1、Designation: D 4460 97 (Reapproved 2005)Standard Practice forCalculating Precision Limits Where Values are Calculatedfrom Other Test Methods1This standard is issued under the fixed designation D 4460; the number immediately following the designation indicates the year oforiginal adoption or, in the
2、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 practice covers techniques for calculating precisionlimits when values are calcula
3、ted from two other methodshaving precision limits.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of r
4、egulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 1188 Test Method for Bulk Specific Gravity and Densityof Compacted Bituminous Mixtures Using Paraffin-CoatedSpecimensD 2041 Test Method for Theoretical Maximum SpecificGravity and Density of Bituminous Paving MixturesD 3
5、203 Test Method for Percent Air Voids in CompactedDense and Open Bituminous Paving MixturesE 177 Practice for Use of the Terms Precision and Bias inASTM Test Methods3. Terminology Definitions3.1 For definitions of terms used in this document, consultPractice E 177, or a standard dictionary, or a sta
6、tistical text.3,4,54. Significance and Use4.1 Precision limits for a test result that is calculated byaddition, subtraction, multiplication, or division of two othertest results that have valid precision limits can be calculateddirectly. This saves the cost and delay of conducting aninterlaboratory
7、study.4.2 At the heart of statistical theory is the concept of afrequency distribution of a random variable. The precisionlimit of the random variable is determined by the standarddeviation of the variable. The standard deviation of a randomvariable that is the sum, difference, product, or quotient
8、of twoother random variables can be calculated simply so long as theindividual variables are independent and the standard devia-tions are small relative to their mean values. These restrictionsare usually met in ASTM methods. In those cases where theserestrictions are not met, other methods can be u
9、sed. Only casescomplying with the restrictions are covered in this standard.5. Procedure5.1 The standard deviation on which precision limits for atest result are based can be calculated from the followingequations:sx 6 y5 =sx21sy2(1)where:sx 6y= standard deviation for determining precision lim-its o
10、f a test result for a new standard based oneither an addition or subtraction of test resultsfrom two other standards,sx= standard deviation from precision statement ofone of the standards on which new standard isbased, andsy= standard deviation from precision statement ofother standard on which new
11、standard is based.The distributions of the test results from the two standardsshould be independent.sxy5 = y2sx21 x2sy2(2)where:sxy= standard deviation for determining precision limitsof test results for a new standard based on theproducts of two other test results from two otherstandards,1This prac
12、tice is under the jurisdiction of ASTM Committee D04 on Road andPaving Materials and is the direct responsibility of Subcommittee D04.94 onStatistical Procedures and Evaluation of Data.Current edition approved June 1, 2005. Published June 2005. Originallyapproved in 1985. Last previous edition appro
13、ved in 2004 as D 4460 97 (2004).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Geary, R. C., “The Frequency
14、 Distribution of a Quotient,” Journal of the RoyalStatistical Society, Vol 93, 1930, pp. 442446.4Fieller, E. C., “The Distribution of the Index in a Normal Bivariate Population,”Biometrika, Vol 24, 1932, pp. 428440.5Ku, H. H., “Notes on the Use of Propagation of Error Formulas,” Journal ofResearch o
15、f the National Bureau of Standards, Vol 70C, No. 4, 1966, pp. 331341.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.sx= standard deviation from precision statement of oneof the standards on which new standard is based,x = mean or av
16、erage value of X variable,sy= standard deviation from precision statement of otherstandard on which new standard is based, andy = mean or average value of Y variable.s xy5y2sx21 x2sy2y4(3)wheresxy = standard deviation for determining precision limits oftest results for a new standard based on the qu
17、otient oftwo test results from two other standards.sx, sy, x, y 5 definitions given above. (4)An example in Appendix X1. illustrates how the equationsare applied.6. Keywords6.1 precision limits; standard deviationAPPENDIX(Nonmandatory Information)X1. EXAMPLE OF CALCULATED PRECISION LIMITSX1.1 Test M
18、ethod D 3203 calculates the percent air voidsin paving mixtures by using values obtained from Test Meth-ods D 1188 and D 2041. Both of these test methods haveprecision statements so a precision statement can be calculatedfor Test Method D 3203.X1.2 Calculating Air Voids:X1.2.1 The equation for calcu
19、lating air voids is:Percent air voids 5 100 1 2bulk sp gr/theoretical maximum sp gr!(X1.1)The bulk specific gravity of Test Method D 1188 is dividedby the theoretical maximum specific gravity of Test MethodD 2041. Therefore, Eq 3 involving a quotient is the proper oneto use in determining a precisio
20、n statement for air voids.X1.2.2 Test Method D 1188 has one of the older precisionstatements which does not give the standard deviation but onlygives the D2S limit for multilaboratory precision. The testingoperations in Test Methods D 1188 and D 2041 are very similarso it is not surprising that the
21、D2S limits for multilaboratoryprecision are almost identical being 0.02 for Test MethodD 1188 and 0.019 for Test Method D 2041. Therefore, the tablefor nonporous aggregate from Test Method D 2041 is used asthe basis for both test methods as follows:Standard DeviationAcceptable Range ofTwo ResultsTes
22、t and type index (1S) (D2S)Single-operator precision 0.0040 0.011Multilaboratory precision 0.0067 0.019During a testing program, the bulk specific gravity (TestMethod D 1188) of an asphalt mixture was determined to be2.423 and the theoretical maximum specific gravity (TestMethod D 2041) was determin
23、ed to be 2.523.X1.3 Eq 3 was used to calculate the single-operatorprecision standard deviation for these specific gravity values.Standard deviation for Test Method D 3203 is as follows:Single-operator precision:s xy52.523!20.004!21 2.423!20.004!22.523!4(X1.2)= 0.0022Multilaboratory precision:sxy52.5
24、23!20.0064!21 2.423!20.0064!22.523!4(X1.3)= 0.0035These standard deviations are in terms of specific gravity.Since Test Method D 3203 is reported in percent they must bemultiplied by 100 to get the required percentages yielding thefollowing values:StandardDeviationRange ofTwo ResultsTest and Type In
25、dex (1S %) (D2S %)Single-operator precision 0.22 0.62Multilaboratory precision 0.35 0.99This is the complete precision statement for Test MethodD 3203 where nonporous aggregates are used.D 4460 97 (2005)2ASTM International takes no position respecting the validity of any patent rights asserted in co
26、nnection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the respo
27、nsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful
28、 consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International,
29、100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).D 4460 97 (2005)3
