# ASTM G172-02 (Reapproved 2010)e1

Designation: G172 − 02 (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.ε1NOTE—Editorially 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, n—that experimental variable, suchas temperature, which is applied to the test material at levelshigher than encountered in normal use.3.1.2 beginning of life, n—this 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, n—the 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, n—a 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, n—occasionally 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), n—the 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 service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1and t(2); f~t!5dF~t!dt. For the normal distribution, the pdf is the“bell shape” curve.3.1.7 F(t), n—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).3.1.8 incomplete data, n—an incomplete data set is onewhere (1) there are some specimens that are still surviving atthe expiration of the allowed test time, or (2) where one ormore specimens is removed from the test prior to expiration ofthe allocated test time. The shape and scale parameters of theabove distributions may be estimated even if some of the testspecimens did not fail. There are three distinct cases where thismight occur.3.1.8.1 multiple censored, n—specimens that were removedprior to the end of the test without failing are referred to as leftcensored or type II censored. Examples would include speci-mens that were lost, dropped, mishandled, damaged or brokendue to stresses not part of the test.Adjustments of failure ordercan be made for those specimens actually failed.3.1.8.2 specimen censored, n—specimens that were stillsurviving when the test was terminated after a set number offailures are considered to be specimen censored. This isanother case of right censored or type I censoring. See 3.1.8.3.3.1.8.3 time censored, n—specimens that were still surviv-ing when the test was terminated after elapse of a set time areconsidered to be time censored. Examples would includeexperiments where exposures are conducted for a predeter-mined length of time.At the end of the predetermined time, allspecimens are removed from the test. Those that are stillsurviving are said to be censored. This is also referred to asright censored or type I censoring. Graphical solutions can stillbe used for parameter estimation. A minimum of ten observedfailures should be used for estimating parameters (that is, slopeand intercept, shape and scale, etc.).3.1.9 material property, n—customarily, service life is con-sidered to be the period of time during which a system meetscritical specifications. Correct measurements are essential toproduce meaningful and accurate service life estimates.3.1.9.1 Discussion—There exists many ASTM recognizedand standardized measurement procedures for determiningmaterial properties. These practices have been developedwithin committees having appropriate expertise, therefore, nofurther elaboration will be provided.3.1.10 R(t), n—the probability that a random unit drawnfrom the 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); R(t)=1−F(t).3.1.11 usage stress, n—the level of the experimental vari-able that is considered to represent the stress occurring innormal use. This value must be determined quantitatively foraccurate estimates to be made. In actual practice, usage stressmay be highly variable, such as those encountered in outdoorenvironments.3.1.12 Weibull distribution, n—for the purposes of thisguide, the Weibull distribution is represented by the equation:F~t! 5 1 2 e2StcDb(1)where:F(t) = probability of failure by time (t) as defined in 3.1.7,t = units of time used for service life,c = scale parameter, andb = shape parameter.3.1.12.1 Discussion—The shape parameter (b), 3.1.12,issocalled because this parameter determines the overall shape ofthe curve. Examples of the effect of this parameter on thedistribution curve are shown in Fig. 1.3.1.12.2 Discussion—The scale parameter (c), 3.1.12,issocalled because it positions the distribution along the scale ofthe time axis. It is equal to the time for 63.2 % failure.NOTE 1—This is arrived at by allowing t to equal c in Eq 1. This thenreduces to Failure Probability=1−e-1. which further reduces to equal 1− 0.368 or 0.632.4. Significance and Use4.1 The nature of accelerated service life estimation nor-mally requires that stresses higher than those experiencedduring service conditions are applied to the material beingevaluated. For non-constant use stress, such as experienced bytime varying weather outdoors, it may in fact be useful tochoose an accelerated stress fixed at a level slightly lower than(say 90 % of) the maximum experienced outdoors. By control-ling all variables other than the one used for acceleratingdegradation, one may model the expected effect of that variableat normal, or usage conditions. If laboratory accelerated testdevices are used, it is essential to provide precise control of thevariables used in order to obtain useful information for servicelife prediction. It is assumed that the same failure mechanismoperating at the higher stress is also the life determiningmechanism at the usage stress. It must be noted that the validityof this assumption is crucial to the validity of the final estimate.4.2 Accelerated service life test data often show differentdistribution shapes than many other types of data. This is dueto the effects of measurement error (typically normallydistributed), combined with those unique effects which skewservice life data towards early failure time (infant mortalityfailures) or late failure times (aging or wear-out failures).Applications of the principles in this guide can be helpful inallowing investigators to interpret such data.4.3 The choice and use of a particular acceleration modeland life distribution model should be based primarily on howwell it fits the data and whether it leads to reasonableprojections when extrapolating beyond the range of data.Further justification for selecting models should be based ontheoretical considerations.NOTE 2—Accelerated service life or reliability data analysis packagesare becoming more readily available in common computer softwarepackages.This makes data reduction and analyses more directly accessibleto a growing number of investigators. This is not necessarily a good thingas the ability to perform the mathematical calculation, without theG172 − 02 (2010)´12fundamental understanding of the mechanics may produce some seriouserrors. See Ref (1).35. Data Analysis5.1 Overview—It is critical to the accuracy of Service LifePrediction estimates based on accelerated tests that the failuremechanism operating at the accelerated stress be the same asthat acting at usage stress. Increasing stress(es), such astemperature, to high levels may introduce errors due to severalfactors. These include, but are not limited to, a change offailure mechanism, changes in physical state, such as changefrom the solid to glassy state, separation of homogenousmaterials into two or more components, migration of stabiliz-ers or plasticisers within the material, thermal decompositionof unstable components and formation of new materials whichmay react differently from the original material.5.2 A variety of factors act to produce deviations from theexpected values. These factors may be of purely a randomnature and act to either increase or decrease service lifedepending on the magnitude and nature of the effect of thefactor. The purity of a lubricant is an example of one suchfactor. An oil clean and free of abrasives and corrosivematerials would be expected to prolong the service life of amoving part subject to wear.Acontaminated oil might prove tobe harmful and thereby shorten service life. Purely randomvariation in an aging factor that can either help or harm aservice life might lead to a normal, or gaussian, distribution.Such distributions are symmetrical about a central tendency,usually the mean.5.2.1 Some non-random factors act to skew service lifedistributions. Defects are generally thought of as factors thatcan only decrease service life (that is, monotonically decreas-ing performance). Thin spots in protective coatings, nicks inextruded wires, chemical contamination in thin metallic filmsare examples of such defects that can cause an overall failureeven though the bulk of the material is far from failure. Thesefactors skew the service life distribution towards early failuretimes.5.2.2 Factors that skew service life towards greater timesalso exist. Preventive maintenance on a test material, highquality raw materials, reduced impurities, and inhibitors orother additives are such factors. These factors produce lifetimedistributions shifted towards increased longevity and are thosetypically found in products having a relatively long productionhistory.5.3 Failure Distribution—There are two main elements tothe data analysis for Accelerated Service Life Predictions. Thefirst element is determining a mathematical description of thelife time distribution as a function of time. The Weibulldistribution has been found to be the most generally useful. AsWeibull parameter estimations are treated in some detail inGuide G166, they will not be covered in depth here. It is theintention of this guide that it be used in conjunction with GuideG166. The methodology presented herein demonstrates how tointegrate the information from Guide G166 with accelerated3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 1 Effect of the Shape Parameter (b) on the Weibull Probability DensityG172 − 02 (2010)´13test data. This integration permits estimates of service life to bemade with greater precision and accuracy as well as in lesstime than would be required if the effect of stress were notaccelerated. Confirmation of the accelerated model should bemade from field data or data collected at typical usageconditions.5.3.1 Establishing, in an accelerated time frame, a descrip-tion of the distribution of frequency (or probability) of failureversus time in service is the objective of this guide. Determi-nation of the shape of this distribution as well as its positionalong the time scale axis is the principal criteria for estimatingservice life.5.4 Acceleration Model—The most common model forsingle variable accelerations is the Arrhenius model. It wasdetermined empirically from observations made by the Swed-ish scientist S. A. Arrhenius. As it is one that is oftenencountered in accelerated testing it will be used as thefundamental model for single variables accel