1、Designation: G 117 02 (Reapproved 2007)Standard Guide forCalculating and Reporting Measures of Precision UsingData from Interlaboratory Wear or Erosion Tests1This standard is issued under the fixed designation G 117; the number immediately following the designation indicates the year oforiginal adop
2、tion or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide covers and offers direction on the handling ofdata from inte
3、rlaboratory tests for wear or erosion. It describesa format for entering data and for subsequently reportingresults on measures of precision in a Committee G02 standard.It indicates methods for calculation of the needed statisticalquantities.1.2 This guide offers guidance based on a Committee G02con
4、sensus, and exists for the purpose of emphasizing the needto use established statistical practices, and to introduce moreuniformity in reporting interlaboratory test results in Commit-tee G02 standards.1.3 An example of how the methods described in this guidemay be applied is available in personal c
5、omputer format (DOStype system) on floppy disk as a spreadsheet (LOTUS, rel. 4)file. The purpose is to facilitate use of the methods in thisguide. The example file contains all needed equations in therecommended format and can be edited to accept new data.ASTM Headquarters or the Chairman of G02 sho
6、uld becontacted for a copy of that computer file. The user must havespreadsheet software (for example, LOTUS or compatible)available.1.4 The methods used in this document are consistent withPractices E 691 and E 177, and with ADJE0691, Conductingan Interlaboratory Study to Determine the Precision of
7、 a TestMethod.22. Referenced Documents2.1 ASTM Standards:3E 177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE 691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodG65 Test Method for Measuring Abrasion Using the DrySand/Rubber Wheel A
8、pparatusG76 Test Method for Conducting Erosion Tests by SolidParticle Impingement Using Gas JetsG77 Test Method for Ranking Resistance of Materials toSliding Wear Using Block-on-Ring Wear Test3. Summary of Guide3.1 Use of this guide in preparation of interlaboratory testresults for inclusion in G02
9、standards involves a sequence ofsteps. First the raw data from the individual laboratories areentered into a table of any suitable form that permits calcula-tion of average values and standard deviations for eachlaboratory. Then those two measures are entered, for eachlaboratory, into a table such a
10、s that shown in Fig. 1. Then thesteps described in this guide are carried out, leading tocalculation of the precision measures that are to be used in thestandard being prepared.4. Significance and Use4.1 This guide is intended to assist in developing statementsof precision and supporting data that w
11、ill be used in CommitteeG02 standards. The methods and approach are drawn fromPractice E 177 and E 691. It was felt that preparation of thisguide and its use in Committee G02 would lead to appropriatestatistical analyses and more uniformity in G02 standardsregarding reporting of interlaboratory resu
12、lts and precision.The guide is not meant to substitute for possible use ofPractices E 177 or E 691 in developing committee standards.5. Procedure5.1 An example of interlaboratory data analyzed and pre-sented in the recommended format is shown in Fig. 1. The datawere obtained from an interlaboratory
13、series of solid particleerosion tests carried out in connection with Practice G76. Thistable format can be used with either PC spreadsheet calculationor hand calculation.5.2 Data tabulation and calculation can be carried out by useof a PC and numeric spreadsheet software (for example,LOTUS), as desc
14、ribed in Table 1, or by any other appropriate1This guide is under the jurisdiction of ASTM Committee G02 on Wear andErosion and is the direct responsibility of Subcommittee G02.20 on Computeriza-tion in Wear.Current edition approved July 1, 2007. Published September 2007. Originallyapproved in 1993.
15、 Last previous edition approved in 2002 as G 11702.2Available from ASTM International Headquarters. Order Adjunct No.ADJE0691. Original adjunct produced in 1990.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book o
16、f ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.means such as hand calculation (Table 2). The formulae wereobtained from Practices E
17、177 or E 691 or from statisticalanalysis texts. Formulae that are used for calculation are givenin Table 1 for spreadsheet calculation (for example, LOTUS)and in Table 2 for hand calculation.5.3 The sequence of steps in assembling and handling thedata is as follows (refer to the designated columns i
18、n Fig. 1):5.3.1 Calculate the average value of the data for each of Nlaboratories. (Column D)5.3.2 Calculate the average value Q of all the laboratoryaverages. (Cell D13)5.3.3 Calculate the standard deviation values for eachlaboratory. Note that the quantity (r 1) is used as the divisorwhere r is th
19、e number of replicate results for each laboratory.(Column E)5.3.4 Calculate the within-laboratory standard deviationvalue W. Note that this is the root-mean-square value of thelaboratory standard deviations, using N as the divisor. Thisquantity is also called the repeatability standard deviation.(Ce
20、ll E13)5.3.5 Calculate the within-laboratory coeffcient of variationin percent. (Cell E17)NOTEColumn and row labels A, B,.and1,2,.arenotrequired.FIG. 1 Example of Recommended Format for Data AnalysisTABLE 1 Formulae Used in PC Spreadsheet Shown in Fig. 1,in Notation Appropriate to Spreadsheet Softwa
21、re(for example, LOTUS)AB13: COUNT(B8B11)C13: AVG(C8C11)D13: AVG(D8D11)E13: SQRT(SUM(K8 . . K11)/B13)G13: SQRT(SUM(L8L11)/(B13-1) + E13*E13*(C13-1)/C13)where:F8: +E8/ E13 H8: ABS(+G8/ L13)K8: +E8*E8and so forthL8: +G8*G8and so forthL13: SQRT(SUM(L8L11)/(B13-1)E17: 100*E13/D13G17: 100*G13/ D13E19: 2.8
22、*E13G19: 2.8*G13AN is used as the divisor in (E12) to obtain the mean value of the variance, whileN-1 is used as the divisor in calculating individual standard deviations (E7E9)since they are estimates of population values. Practice E 691 should be consultedfor further explanation.TABLE 2 Formulae U
23、sed in Calculating Quantities for Fig. 1,Given in Usual Mathematical NotationB13: N = (n Number of laboratoriesC13: R = (1/N)(r Average number of replicatesD13: Q = (1/N)(q Average of the quantity measuredE13: W = (1/N)(s20.5Within-laboratory standard deviationG13: B = (1/(N 1)(qQ)2+ (1/N)(s2(R 1)/R
24、0.5F8: s/W h-statisticH8: d/sxk-statisticK8: s2cell standard deviationL8: d2cell deviation squaredL13: (1/(N-1)(q-Q)20.5standard deviation of cell averagesProvisional between-laboratory standarddeviationE17: 100W/Q Percent coefficient of variation, within-laboratoryG17: 100B/Q Percent coefficient of
25、 variation, between-laboratoryE19: 2.8W 95 % confidence limits, within-laboratoryG19: 2.8B 95 % confidence limits, between-laboratoryG 117 02 (2007)25.3.6 Calculate the k-statistic values for each laboratory, bydividing each laboratory standard deviation by the within-laboratory standard deviation.
26、(Column F)5.3.7 Calculate the deviation of the average for each labo-ratory from the average for all laboratories. (Column G)5.3.8 Calculate the between-laboratory standard deviationvalue B. Note that this is the square root of the sum of themean-square value of the deviations from the average, usin
27、gN 1 as the divisor, and the square of the within-laboratorystandard deviation multiplied by the quantity (r 1)/r. This isalso called the provisional reproducibility standard deviation.(Cell G13)NOTE 1It is termed provisional since the final reproducibility stan-dard deviation will be the larger of
28、the two calculated measures, therepeatability and the reproducibility standard deviations.5.3.9 Calculate the between-laboratory coeffcient of varia-tion in percent. (Cell G17)5.3.10 Calculate the h-statistic values for each laboratory,by dividing each laboratory deviation from average by thebetween
29、-laboratory standard deviation. (Column H)5.3.11 Select the larger of the two quantities calculated in5.3.4 and 5.3.8 for the (final) reproducibility standard devia-tion. An example is shown at the bottom of Fig. 1.5.3.12 Calculate the 95 % limits of repeatability and repro-ducibility by multiplying
30、 the within-laboratory standard devia-tion and the (final) between-laboratory standard deviation,respectively, by the factor, 2.83. (Cells E19 and G19)NOTE 2These limits are the maximum differences between two testresults that can be expected to occur in 95 % of the cases.5.3.13 Refer to Practice E
31、691, Table 12, and determinecritical values of k and h for the number of laboratories andreplicates involved. Examine the values in the k-statistic andh-statistic columns. Any values greater than the respectivecritical values indicate data outliers for that laboratory whichshould be inspected for va
32、lidity. (Cells F22 and H22)6. Report6.1 Examples of the recommended tabular format for theresults of the calculations are shown in Fig. 2 for threestandards from Committee G02.6.2 A recommended version of a statement of precision,drawn from Practice E 177, is as follows for the exampleshown in Fig.
33、1:Average Test Value: 8.70 mm3/g95 % repeatability limit (within-lab) 1.27 mm3/g95 % reproducibility limit (between-labs) 7.18 mm3/g7. Keywords7.1 erosion; precision; repeatability; reproducibility; wearG 117 02 (2007)3FIG. 2 Examples Using Data from Three Committee G02 Standards (Test Methods G65,
34、G76, and G77)G 117 02 (2007)4APPENDIXX1. GUIDELINES ASSOCIATED WITH PRACTICE E 691X1.1 IntroductionX1.1.1 This Appendix will summarize certain guidelinesfound in Practice E 691. The purpose of this summary is toemphasize several key guidelines in any interlaboratory study(ILS) of wear and erosion. T
35、he reader is directed to PracticeE 691 as the definitive document for more details and addi-tional considerations.X1.2 General ConsiderationsX1.2.1 Tests performed on presumably identical materialsin presumably identical circumstances do not, in general, yieldidentical results. This is attributed to
36、 unavoidable randomerrors inherent in every test procedure; the factors that mayinfluence the outcome of a test cannot all be completelycontrolled. The general term for expressing the closeness oftest results to the “true” value or the accepted reference isaccuracy. To be of practical value, standar
37、d procedures arerequired for determining the accuracy of a test method, both interms of its bias and in terms of its precision. Precision,asdiscussed in Practice E 691, is expressed in terms of twomeasurement concepts: repeatability and reproducibility. Un-der repeatability conditions, the controlli
38、ng factors are kept orremain reasonably constant and usually contribute only mini-mally to the variability. Under reproducibility conditions, thefactors are generally different (that is, they change fromlaboratory to laboratory) and usually contribute appreciably tothe variability of test results. T
39、o obtain reasonably estimates ofrepeatability and reproducibility precision, it is necessary in aninterlaboratory study to guard against excessively sanitizeddata in the sense that only the uniquely best operators areinvolved or that a laboratory takes unusual steps to get “good”results. It is also
40、important to recognize and consider how totreat “poor” results that may have unacceptable causes, forexample, departures from the prescribed procedure.X1.3 Number of LaboratoriesX1.3.1 It is important that enough laboratories be includedin the ILS to be a reasonable cross-section of the population o
41、fqualified laboratories, that the loss or poor performance of afew laboratories will not be fatal to the study, and that the ILSprovides a reasonably satisfactory estimate of the reproducibil-ity. According to Practice E 691, under no circumstancesshould the final statement of precision of a test me
42、thod bebased on acceptable test results for each material from fewerthan 6 laboratories.X1.3.2 This being said, it is often the case that test methodsdeveloped by G02 members are in use in only a few labora-tories. In such cases, provisional interlaboratory testing may goforward involving as few as
43、3 laboratories, but no fewer. Theresponsible subcommittee must plan to conduct another ILSlater that includes at least 6 laboratories, and then to use thoseresults to replace the provisional data from the first ILS.X1.4 Number of MaterialsX1.4.1 An ILS of a test method should include at least threem
44、aterials representing different test levels, and for develop-ment of broadly applicable precision statements, six or morematerials should be included in the study, according to PracticeE 691. The materials involved in any one ILS should differprimarily only in the level of the property measured by t
45、he testmethod. When it is known, or suspected, that different classesof materials will exhibit different levels of precision whentested by the test method, consideration should be given toconducting separate interlaboratory studies for each class ofmaterial. Each material in an ILS should be made to
46、 be orselected to be as homogeneous as possible prior to its subdi-vision into test units or test specimens.X1.5 Number of Replicate MeasurementsX1.5.1 It is generally sound to limit the number of testresults on each material in each laboratory to a small number,such as three or four. The minimum nu
47、mber of test results perlaboratory will normally be three or four for a physical test.This should apply to wear or erosion tests. As many as tenreplicates may be needed when test results are apt to varyconsiderably. Generally, the time and effort invested in an ILSis better spent on examining more m
48、aterials across morelaboratories than on recording a large number of test results permaterial within a few laboratories.X1.6 Consideration of OutliersX1.6.1 If an investigation of the ILS data discloses noclerical, sampling, or procedural errors, any unusual datashould be retained, and the precision
49、 statistics based on themshould be published. If, on the other hand, a cause for unusualdata was found during the investigation, the task group hasseveral options to consider. If the laboratory clearly andseriously deviated from the test method, the test results for thatlaboratory must be removed from the ILS calculations. How-ever, despite the danger of a questioned laboratory having priorknowledge, it may be appropriate to ask that laboratory toretest one or more materials following the correct procedure,and then include the ne
