# ASTM E691-16

Designation: E691 − 16 An American National StandardStandard Practice forConducting an Interlaboratory Study to Determine thePrecision of a Test Method1This standard is issued under the fixed designation E691; the number immediately following the designation indicates the year oforiginal adoption or, in the case of 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 This practice describes the techniques for planning,conducting, analyzing, and treating the results of an interlabo-ratory study (ILS) of a test method. The statistical techniquesdescribed in this practice provide adequate information forformulating the precision statement of a test method.1.2 This practice does not concern itself with the develop-ment of test methods but rather with gathering the informationneeded for a test method precision statement after the devel-opment stage has been successfully completed. The dataobtained in the interlaboratory study may indicate, however,that further effort is needed to improve the test method.1.3 Since the primary purpose of this practice is the devel-opment of the information needed for a precision statement, theexperimental design in this practice may not be optimum forevaluating materials, apparatus, or individual laboratories.1.4 Field of Application—This practice is concerned exclu-sively with test methods which yield a single numerical figureas the test result, although the single figure may be the outcomeof a calculation from a set of measurements.1.4.1 This practice does not cover methods in which themeasurement is a categorization; however, for many practicalpurposes categorical outcomes can be scored, such as zero-onescoring for binary measurements or as integers, ranks forexample, for well-ordered categories and then the test resultcan be defined as an average, or other summary statistic, ofseveral individual scores.1.5 This standard may involve hazardous materials,operations, and equipment. This standard does not purport toaddress all of the safety problems associated with its use. It isthe responsibility of the user of this standard to establishappropriate safety and health practices and determine theapplicability of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E29 Practice for Using Significant Digits in Test Data toDetermine Conformance with SpecificationsE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE1169 Practice for Conducting Ruggedness TestsE1402 Guide for Sampling DesignE2282 Guide for Defining the Test Result of a Test Method3. Terminology3.1 Definitions—Terminology E456 provides a more exten-sive list of terms in E11 standards.3.1.1 accuracy, n—the closeness of agreement between atest result and an accepted reference value. E1773.1.2 bias, n—the difference between the expectation of thetest results and an accepted reference value. E1773.1.3 interlaboratory study, (ILS) in ASTM, n—a designedprocedure for obtaining a precision statement for a test method,involving multiple laboratories, each generating replicate testresults on one or more materials.3.1.4 observation, n—the process of obtaining informationregarding the presence or absence of an attribute of a testspecimen, or of making a reading on a characteristic ordimension of a test specimen. E22823.1.5 precision, n—the closeness of agreements betweenindependent test results obtained under stipulated conditions.E1773.1.6 repeatability, n—precision under repeatabilityconditions. E1773.1.7 repeatability conditions, n—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. E1771This practice is under the jurisdiction ofASTM 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, 2016. Published October 2016. Originallyapproved in 1979. Last previous edition approved in 2015 as E691 – 15. DOI:10.1520/E0691-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.8 repeatability limit (r), n—the 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 %). E1773.1.9 repeatability standard deviation, (sr), n—the standarddeviation of test result obtained under repeatability conditions.E1773.1.10 reproducibility, n—precision under reproducibilityconditions. E1773.1.11 reproducibility conditions, n—conditions where testresults are obtained with the same method on identical testitems in different laboratories with different operators usingdifferent equipment. E1773.1.12 reproducibility limit (R), n—the value below whichthe absolute difference between two test results obtained underreproducibility conditions may be expected to occur with aprobability of approximately 0.95 (95 %). E1773.1.13 reproducibility standard deviation (sR), n—the stan-dard deviation of test results obtained under reproducibilityconditions. E1773.1.14 ruggedness test, n—a planned experiment in whichenvironmental factors or test conditions are deliberately variedin order to evaluate the effects of such variation. E11693.1.15 test determination, n—the value of a characteristic ordimension of a single test specimen derived from one or moreobserved values. E22823.1.16 test method, n—a definitive procedure that producesa test result. E22823.1.17 test observation, n—see observation. E22823.1.18 test result, n—the value of a characteristic obtainedby carrying out a specified test method. E22823.1.19 test specimen, n—the portion of a test unit needed toobtain a single test determination. E22823.1.20 test unit, n—the total quantity of material (containingone or more test specimens) needed to obtain a test result asspecified in the test method; see test result. E22823.2 Definitions of Terms Specific to This Standard:3.2.1 average of the cell averages, x=,n—the average of thecell averages for a particular material.3.2.2 between-laboratory consistency statistic, h, n—theratio of the cell deviation to the standard deviation of the cellaverages.3.2.2.1 Discussion—This statistic is an indicator of how onelaboratory’s cell average compares with the average of theother laboratories for a particular material (see X1.2.2).3.2.3 between-laboratory standard deviation, sL,n—thesample standard deviation attributable to differences of testresult means among laboratories.3.2.4 between-laboratory variance, sL2,n—the sample vari-ance component attributable to differences of test result meansamong laboratories.3.2.4.1 Discussion—This statistic is estimated indirectlyfrom the variance of cell averages and the repeatabilityvariance. In situations where there is good agreement amonglaboratories the estimate of this variance component may beclose to zero or be negative. In the latter case, the estimate isset to zero. (See Note 2 and X1.1.2).3.2.5 cell, n—the intersection of a row and column in atwo-way classification table, in which the rows represent thelaboratories and the columns represent the materials.3.2.5.1 Discussion—The table holds the test results from aninterlaboratory study, and each cell contains the test resultsfrom a particular laboratory on a particular material (seeSection 7 and Table 1).3.2.6 cell average, x¯, n—the average of the test results in aparticular cell.3.2.7 cell deviation, d, n—the cell average minus the aver-age of the cell averages.3.2.8 cell standard deviation, s, n—the standard deviation ofthe test results in a particular cell.3.2.9 repeatability variance, sr2,n—the sample variance oftest results obtained under repeatability conditions.3.2.9.1 Discussion—This statistic is estimated for a materialas the pooled within-laboratory variances over all of thelaboratories in the ILS.3.2.10 reproducibility variance, sR2,n—the sample varianceof test results obtained under reproducibility conditions.3.2.10.1 Discussion—This statistic is estimated as the sumof the two variance components due to between-laboratories,sL2, and within-laboratories, sr2.3.2.11 standard deviation of the cell averages, sx¯,n—thestandard deviation of the cell averages for a particular material.3.2.12 variance of the cell averages, sx¯2,n—the samplevariance of the cell averages for a particular material.3.2.13 within-laboratory consistency statistic, k, n—the ra-tio of the cell standard deviation to the repeatability standarddeviation.3.2.13.1 Discussion—This statistic is an indicator of howone laboratory’s cell standard deviation under repeatabilityconditions compares with the repeatability standard deviationestimated from all laboratories for a particular material (seeX1.2.3).4. Significance and Use4.1 ASTM regulations require precision statements in alltest methods in terms of repeatability and reproducibility. Thispractice may be used in obtaining the needed information assimply as possible. This information may then be used toprepare a precision statement in accordance with PracticeE177. Knowledge of the test method precision is useful incommerce and in technical work when comparing test resultsagainst standard values (such as specification limits) or be-tween data sources (different laboratories, instruments, etc.).4.1.1 When a test method is applied to a large number ofportions of a material that are as nearly alike as possible, thetest results obtained will not all have the same value. Ameasure of the degree of agreement among these test resultsdescribes the precision of the test method for that material.Numerical measures of the variability between such test resultsprovide inverse measures of the precision of the test method.E691 − 162Greater variability implies smaller (that is, poorer) precisionand larger imprecision.4.1.2 Precision is reported as a standard deviation, coeffi-cient of variation (relative standard deviation), variance, or aprecision limit (a data range indicating no statistically signifi-cant difference between test results).4.1.3 This practice is designed only to estimate the precisionof a test method. However, when accepted reference values areavailable for the property levels, the test result data obtainedaccording to this practice may be used in estimating the bias ofthe test method. For a discussion of bias estimation and therelationships between precision, bias, and accuracy, see Prac-tice E177.4.2 The procedures presented in this practice consist ofthree basic steps: planning the interlaboratory study, guidingthe testing phase of the study, and analyzing the test result data.4.2.1 The planning phase includes forming the ILS taskgroup, the study design, selection and number of participatinglaboratories, selection of test materials, and writing the ILSprotocol. A well-developed test method, including a rugged-ness test to determine control of test method conditions, isessential.NOTE 1—In this practice, the term test method is used both for the actualmeasurement process and for the written description of the process, whilethe term protocol is used for the directions given to the laboratories forconducting the ILS.4.2.2 The testing phase includes material preparation anddistribution, liaison with the participating laboratories, andhandling of test result data received from the laboratories.4.2.3 The data analysis utilizes tabular, graphical, and sta-tistical diagnostic tools for evaluating the consistency of thedata so that unusual values may be detected and investigated,and also includes the calculation of the numerical measures ofprecision of the test method pertaining to repeatability andreproducibility.4.3 The information in this practice is arranged as follows:SectionScope 1Referenced Documents 2Terminology 3Significance and Use 4Concepts of Test Method Precision 5Planning the Interlaboratory Study (ILS) SectionILS Membership 6Basic Design 7Test Method 8Laboratories 9Materials 10Number of Test Results per Material 11Protocol 12Conducting the Testing Phase of the ILS SectionPilot Run 13Full Scale Run 14Calculation and Display of Statistics SectionCalculation of the Statistics 15Tabular and Graphical Display of Statistics 16Data Consistency SectionFlagging Inconsistent Results 17Investigation 18Task Group Actions 19Glucose ILS Consistency 20Precision Statement Information SectionRepeatability and Reproducibility 21SectionKeywords 22Tables TableGlucose in Serum Example 1–4, 6–8Critical Values of Consistency Statistics, h and k 5Figures FigureGlucose in Serum Example 1–3Appendixes AppendixTheoretical Considerations Appendix X1Pentosans in Pulp Example Appendix X2Spreadsheet for E691 Calculations Appendix X35. Concepts of Test Method Precision5.1 Repeatability and Reproducibility—These two termsdeal with the variability of test results obtained under specifiedlaboratory conditions and represent the two extremes of testmethod precision. Repeatability concerns the variability be-tween independent test results obtained within a single labo-ratory in the shortest practical period of time by a singleoperator with a specific set of test apparatus using testspecimens (or test units) taken at random from a single quantityof homogeneous material obtained or prepared for the ILS.Reproducibility deals with the variability between single testresults obtained in different laboratories, each of which hasapplied the test method to test specimens (or test units) takenat random from a single quantity of homogeneous materialobtained or prepared for the ILS.5.1.1 Repeatability Conditions—The single-operator,single-set-of-apparatus requirement means that for a particularstep in the measurement process the same combination ofoperator and apparatus is used for every test result and on everymaterial. Thus, one operator may prepare the test specimens, asecond measure the dimensions and a third measure thebreaking force. “Shortest practical period of time“ means thatthe test results, at least for one material, are obtained in a timenot less than in normal testing and not so long as to permitsignificant changes in test material, equipment or environment.5.1.2 Reproducibility Conditions—The factors that contrib-ute to variability in a single laboratory, such as operator,equipment used, calibration of the equipment, and environment(for example, temperature, humidity, air polluti