1、Designation: C670 10Standard Practice forPreparing Precision and Bias Statements for Test Methodsfor Construction Materials1This standard is issued under the fixed designation C670; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, t
2、he 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. Scope*1.1 This practice supplements
3、 Practice E177, in order toprovide guidance in preparing precision and bias statements forASTM test methods pertaining to certain construction materi-als (Note 1). Recommended forms for precision and biasstatements are included. A discussion of the purpose andsignificance of these statements for the
4、 users of those testmethods is also provided.NOTE 1Although under the jurisdiction of Committee C09, thispractice was developed jointly by Committees C01, D04, and C09, andhas been endorsed by all three committees. It has subsequently beenadopted for use by Committee D18.2. Referenced Documents2.1 A
5、STM Standards:2C109/C109M Test Method for Compressive Strength ofHydraulic Cement Mortars (Using 2-in. or 50-mm CubeSpecimens)C802 Practice for Conducting an Interlaboratory Test Pro-gram to Determine the Precision of Test Methods forConstruction MaterialsE177 Practice for Use of the Terms Precision
6、 and Bias inASTM Test Methods3. Terminology3.1 Definitions of Terms Specific to This Standard:3.2 one-sigma limit (1s)the fundamental statistic underly-ing all indexes of precision is the standard deviation of thepopulation of measurements characteristic of the test methodwhen the latter is applied
7、under specifically prescribed condi-tions (a given system of causes). The terminology “one-sigmalimit” (abbreviated (1s) is used in Practice E177 to denote theestimate of the standard deviation or sigma that is characteristicof the total statistical population. The one-sigma limit is anindication of
8、 the variability (as measured by the deviationsabove and below the average) of a large group of individualtest results obtained under similar conditions.3.2.1 single-operator one-sigma limitthe one-sigma limitfor single-operator precision is a quantitative estimate of thevariability of a large group
9、 of individual test results when thetests have been made on the same material by a single operatorusing the same apparatus in the same laboratory over arelatively short period of time. This statistic is the basic oneused to calculate the single-operator index of precision given inthe precision state
10、ment for guidance of the operator.3.2.2 multilaboratory one-sigma limitthe one-sigma limitfor multilaboratory precision is a quantitative estimate of thevariability of a large group of individual test results when eachtest has been made in a different laboratory and every effort hasbeen made to make
11、 the test portions of the material as nearlyidentical as possible. Under normal circumstances the esti-mates of one-sigma limit for multilaboratory precision arelarger than those for single-operator precision, because differ-ent operators and different apparatus are being used in differentlaboratori
12、es for which the environment may be different.3.2.3 one-sigma limit in percent (1s%)in some cases thecoefficient of variation is used in place of the standarddeviation as the fundamental statistic. This statistic is termedthe “one-sigma limit in percent” (abbreviated (1s%) and is theappropriate stan
13、dard deviation (1s) divided by the average ofthe measurements and expressed as a percent. When it isappropriate to use (1s%) in place of (1s) is discussed in Section6.3.3 Acceptable Range of Results:3.3.1 acceptable difference between two resultsthe “dif-ference two-sigma limit (d2s)” or “difference
14、 two-sigma limitin percent (d2s%),” as defined in Practice E177, has beenselected as the appropriate index of precision in most precisionstatements. These indexes indicate a maximum acceptabledifference between two results obtained on test portions of thesame material under the applicable system of
15、causes describedin 4.1.1 and 4.1.2 (or whatever other system of causes isappropriate). The (d2s) index is the difference between two1This practice is under the jurisdiction of ASTM Committee C09 on Concreteand Concrete Aggregates and is the direct responsibility of Subcommittee C09.94on Evaluation o
16、f Data (Joint C09 and C01).Current edition approved Oct. 1, 2010. Published November 2010. Originallyapproved in 1971. Last previous edition approved in 2003 as C670-03. DOI:10.1520/C0670-10.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serv
17、iceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1*A Summary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, Uni
18、ted States.individual test results that would be equaled or exceeded in thelong run in only 1 case in 20 in the normal and correctoperation of the method. The (d2s%) index is the differencebetween two individual test results expressed as a percent oftheir average that meets the same requirements. Th
19、ese indexesare calculated by multiplying the appropriate standard devia-tion (1s) or coefficient of variation (1s%) by the factor 2=2(equal to 2.83).3.3.2 acceptable range of more than two resultsin caseswhere the test method calls for more than two test results to beobtained, the range (difference
20、between highest and lowest) ofthe group of test results must be compared to a maximumacceptable range for the applicable system of causes andnumber of test results. The range for different numbers of testresults including two that would be equaled or exceeded inonly 1 case in 20 is obtained by multi
21、plying the appropriatestandard deviation (1s) or coefficient of variation (1s%) by theappropriate factor from the second column of Table 1 (Note 2):NOTE 2It is important to note that when more than two test results areobtained, an index of precision for the difference between two results cannot be u
22、sed as a criterion for judging acceptability of the range of thegroup or for other pairs of results selected from the group.3.3.3 variations for single operatorsthe system of causesdesignated for obtaining the quantitative guide to acceptableperformance by an operator as stated in 4.1.1 leads to sin
23、gle-operator precision, using the system of modifiers given inPractice E177 (Note 3). When two results by the same operatordiffer by more than (d2s) or (d2s%) or the range of more thantwo results exceeds that obtained by the method described in3.3.2 there is a significantly large probability that an
24、 error hasoccurred and retests should be made as directed in Note 4.NOTE 3Single-operator precision is often referred to as “repeatabil-ity,” and multilaboratory precision is often referred to as “reproducibility.”NOTE 4It is beyond the scope of this practice to describe in detailwhat action should
25、be taken in all cases when results occur that differ bymore than the (d2s) limits or by more than the maximum allowable range.Such an occurrence is a warning that there may have been some error inthe test procedure, or some departure from the prescribed conditions of thetest on which the limits appe
26、aring in the test method are based; forexample, faulty or misadjusted apparatus, improper conditions in thelaboratory, etc. In judging whether or not results are in error, informationother than the difference between two test results is needed. Often a reviewof the circumstances under which the test
27、 results in question were obtainedwill reveal some reason for a departure. In this case the data should bediscarded and new test results obtained and evaluated separately. If nophysical reason for a departure is found, retests should still be made, butthe original tests should not be completely igno
28、red. If the second set ofresults also differs by more than the applicable limit, the evidence is verystrong that something is wrong or that a real difference exists between thetwo samples tested. If the second set produces a result within the limit, itmay be taken as a valid test, but the operator o
29、r laboratory may then besuspected of producing erratic results, and a closer examination of theprocedures would be in order. If knowledge about the test method inquestion indicates that certain actions may be appropriate in cases wheredeviant results occur, then such information should be included i
30、n the testmethod, but details of how this should be done will depend upon theparticular test method.3.3.4 variations between laboratoriesthe system ofcauses designated for obtaining the quantitative guide foracceptance of results by different laboratories as given in 4.1.2is multilaboratory precisio
31、n, using the system of modifiersgiven in Practice E177 (Note 3). When results differ by morethan (d2s) there is a significantly large probability that one orboth laboratories are in error or that a difference exists in theportions of material being used for the tests. In such cases,retests should be
32、 made. When possible, newly drawn testsamples should be used for such retests as directed in Note 4.3.4 Number of Tests:3.4.1 single test resultsthe number of tests run must betaken into account when evaluating testing variations. Usually,the statistics used in evaluating precision and the indexes o
33、fprecision based on them are based on the population distribu-tion of single test results. When this is the case, the index ofprecision may be used in comparing single tests results only,not averages of two or more tests.3.4.2 test results based on averagesif the precision state-ment is based on tes
34、t results that are averages of two or moremeasurements, then the number of measurements averagedmust be stated, and in using the index of precision, averages ofexactly that number of measurements must be used. In somecases a test result is defined in the method as the average of twoor more individua
35、l measurements. In such cases the index ofprecision for a test result applies to a test result as so defined,although indexes of precision for ranges of individual mea-surements within a laboratory may also be included as de-scribed in 3.3.3.3.4.3 precision of individual measurements averaged toobta
36、in a test resultwhen two or more measurements areaveraged to obtain a test result, the range of the individualmeasurements may be examined to determine whether thelatter meet the criterion of being valid individual measurementsunder the conditions of the test method. The maximumacceptable range for
37、individual measurements is obtained bymultiplying the appropriate standard deviation (1s) or, coeffi-cient of variation (1s%) obtained from averages by the appro-priate factor from the second column of Table 2 (Note 5). Themaximum acceptable range for individual measurements ob-tained by this method
38、 may be included in the precisionstatement as an index of precision for individual measurementsin the same laboratory as described in Example 8.NOTE 5This procedure is only valid if the individual measurementsare subject to the same sources of variation as the test result. For example,the single-ope
39、rator precision of Test Method C109/C109M mortar cubes iscalculated from test results that include a contribution from variationamong batches of mortar. Variation among individual cubes from a singlebatch does not contain this component of variation. Therefore, differencesTABLE 1 Maximum Acceptable
40、RangeNumber ofTest ResultsMultiplier of (1s) or (1s%) forMaximum Acceptable RangeA22.833343653964074.284394410 4.5AValues were obtained from Table A7 of “Order Statistics and Their Use inTesting and Estimation,” Vol 1, by Leon Harter, Aerospace Research Laboratories,United States Air Force.C670 102a
41、mong individual cubes from a single batch cannot be inferred from thesingle-operator standard deviation given in Test Method C109/C109M andthe values in Table 2.3.4.4 multilaboratory precision expressed as a maximumallowable difference between two averageswhen the testmethod calls for the reporting
42、of more than one test result,multi-laboratory precision may be expressed as a maximumallowable difference between averages of such groups, onefrom each laboratory, and both the (d2s) or (d2s%) limit forindividual results and this maximum allowable difference oftwo averages may be included in the mul
43、tilaboratory precisionstatement (Note 6). The maximum allowable difference foraverages of a given number of test results, n, is obtained bydividing the appropriate (d2s) or (d2s%) limit by the squareroot of n.NOTE 6Note that this is not the same as the situation where a testresult is defined as the
44、average of two or more individual measurements.A given test method may include both features. It is important to bear inmind, however, that when more than one result is obtained in one or bothlaboratories, the (d2s) or (d2s%) limit may not be used as a criterion forjudging the differences between se
45、lected pairs of results from the twolaboratories.3.5 field versus laboratory testsprecision indexes forASTM test methods are normally based on results obtained inlaboratories by competent operators using well-controlledequipment on test portions of materials for which precautionshave been taken to e
46、nsure that they are as nearly alike aspossible. Such precautions and the same level of competencemay not be practicable for the usual quality control or routineacceptance testing. Therefore, the normal testing variationamong laboratories engaged in quality control and acceptancetesting of commercial
47、 materials may be larger than indicatedby the relationship derived from the one-sigma limit formultilaboratory precision. In this case it is recommended thatstudies be made to determine the one-sigma limit for testsmade under field conditions and realistic adjustments inspecification tolerances be m
48、ade accordingly.4. General Concepts4.1 A precision statement meeting the requirements of thispractice normally contains two main elements described asfollows:4.1.1 Single-Operator PrecisionAmeasure of the greatestdifference between two results that would be consideredacceptable when properly conduct
49、ed repetitive determinationsare made on the same material by a competent operator.4.1.2 Multilaboratory PrecisionA measure of the greatestdifference between two test results that would be consideredacceptable when properly conducted determinations are madeby two different operators in different laboratories on portionsof a material that are intended to be identical, or as nearlyidentical as possible.4.2 Other Measures of PrecisionThe two elements de-scribed in 4.1.1 and 4.1.2 involve the main systems of causesof interest to users of test methods involving con
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