ASTM_D_4460_-_22a.pdf

Designation:D446022aStandard Practice forCalculating Precision Limits Where Values Are Calculatedfrom Other Test Methods1This standard is issued under the fixed designation D4460;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.1.Scope1.1 Material and mixture properties such as air voids andvoids in mineral aggregates(VMA)are calculated from two orthree test results,combined in simple mathematical relation-ships.The standard deviation equations for these calculatedvalues can be developed using a mathematical process called“propagation of errors”(also called“propagation of uncer-tainty”).This practice includes uncertainty equations for fourforms or material and mixture equations:when two test resultsare(1)added or subtracted,(2)multiplied together,(3)onedivided by the other,and(4)two test results divided by a third.1.2 This approach to calculating standard deviation equa-tions is only valid when the distributions of the test results fromthe two standards are independent(that is,not correlated).1.3 The accuracy of a calculated standard deviation isdependent on the accuracy of the standard deviations used forthe individual test result methods.1.4 Values for the mean and standard deviation for each testmethod are needed to determine the standard deviation for acalculated value.1.5 Examples of how to use these equations are shown inAppendix X1.1.6 Abrief explanation of how standard deviation equationsare derived for more complicated material and mixture equa-tions is also included.1.7 The text of this standard references notes and footnoteswhich provide explanatory material.These notes and footnotes(excluding those in tables and figures)shall not be consideredas requirements of the standard.1.8 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,health,and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.9 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade(TBT)Committee.2.Referenced Documents2.1 ASTM Standards:2C127 Test Method for Relative Density(Specific Gravity)and Absorption of Coarse AggregateC128 Test Method for Relative Density(Specific Gravity)and Absorption of Fine AggregateD1188/D1188M Test Method for Bulk Specific Gravity andDensity of Compacted Asphalt Mixtures Using CoatedSamplesD2172/D2172M Test Methods for Quantitative Extraction ofAsphalt Binder from Asphalt MixturesD2726/D2726M Test Method for Bulk Specific Gravity andDensity of Non-Absorptive Compacted Asphalt MixturesD4125/D4125M Test Methods for Asphalt Content of As-phalt Mixtures by the Nuclear MethodD6307 Test Method for Asphalt Content of Asphalt Mixtureby Ignition MethodD6752/D6752M Test Method for Bulk Specific Gravity andDensity of Compacted Asphalt Mixtures Using AutomaticVacuum Sealing MethodE177 Practice for Use of the Terms Precision and Bias inASTM Test Methods3.Terminology3.1 For definitions of terms used in this document,consultPractice E177,or a standard dictionary,or a statistical text.3,4,51This practice 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 Nov.1,2022.Published November 2022.Originallyapproved in 1985.Last previous edition approved in 2022 as D4460 22.DOI:10.1520/D4460-22A.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 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 of the National Bureau of Standards,Vol 70C,No.4,1966,pp.331341.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade(TBT)Committee.14.Significanc