ASTM_G_166_-_00_2011.pdf

Designation:G16600(Reapproved 2011)Standard Guide forStatistical Analysis of Service Life Data1This standard is issued under the fixed designation G166;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 This guide presents briefly some generally acceptedmethods of statistical analyses which are useful in the inter-pretation of service life data.It is intended to produce acommon terminology as well as developing a common meth-odology and quantitative expressions relating to service lifeestimation.1.2 This guide does not cover detailed derivations,orspecial cases,but rather covers a range of approaches whichhave found application in service life data analyses.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 model is emphasized in thisguide and example calculations of situations commonly en-countered in analysis of service life data are covered in detail.1.5 The choice and use of a particular life distribution modelshould be based primarily on how well it fits the data andwhether it leads to reasonable projections when extrapolatingbeyond the range of data.Further justification for selecting amodel should be based on theoretical considerations.2.Referenced Documents2.1 ASTM Standards:2G169 Guide for Application of Basic Statistical Methods toWeathering Tests3.Terminology3.1 Definitions:3.1.1 material propertycustomarily,service life is consid-ered to be the period of time during which a system meetscritical specifications.Correct measurements are essential toproducing meaningful and accurate service life estimates.3.1.1.1 DiscussionThere exists many ASTM recognizedand standardized measurement procedures for determiningmaterial properties.As these practices have been developedwithin committees with appropriate expertise,no further elabo-ration will be provided.3.1.2 beginning of lifethis is usually determined to be thetime of manufacture.Exceptions may include time of deliveryto the end user or installation into field service.3.1.3 end of lifeOccasionally this is simple and obvioussuch as the breaking of a chain or burning out of a light bulbfilament.In other instances,the end of life may not be socatastrophic and free from argument.Examples may includefading,yellowing,cracking,crazing,etc.Such cases needquantitative measurements and agreement between evaluatorand user as to the precise definition of failure.It is also possibleto model more than one failure mode for the same specimen.(for example,The time to produce a given amount of yellowingmay be measured on the same specimen that is also tested forcracking.)3.1.4 F(t)The 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 to thepercent failure by time(t).3.1.5 R(t)The probability that a random unit drawn fromthe population will survive at least until time(t).Also R(t)=the fraction of units in the population that will survive at leastuntil time(t)Rt!5 1 2 Ft!(1)3.1.6 pdfthe probability density function(pdf),denoted byf(t),equals the probability of failure between any two points oftime t(1)and t(2).Mathematicallyft!5dFt!dt.For the normaldistribution,the pdf is the“bell shape”curve.3.1.7 cdfthe cumulative distribution function(cdf),de-noted by F(t),represents the probability of failure(or thepopulation fraction failing)by time=(t).See section 3.1.4.3.1.8 weibull distributionFor the purposes of this guide,the Weibull distribution is represented by the equation:Ft!5 1 2 e2StcDb(2)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 1,2011.Published August 2011.Originallyapproved in 2000.Last previous edition approved in 2005 as G166 00(2005).DOI:10.1520/G0166-00R11.2For 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 where:F(t)=defined in paragraph 3.1.4t=units of time used for service lifec=scale parameterb=shape parameter3.1.8.1 The shape parameter(b),section 3.1.6,is so calledbecause this parameter determines the overall shape of thecurve.Examples of the effect of this parameter on the distri-bution curve are shown in Fig.1,section 5.3.3.1.8.2 The scale parameter(c),section 3.1.6,is so calledbecause it po