1、Designation: E177 14 An American National StandardStandard Practice forUse of the Terms Precision and Bias in ASTM Test Methods1This standard is issued under the fixed designation E177; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revisio
2、n, 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 U.S. Department of Defense.1. Scope1.1 The purpose of th
3、is 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
4、for 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
5、 to use.2. Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE1488 Guide for Statistical Procedures to Use in Developingand Applying Test MethodsE2282 Guide for De
6、fining the Test Result of a Test MethodE2586 Practice for Calculating and Using Basic StatisticsE2587 Practice for Use of Control Charts in StatisticalProcess Control3. Terminology3.1 DefinitionsTerminology E456 provides a more exten-sive list of terms in E11 standards.3.1.1 accepted reference value
7、, 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 some national or international organization, or(3) a consensus or certif
8、ied value, based on collaborativeexperimental work under the auspices of a scientific orengineering group.3.1.1.1 DiscussionA national or internationalorganization, referred to in 3.1.1 (2), generally maintainsmeasurement standards to which the reference values obtainedare traceable.3.1.2 accuracy,
9、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 or bias compo-nent.3.1.3 bias, nthe difference between the expectat
10、ion 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 difference from the accepted reference value isreflected by a lar
11、ger bias value.3.1.4 characteristic, na property of items in a sample orpopulation which, when measured, counted or otherwiseobserved, helps to distinguish between the items. E22823.1.5 coeffcient of variation, CV, nfor a nonnegativecharacteristic, the ratio of the standard deviation to the meanfor
12、a population or sample. E25863.1.6 intermediate precision, nthe closeness of agreementbetween test results obtained under specified intermediateprecision conditions.3.1.6.1 DiscussionThe specific measure and the specificconditions must be specified for each intermediate measure ofprecision; thus, “s
13、tandard deviation of test results amongoperators in a laboratory,” or “day-to-day standard deviationwithin a laboratory for the same operator.”3.1.6.2 DiscussionBecause the training of operators, theagreement of different pieces of equipment in the samelaboratory and the variation of environmental c
14、onditions 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.1
15、This 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 May 1, 2014. Published May 2014. Originallyapproved in 1961. Last previous edition appr
16、oved in 2013 as E177 13. DOI:10.1520/E0177-14.2For 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 onthe ASTM website.Copyright ASTM
17、International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.7 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
18、 that is as nearly homogeneous as possible,and with changing conditions such as operator, measuringequipment, location within the laboratory, and time.3.1.8 observation, nthe process of obtaining informationregarding the presence or absence of an attribute of a testspecimen, or of making a reading o
19、n a characteristic ordimension of a test specimen. E22823.1.9 observed value, nthe value obtained by making anobservation. E22823.1.10 precision, nthe closeness of agreement betweenindependent test results obtained under stipulated conditions.3.1.10.1 DiscussionPrecision depends on random errorsand
20、does not relate to the accepted reference value.3.1.10.2 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.3.1.10.3 Discussion“Independent test results” mea
21、ns 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 particular setsof extreme stipulated conditions.3.1.11 repeatabi
22、lity, nprecision under repeatability condi-tions.3.1.11.1 DiscussionRepeatability is one of the concepts orcategories of the precision of a test method.3.1.11.2 DiscussionMeasures of repeatability defined inthis compilation are repeatability standard deviation and re-peatability limit.3.1.12 repeata
23、bility 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.3.1.12.1 DiscussionSee precision, The “same operator,same equipment” requirement
24、means that for a particular 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.3.1.12.2 Di
25、scussionBy “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,equipment or environment.3.1.13 repeatability limit (r), nthe v
26、alue below which theabsolute difference between two individual test results obtainedunder repeatability conditions may be expected to occur with aprobability of approximately 0.95 (95 %).3.1.13.1 DiscussionThe repeatability limit is2.8 1.96 =2! times the repeatability standard deviation. Thismultipl
27、ier is independent of the size of the interlaboratorystudy.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 likely to be poor when fewer thaneight laboratories are studied.3.1.14 repeatability standard deviati
28、on (sr), nthe standarddeviation of test results obtained under repeatability condi-tions.3.1.14.1 DiscussionIt is a measure of the dispersion of thedistribution of test results under repeatability conditions.3.1.14.2 DiscussionSimilarly, “repeatability variance”and “repeatability coefficient of vari
29、ation” 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.3.1.14.3 DiscussionThe repeatability standard deviation,usually conside
30、red a property of the test method, will generallybe smaller than the within-laboratory standard deviation. (Seewithin-laboratory standard deviation.)3.1.15 reproducibility, nprecision under reproducibilityconditions.3.1.16 reproducibility conditions, nconditions where testresults are obtained with t
31、he same method on identical testitems in different laboratories with different operators usingdifferent equipment.3.1.16.1 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
32、taken at random from a single quantity ofmaterial that is as nearly homogeneous as possible.A different laboratory of necessity means a differentoperator, different equipment, and different location andunder different supervisory control.3.1.17 reproducibility limit (R), nthe value below whichthe ab
33、solute difference between two test results obtained underreproducibility conditions may be expected to occur with aprobability of approximately 0.95 (95 %).3.1.17.1 DiscussionThe reproducibility limit is2.8 1.96 =2! times the reproducibility standard deviation.The multiplier is independent of the si
34、ze of the interlaboratorystudy (that is, of the number of laboratories participating).3.1.17.2 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.3.1.18 repr
35、oducibility standard deviation (sR), nthe stan-dard deviation of test results obtained under reproducibilityconditions.3.1.18.1 DiscussionOther measures of the dispersion oftest results obtained under reproducibility conditions are the“reproducibility variance” and the “reproducibility coefficientof
36、 variation.”3.1.18.2 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 betweenE177 142operators, equipment and environments)
37、 with material factors(that is, the differences between properties of the materialsother than that property of interest).3.1.19 standard deviation, nof a population, , the squareroot of the average or expected value of the squared deviationof a variable from its mean; of a sample, s, the square root
38、of the sum of the squared deviations of the observed values inthe sample divided by the sample size minus 1. E25863.1.20 test determination, nthe value of a characteristic ordimension of a single test specimen derived from one or moreobserved values. E22823.1.21 test method, na definitive procedure
39、that producesa test result. E22823.1.22 test result, nthe value of a characteristic obtainedby carrying out a specified test method. E22823.1.23 test specimen, nthe portion of a test unit needed toobtain a single test determination. E22823.1.24 test unit, nthe total quantity of material (containingo
40、ne or more test specimens) needed to obtain a test result asspecified in the test method. See test result. E22823.1.25 trueness, nthe closeness of agreement between thepopulation mean of the measurements or test results and theaccepted reference value.3.1.25.1 Discussion“Population mean” is, concept
41、ually,the average value of an indefinitely large number of test results3.1.26 variance, 2,s2,nsquare of the standard deviationof the population or sample. E25863.1.27 within-laboratory standard deviation, nthe stan-dard deviation of test results obtained within a laboratory for asingle material unde
42、r conditions that may include such ele-ments as different operators, equipment, and longer timeintervals.3.1.27.1 DiscussionBecause the training of operators, theagreement of different pieces of equipment in the samelaboratory and the variation of environmental conditions withlonger time intervals d
43、epend on the degree 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 ofprecision a
44、nd bias. 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 proposedapplication
45、s. A statement 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, reasonablycom
46、petent laboratories. For a discussion of precision, see 8.1.4.3 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 9.1).4.3.1 An alternative
47、 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 E177, embraces both precision and bias (see 9.3).5. Test M
48、ethod5.1 Section 2 of the ASTM Regulations describes a testmethod as “a definitive procedure for the identification,measurement, and evaluation of one or more qualities,characteristics, or properties of a material, product, system orservice that produces a test result.”5.2 In this practice only quan
49、titative 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 that 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, see 7.1.5.3 A well-written test m
