen derived from one or moreobserved values. E 22823.1.19 test method, na definitive procedure that produ
37、cesa test result. E 22823.1.20 test observation, nsee observation. E 2282E1770823.1.21 test result, nthe value of a characteristic obtainedby carrying out a specified test method. E 22823.1.22 test specimen, nthe portion of a test unit needed toobtain a single test determination. E 22823.1.23 test u
38、nit, nthe total quantity of material (containingone or more test specimens) needed to obtain a test result asspecified in the test method. See test result. E 22823.1.24 trueness, nthe closeness of agreement between thepopulation mean of the measurements or test results and theaccepted reference valu
39、e.3.1.24.1 Discussion“Population mean” is, conceptually,the average value of an indefinitely large number of test results3.1.25 within-laboratory standard deviation, nthe stan-dard deviation of test results obtained within a laboratory for asingle material under conditions that may include such ele-
40、ments as different operators, equipment, and longer timeintervals.3.1.25.1 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 degree of within-laborator
41、ycontrol, 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 ofprecision and bias. This practice discusses these
42、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 statement of precision is not inte
43、nded 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 laboratories. For a discussion o
44、f 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 alternative term for bias is trueness
45、, 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 17 and Note 3).4.5 ATable of Con
46、tents 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 CONCEPTSAccepted Reference Value
47、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 Laboratory Precisions 21Reproducibility
48、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 27STATEMENTS OF PRECISION AND BI
49、ASExamples 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 properties 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
