1、Designation: E177 10E177 13 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 Department of Defense.1. Scope1.1 The purpose of
3、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 be wri
4、tten 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 regulatoryrequirements pr
5、ior to use.2. Referenced Documents2.1 ASTM Standards:2E178 Practice for Dealing With Outlying ObservationsE456 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
6、in Developing and Applying Test MethodsE2282 Guide 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 Definitions:Definitions3.1.1 Terminology E456 provides a m
7、ore extensive list of terms in E11 standards.Terminology E456 provides a moreextensive list of terms in E11 standards.3.1.1 accepted reference 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 p
8、rinciples, (2) an assigned or certified value, based on experimental work ofsome national or international organization, or (3) a consensus or certified value, based on collaborative experimental work underthe auspices of a scientific or engineering group.3.1.1.1 DiscussionA national or internationa
9、l organization, referred to in 3.1.23.1.1 (2), generally maintains measurement standards to which thereference values obtained are traceable.3.1.2 accuracy, nthe closeness of agreement between a test result and an accepted reference value.3.1.2.1 Discussion1 This practice is under the jurisdiction o
10、f 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 Oct. 1, 2010May 1, 2013. Published November 2010May 2013. Originally approved in 1961. Last previous edition approved in 200820
11、10 asE177 08.E177 10. DOI: 10.1520/E0177-10.10.1520/E0177-13.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.
12、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 technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior edi
13、tions 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 Box C700, West Conshohocken, PA 19428-2959. United States1The term accuracy, when applied to a set of test
14、 results, involves a combination of a random component and of a commonsystematic error or bias component.3.1.3 bias, nthe difference between the expectation of the test results and an accepted reference value.3.1.3.1 DiscussionBias is the total systematic error as contrasted to random error.There ma
15、y be one or more systematic error components contributingto the bias. A larger systematic difference from the accepted reference value is reflected by 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
16、 distinguish between the items. E22823.1.5 coeffcient of variation, CV, nfor a nonnegative characteristic, the ratio of the standard deviation to the mean for apopulation or sample. E25863.1.6 intermediate precision, nthe closeness of agreement between test results obtained under specified intermedi
17、ate precisionconditions.3.1.6.1 DiscussionThe specific measure and the specific conditions must be specified for each intermediate measure of precision; thus, “standarddeviation of test results among operators in a laboratory,” or “day-to-day standard deviation within a laboratory for the sameoperat
18、or.”3.1.6.2 DiscussionBecause the training of operators, the agreement of different pieces of equipment in the same laboratory and the variation ofenvironmental conditions with longer time intervals all depend on the degree of within-laboratory control, the intermediatemeasures of precision are like
19、ly to vary appreciably from laboratory to laboratory. Thus, intermediate precisions may be morecharacteristic of individual laboratories than of the test method.3.1.7 intermediate precision conditions, nconditions under which test results are obtained with the same test method using testunits or tes
20、t specimens taken at random from a single quantity of material that is as nearly homogeneous as possible, and withchanging conditions such as operator, measuring equipment, location within the laboratory, and time.3.1.8 observation, nthe process of obtaining information regarding the presence or abs
21、ence 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 value obtained by making an observation. E22823.1.10 precision, nthe closeness of agreement between independent test results obtained under stipulated c
22、onditions.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 precision usually is expressed in terms of imprecision and computed as a standard deviation of the test results. Lessprecision is reflected by a large
23、r standard deviation.3.1.10.3 Discussion“Independent test results” means results obtained in a manner not influenced by any previous result on the same or similar testobject. Quantitative measures of precision depend critically on the stipulated conditions. Repeatability and reproducibilitycondition
24、s are particular sets of extreme stipulated conditions.3.1.11 repeatability, nprecision under repeatability conditions.3.1.11.1 DiscussionRepeatability is one of the concepts or categories of the precision of a test method.E177 1323.1.11.2 DiscussionMeasures of repeatability defined in this compilat
25、ion are repeatability standard deviation and repeatability limit.3.1.12 repeatability conditions, nconditions where independent test results are obtained 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.
26、1.12.1 DiscussionSee precision, The “same operator, same equipment” requirement means that for a particular step in the measurement process, thesame combination of operator and equipment is used for every test result. Thus, one operator may prepare the test specimens, asecond measure the dimensions
27、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 the 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 chan
28、ge in test material, equipment or environment.3.1.13 repeatability limit (r), nthe value below which the absolute difference between two individual test results obtainedunder repeatability conditions may be expected to occur with a probability of approximately 0.95 (95 %).3.1.13.1 DiscussionThe repe
29、atability limit is2.81.96=2! times the repeatability standard deviation. This multiplier is independent of the size of the interlaboratory study.3.1.13.2 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 poo
30、r when fewer than eight laboratories are studied.3.1.14 repeatability standard deviation (sr), nthe standard deviation of test results obtained under repeatability conditions.3.1.14.1 DiscussionIt is a measure of the dispersion of the distribution of test results under repeatability conditions.3.1.1
31、4.2 DiscussionSimilarly, “repeatability variance” and “repeatability coefficient of variation” could be defined and used as measures of thedispersion of test results under repeatability conditions.In an interlaboratory study, this is the pooled standard deviation of testresults obtained under repeat
32、ability conditions.3.1.14.3 DiscussionThe repeatability standard deviation, usually considered a property of the test method, will generally be smaller than thewithin-laboratory standard deviation. (See within-laboratory standard deviation.)3.1.15 reproducibility, nprecision under reproducibility co
33、nditions.3.1.16 reproducibility conditions, nconditions where test results are obtained with the same method on identical test items indifferent laboratories with different operators using different equipment.3.1.16.1 DiscussionIdentical material means either the same test units or test specimens ar
34、e 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 that is as nearly homogeneous as possible.A different laboratory of necessity means a different operator, different equipment, and different location an
35、d under differentsupervisory control.E177 1333.1.17 reproducibility limit (R), nthe value below which the absolute difference between two test results obtained underreproducibility conditions may be expected to occur with a probability of approximately 0.95 (95 %).3.1.17.1 DiscussionThe reproducibil
36、ity limit is2.81.96=2! times the reproducibility standard deviation. The multiplier is independent of the size of the interlaboratory study(that is, of 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
37、(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 standard deviation of test results obtained under reproducibilityconditions.3.1.18.1 DiscussionOther measures of the dispersion of test results obtain
38、ed under reproducibility conditions are the “reproducibility variance” andthe “reproducibility coefficient of variation.”3.1.18.2 DiscussionThe reproducibility standard deviation includes, in addition to between-laboratory variability, the repeatability standard deviationand a contribution from the
39、interaction of laboratory factors (that is, differences between operators, equipment and environments)with material factors (that is, the differences between properties of the materials other than that property of interest).3.1.19 standard deviation, nof a population, , the square root of the averag
40、e 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 observed 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
41、 test specimen derived from one or moreobserved values. E22823.1.21 test method, na definitive procedure that produces a test result. E22823.1.21 test observation, nsee observation. E22823.1.22 test result, nthe value of a characteristic obtained by carrying out a specified test method. E22823.1.23
42、test specimen, nthe portion of a test unit needed to obtain a single test determination. E22823.1.23 test unit,sample, nthe total quantity of material (containing one or more test specimens) needed to obtain a test resultas specified in the test method. See test result. E22823.1.24 test specimen, nt
43、he 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 theaccepted reference value.3.1.25.1 Discussion“Population mean” is, conceptually, the average value of an i
44、ndefinitely 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 deviation of test results obtained within a laboratory for a singlematerial under conditions that may includ
45、e 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 laboratory and the variation ofenvironmental conditions with longer time intervals depend on the degree of wit
46、hin-laboratory control, the within-laboratorystandard deviation is likely to vary appreciably from laboratory to laboratory.E177 1344. Significance and Use4.1 Part A of the “Blue Book,” Form and Style for ASTM Standards, requires that all test methods include statements ofprecision and bias. This pr
47、actice discusses these two concepts and provides guidance for their use in statements about test methods.4.2 PrecisionA statement of precision allows potential users of a test method to assess in general terms the test methodsusefulness with respect to variability in proposed applications. A stateme
48、nt 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 expected between test results when the method is used in one, or in two or more, reasonably competent la
49、boratories. 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 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 earli
