ASTM_G_172_-_02_2010e1.pdf

Designation:G17202(Reapproved 2010)1Standard Guide forStatistical Analysis of Accelerated Service Life Data1This standard is issued under the fixed designation G172;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.1NOTEEditorially corrected designation and footnote 1 in November 20131.Scope1.1 This guide briefly presents some generally acceptedmethods of statistical analyses that are useful in the interpre-tation of accelerated service life data.It is intended to producea common terminology as well as developing a commonmethodology and quantitative expressions relating to servicelife estimation.1.2 This guide covers the application of the Arrheniusequation to service life data.It serves as a general model fordetermining rates at usage conditions,such as temperature.Itserves as a general guide for determining service life distribu-tion at usage condition.It also covers applications where morethan one variable act simultaneously to affect the service life.For the purposes of this guide,the acceleration model used formultiple stress variables is the Eyring Model.This model wasderived from the fundamental laws of thermodynamics and hasbeen shown to be useful for modeling some two variableaccelerated service life data.It can be extended to more thantwo variables.1.3 Only those statistical methods that have found wideacceptance in service life data analyses have been consideredin this guide.1.4 The Weibull life distribution is emphasized in this guideand example calculations of situations commonly encounteredin analysis of service life data are covered in detail.It is theintention of this guide that it be used in conjunction with GuideG166.1.5 The accuracy of the model becomes more critical as thenumber of variables increases and/or the extent of extrapola-tion from the accelerated stress levels to the usage levelincreases.The models and methodology used in this guide areshown for the purpose of data analysis techniques only.Thefundamental requirements of proper variable selection andmeasurement must still be met for a meaningful model toresult.2.Referenced Documents2.1 ASTM Standards:2G166 Guide for Statistical Analysis of Service Life DataG169 Guide for Application of Basic Statistical Methods toWeathering Tests3.Terminology3.1 Terms Commonly Used in Service Life Estimation:3.1.1 accelerated stress,nthat experimental variable,suchas temperature,which is applied to the test material at levelshigher than encountered in normal use.3.1.2 beginning of life,nthis is usually determined to bethe time of delivery to the end user or installation into fieldservice.Exceptions may include time of manufacture,time ofrepair,or other agreed upon time.3.1.3 cdf,nthe cumulative distribution function(cdf),denoted by F(t),represents the probability of failure(or thepopulation fraction failing)by time=(t).See 3.1.7.3.1.4 complete data,na complete data set is one where allof the specimens placed on test fail by the end of the allocatedtest time.3.1.5 end of life,noccasionally this is simple and obvious,such as the breaking of a chain or burning out of a light bulbfilament.In other instances,the end of life may not be socatastrophic or obvious.Examples may include fading,yellowing,cracking,crazing,etc.Such cases need quantitativemeasurements and agreement between evaluator and user as tothe precise definition of failure.For example,when somecritical physical parameter(such as yellowing)reaches apre-defined level.It is also possible to model more than onefailure mode for the same specimen(that is,the time to reacha specified level of yellowing may be measured on the samespecimen that is also tested for cracking).3.1.6 f(t),nthe probability density function(pdf),equalsthe probability of failure between any two points of time t(1)1This guide is under the jurisdiction of ASTM Committee G03 on Weatheringand Durability and is the direct responsibility of Subcommittee G03.08 on ServiceLife Prediction.Current edition approved July 1,2010.Published July 2010.Originally approvedin 2002.Last previous edition approved in 2002 as G172-02.DOI:10.1520/G0172-02R10.2For 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.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 and t(2);ft!5dFt!dt.For the normal distribution,the pdf is the“bell shape”curve.3.1.7 F(t),nthe probability that a random unit drawn fromthe population will fail by time(t).Also F(t)=the decimalfraction of units in the population that will fail by time(t).Thedecimal fraction multiplied by 100 is numerically equal