1、Designation: E177 13E177 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
2、revision, 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 purpos
3、e of this practice is to present concepts necessary to the understanding of the terms “precision” and “bias” as usedin quantitative test methods. This practice also describes methods of expressing precision and bias and, in a final section, givesexamples of how statements on precision and bias may b
4、e written for ASTM test methods.1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatoryrequiremen
5、ts prior to use.2. Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test MethodE1488 Guide for Statistical Procedures to Use in Developing and Applying Test MethodsE2282 Gu
6、ide for Defining the Test Result of a Test MethodE2586 Practice for Calculating and Using Basic StatisticsE2587 Practice for Use of Control Charts in Statistical Process Control3. Terminology3.1 DefinitionsTerminology E456 provides a more extensive list of terms in E11 standards.3.1.1 accepted refer
7、ence value, na value that serves as an agreed-upon reference for comparison, and which is derived as: (1)a theoretical or established value, based on scientific principles, (2) an assigned or certified value, based on experimental work ofsome national or international organization, or (3) a consensu
8、s or certified value, based on collaborative experimental work underthe auspices of a scientific or engineering group.3.1.1.1 DiscussionAnational or international organization, referred to in 3.1.1 (2), generally maintains measurement standards to which the referencevalues obtained are traceable.3.1
9、.2 accuracy, nthe closeness of agreement between a test result and an accepted reference value.3.1.2.1 DiscussionThe term accuracy, when applied to a set of test results, involves a combination of a random component and of a commonsystematic error or bias component.3.1.3 bias, nthe difference betwee
10、n the expectation of the test results and an accepted reference value.1 This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved May 1, 2013May
11、 1, 2014. Published May 2013May 2014. Originally approved in 1961. Last previous edition approved in 20102013 asE177 10.E177 13. DOI: 10.1520/E0177-13.10.1520/E0177-14.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual
12、Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be tec
13、hnically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO
14、 Box C700, West Conshohocken, PA 19428-2959. United States13.1.3.1 DiscussionBias is the total systematic error as contrasted to random error.There may be one or more systematic error components contributingto the bias. A larger systematic difference from the accepted reference value is reflected by
15、 a larger bias value.3.1.4 characteristic, na property of items in a sample or population which, when measured, counted or otherwise observed,helps to distinguish between the items. E22823.1.5 coeffcient of variation, CV, nfor a nonnegative characteristic, the ratio of the standard deviation to the
16、mean for apopulation or sample. E25863.1.6 intermediate precision, nthe closeness of agreement between test results obtained under specified intermediate precisionconditions.3.1.6.1 DiscussionThe specific measure and the specific conditions must be specified for each intermediate measure of precisio
17、n; thus, “standarddeviation of test results among operators in a laboratory,” or “day-to-day standard deviation within a laboratory for the sameoperator.”3.1.6.2 DiscussionBecause the training of operators, the agreement of different pieces of equipment in the same laboratory and the variation ofenv
18、ironmental conditions with longer time intervals all depend on the degree of within-laboratory control, the intermediatemeasures of precision are likely to vary appreciably from laboratory to laboratory. Thus, intermediate precisions may be morecharacteristic of individual laboratories than of the t
19、est method.3.1.7 intermediate precision conditions, nconditions under which test results are obtained with the same test method using testunits or test specimens taken at random from a single quantity of material that is as nearly homogeneous as possible, and withchanging conditions such as operator
20、, measuring equipment, location within the laboratory, and time.3.1.8 observation, nthe process of obtaining information regarding the presence or absence of an attribute of a test specimen,or of making a reading on a characteristic or dimension of a test specimen. E22823.1.9 observed value, nthe va
21、lue obtained by making an observation. E22823.1.10 precision, nthe closeness of agreement between independent test results obtained under stipulated conditions.3.1.10.1 DiscussionPrecision depends on random errors and does not relate to the accepted reference value.3.1.10.2 DiscussionThe measure of
22、precision usually is expressed in terms of imprecision and computed as a standard deviation of the test results. Lessprecision is reflected by a larger standard deviation.3.1.10.3 Discussion“Independent test results” means results obtained in a manner not influenced by any previous result on the sam
23、e or similar testobject. Quantitative measures of precision depend critically on the stipulated conditions. Repeatability and reproducibilityconditions are particular sets of extreme stipulated conditions.3.1.11 repeatability, nprecision under repeatability conditions.3.1.11.1 DiscussionRepeatabilit
24、y is one of the concepts or categories of the precision of a test method.3.1.11.2 DiscussionMeasures of repeatability defined in this compilation are repeatability standard deviation and repeatability limit.E177 1423.1.12 repeatability conditions, nconditions where independent test results are obtai
25、ned with the same method on identical testitems in the same laboratory by the same operator using the same equipment within short intervals of time.3.1.12.1 DiscussionSee precision, The “same operator, same equipment” requirement means that for a particular step in the measurement process, thesame c
26、ombination of operator and equipment is used for every test result. Thus, one operator may prepare the test specimens, asecond measure the dimensions and a third measure the mass in a test method for determining density.3.1.12.2 DiscussionBy “in the shortest practical period of time” is meant that t
27、he test results, at least for one material, are obtained in a time periodnot less than in normal testing and not so long as to permit significant change in test material, equipment or environment.3.1.13 repeatability limit (r), nthe value below which the absolute difference between two individual te
28、st results obtainedunder repeatability conditions may be expected to occur with a probability of approximately 0.95 (95 %).3.1.13.1 DiscussionThe repeatability limit is2.81.96=2! times the repeatability standard deviation. This multiplier is independent of the size of the interlaboratory study.3.1.1
29、3.2 DiscussionThe approximation to 0.95 is reasonably good (say 0.90 to 0.98) when many laboratories (30 or more) are involved, but is likelyto be poor when fewer than eight laboratories are studied.3.1.14 repeatability standard deviation (sr), nthe standard deviation of test results obtained under
30、repeatability conditions.3.1.14.1 DiscussionIt is a measure of the dispersion of the distribution of test results under repeatability conditions.3.1.14.2 DiscussionSimilarly, “repeatability variance” and “repeatability coefficient of variation” could be defined and used as measures of thedispersion
31、of test results under repeatability conditions.In an interlaboratory study, this is the pooled standard deviation of testresults obtained under repeatability conditions.3.1.14.3 DiscussionThe repeatability standard deviation, usually considered a property of the test method, will generally be smalle
32、r than thewithin-laboratory standard deviation. (See within-laboratory standard deviation.)3.1.15 reproducibility, nprecision under reproducibility conditions.3.1.16 reproducibility conditions, nconditions where test results are obtained with the same method on identical test items indifferent labor
33、atories with different operators using different equipment.3.1.16.1 DiscussionIdentical material means either the same test units or test specimens are tested by all the laboratories as for a nondestructive testor test units or test specimens are taken at random from a single quantity of material th
34、at is as nearly homogeneous as possible.A different laboratory of necessity means a different operator, different equipment, and different location and under differentsupervisory control.3.1.17 reproducibility limit (R), nthe value below which the absolute difference between two test results obtaine
35、d underreproducibility conditions may be expected to occur with a probability of approximately 0.95 (95 %).E177 1433.1.17.1 DiscussionThe reproducibility limit is2.81.96=2! times the reproducibility standard deviation. The multiplier is independent of the size of the interlaboratory study(that is, o
36、f the number of laboratories participating).3.1.17.2 DiscussionThe approximation to 0.95 is reasonably good (say 0.90 to 0.98) when many laboratories (30 or more) are involved but is likelyto be poor when fewer than eight laboratories are studied.3.1.18 reproducibility standard deviation (sR), nthe
37、standard deviation of test results obtained under reproducibilityconditions.3.1.18.1 DiscussionOther measures of the dispersion of test results obtained under reproducibility conditions are the “reproducibility variance” andthe “reproducibility coefficient of variation.”3.1.18.2 DiscussionThe reprod
38、ucibility standard deviation includes, in addition to between-laboratory variability, the repeatability standard deviationand a contribution from the interaction of laboratory factors (that is, differences between operators, equipment and environments)with material factors (that is, the differences
39、between properties of the materials other than that property of interest).3.1.19 standard deviation, nof a population, , the square root of the average or expected value of the squared deviation ofa variable from its mean; of a sample,s, the square root of the sum of the squared deviations of the ob
40、served values in the sampledivided by the sample size minus 1. E25863.1.20 test determination, nthe value of a characteristic or dimension of a single test specimen derived from one or moreobserved values. E22823.1.21 test method, na definitive procedure that produces a test result. E22823.1.22 test
41、 result, nthe value of a characteristic obtained by carrying out a specified test method. E22823.1.23 test specimen, nthe portion of a test unit needed to obtain a single test determination. E22823.1.24 test sample,unit, nthe total quantity of material (containing one or more test specimens) needed
42、to obtain a test resultas specified in the test method. See test result. E22823.1.24 test specimen, nthe portion of a test sample needed to obtain a single test determination. E22823.1.25 trueness, nthe closeness of agreement between the population mean of the measurements or test results and theacc
43、epted reference value.3.1.25.1 Discussion“Population mean” is, conceptually, the average value of an indefinitely large number of test results3.1.26 variance, 2, s2, n square of the standard deviation of the population or sample. E25863.1.27 within-laboratory standard deviation, nthe standard deviat
44、ion of test results obtained within a laboratory for a singlematerial under conditions that may include such elements as different operators, equipment, and longer time intervals.3.1.27.1 DiscussionBecause the training of operators, the agreement of different pieces of equipment in the same laborato
45、ry and the variation ofenvironmental conditions with longer time intervals depend on the degree of within-laboratory control, the within-laboratorystandard deviation is likely to vary appreciably from laboratory to laboratory.4. Significance and Use4.1 Part A of the “Blue Book,” Form and Style for A
46、STM Standards, requires that all test methods include statements ofprecision and bias. This practice discusses these two concepts and provides guidance for their use in statements about test methods.E177 1444.2 PrecisionA statement of precision allows potential users of a test method to assess in ge
47、neral terms the test methodsusefulness with respect to variability in proposed applications. A statement of precision is not intended to exhibit values that canbe exactly duplicated in every users laboratory. Instead, the statement provides guidelines as to the magnitude of variability thatcan be ex
48、pected between test results when the method is used in one, or in two or more, reasonably competent laboratories. Fora discussion of precision, see 8.1.4.3 BiasA statement of bias furnishes guidelines on the relationship between a set of typical test results produced by the testmethod under specific
49、 test conditions and a related set of accepted reference values (see 9.1).4.3.1 An alternative term for bias is trueness, which has a positive connotation, in that greater bias is associated with lessfavorable trueness. Trueness is the systematic component of accuracy.4.4 AccuracyThe term “accuracy,” used in earlier editions of Practice E177, embraces both precision and bias (see 9.3).5. Test Method5.1 Section 2 of the ASTM Regulations describes a test method as “a definitive procedure for the identification,
