1、Designation: G172 03 (Reapproved 2010)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
2、 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 NOTEEditorially corrected designation and footnote 1 in November 20131. Scope1.1 This guide briefly prese
3、nts some generally accepted methods of statistical analyses that are useful in the interpretation ofaccelerated service life data. It is intended to produce a common terminology as well as developing a common methodology andquantitative expressions relating to service life estimation.1.2 This guide
4、covers the application of theArrhenius equation to service life data. It serves as a general model for determiningrates at usage conditions, such as temperature. It serves as a general guide for determining service life distribution at usagecondition. It also covers applications where more than one
5、variable act simultaneously to affect the service life. For the purposesof this guide, the acceleration model used for multiple stress variables is the Eyring Model. This model was derived from thefundamental laws of thermodynamics and has been shown to be useful for modeling some two variable accel
6、erated service lifedata. It can be extended to more than two variables.1.3 Only those statistical methods that have found wide acceptance in service life data analyses have been considered in thisguide.1.4 The Weibull life distribution is emphasized in this guide and example calculations of situatio
7、ns commonly encountered inanalysis of service life data are covered in detail. It is the intention of this guide that it be used in conjunction with Guide G166.1.5 The accuracy of the model becomes more critical as the number of variables increases and/or the extent of extrapolationfrom the accelera
8、ted stress levels to the usage level increases. The models and methodology used in this guide are shown for thepurpose of data analysis techniques only. The fundamental requirements of proper variable selection and measurement must stillbe met for a meaningful model to result.2. Referenced Documents
9、2.1 ASTM Standards:2G166 Guide for Statistical Analysis of Service Life DataG169 Guide for Application of Basic Statistical Methods to Weathering Tests3. Terminology3.1 Terms Commonly Used in Service Life Estimation:3.1.1 accelerated stress, nthat experimental variable, such as temperature, which is
10、 applied to the test material at levels higherthan encountered in normal use.3.1.2 beginning of life, nthis is usually determined to be the time of delivery to the end user or installation into field service.Exceptions may include time of manufacture, time of repair, or other agreed upon time.3.1.3
11、cdf, nthe cumulative distribution function (cdf), denoted by F(t), represents the probability of failure (or the populationfraction failing) by time = (t). See 3.1.7.3.1.4 complete data, na complete data set is one where all of the specimens placed on test fail by the end of the allocated testtime.1
12、 This guide is under the jurisdiction of ASTM Committee G03 on Weathering and Durability and is the direct responsibility of Subcommittee G03.08 on Service LifePrediction.Current edition approved July 1, 2010. Published July 2010. Originally approved in 2002. Last previous edition approved in 2002 a
13、s G172 - 03.G172 - 02. DOI:10.1520/G0172-03R10.10.1520/G0172-02R10.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM we
14、bsite.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult pri
15、or editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.5 end of life, noccasionally this is s
16、imple 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 so catastrophic or obvious. Examples may include fading, yellowing,cracking, crazing, etc. Such cases need quantitative measurements and agreement between evaluat
17、or and user as to the precisedefinition of failure. For example, when some critical physical parameter (such as yellowing) reaches a pre-defined level. It is alsopossible to model more than one failure mode for the same specimen (that is, the time to reach a specified level of yellowing maybe measur
18、ed on the same specimen that is also tested for cracking).3.1.6 f(t), nthe probability density function (pdf), equals the probability of failure between any two points of time t(1) 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
19、a random unit drawn from the population will fail by time (t).Also F(t) = the decimal fractionof units in the population that will fail by time (t).The decimal fraction multiplied by 100 is numerically equal to the percent failureby time (t).3.1.8 incomplete data, nan incomplete data set is one wher
20、e (1) there are some specimens that are still surviving at theexpiration of the allowed test time, or (2) where one or more specimens is removed from the test prior to expiration of the allocatedtest time. The shape and scale parameters of the above distributions may be estimated even if some of the
21、 test specimens did notfail. There are three distinct cases where this might occur.3.1.8.1 multiple censored, nspecimens that were removed prior to the end of the test without failing are referred to as leftcensored or type II censored. Examples would include specimens that were lost, dropped, misha
22、ndled, damaged or broken due tostresses not part of the test. Adjustments of failure order can be made for those specimens actually failed.3.1.8.2 specimen censored, nspecimens that were still surviving when the test was terminated after a set number of failuresare considered to be specimen censored
23、. This is another case of right censored or type I censoring. See 3.1.8.3.3.1.8.3 time censored, nspecimens that were still surviving when the test was terminated after elapse of a set time areconsidered to be time censored. Examples would include experiments where exposures are conducted for a pred
24、etermined lengthof time. At the end of the predetermined time, all specimens are removed from the test. Those that are still surviving are said tobe censored. This is also referred to as right censored or type I censoring. Graphical solutions can still be used for parameterestimation. A minimum of t
25、en observed failures should be used for estimating parameters (that is, slope and intercept, shape andscale, etc.).3.1.9 material property, ncustomarily, service life is considered to be the period of time during which a system meets criticalspecifications. Correct measurements are essential to prod
26、uce meaningful and accurate service life estimates.3.1.9.1 DiscussionThere exists many ASTM recognized and standardized measurement procedures for determining material properties. Thesepractices have been developed within committees having appropriate expertise, therefore, no further elaboration wil
27、l be provided.3.1.10 R(t), nthe probability that a random unit drawn from the population will survive at least until time (t). Also R(t) = thefraction of units in the population that will survive at least until time (t); R(t) = 1 F(t).3.1.11 usage stress, nthe level of the experimental variable that
28、 is considered to represent the stress occurring in normal use.This value must be determined quantitatively for accurate estimates to be made. In actual practice, usage stress may be highlyvariable, such as those encountered in outdoor environments.3.1.12 Weibull distribution, nfor the purposes of t
29、his guide, the Weibull distribution is represented by the equation:Ft! 512e2StcDb (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 DiscussionThe shape parameter (b), 3.1.12, is so calle
30、d because this parameter determines the overall shape of the curve. Examples of theeffect of this parameter on the distribution curve are shown in Fig. 1.3.1.12.2 DiscussionG172 02 (2010)12The scale parameter (c), 3.1.12, is so called because it positions the distribution along the scale of the time
31、 axis. It is equal to thetime for 63.2 % failure.NOTE 1This is arrived at by allowing t to equal c in Eq 1. This then reduces to Failure Probability = 1 e-1. which further reduces to equal 1 0.368or 0.632.4. Significance and Use4.1 The nature of accelerated service life estimation normally requires
32、that stresses higher than those experienced during serviceconditions are applied to the material being evaluated. For non-constant use stress, such as experienced by time varying weatheroutdoors, it may in fact be useful to choose an accelerated stress fixed at a level slightly lower than (say 90 %
33、of) the maximumexperienced outdoors. By controlling all variables other than the one used for accelerating degradation, one may model theexpected effect of that variable at normal, or usage conditions. If laboratory accelerated test devices are used, it is essential toprovide precise control of the
34、variables used in order to obtain useful information for service life prediction. It is assumed that thesame failure mechanism operating at the higher stress is also the life determining mechanism at the usage stress. It must be notedthat the validity of this assumption is crucial to the validity of
35、 the final estimate.4.2 Accelerated service life test data often show different distribution shapes than many other types of data. This is due to theeffects of measurement error (typically normally distributed), combined with those unique effects which skew service life datatowards early failure tim
36、e (infant mortality failures) or late failure times (aging or wear-out failures).Applications of the principlesin this guide can be helpful in allowing investigators to interpret such data.4.3 The choice and use of a particular acceleration model and life distribution model should be based primarily
37、 on how wellit fits the data and whether it leads to reasonable projections when extrapolating beyond the range of data. Further justification forselecting models should be based on theoretical considerations.NOTE 2Accelerated service life or reliability data analysis packages are becoming more read
38、ily available in common computer software packages.This makes data reduction and analyses more directly accessible to a growing number of investigators. This is not necessarily a good thing as the abilityto perform the mathematical calculation, without the fundamental understanding of the mechanics
39、may produce some serious errors. See Ref (1).35. Data Analysis5.1 OverviewIt is critical to the accuracy of Service Life Prediction estimates based on accelerated tests that the failuremechanism operating at the accelerated stress be the same as that acting at usage stress. Increasing stress(es), su
40、ch as temperature,3 The boldface numbers in parentheses refer to the list of references at the end of this standard.FIG. 1 Effect of the Shape Parameter (b) on the Weibull Probability DensityG172 02 (2010)13to high levels may introduce errors due to several factors. These include, but are not limite
41、d to, a change of failure mechanism,changes in physical state, such as change from the solid to glassy state, separation of homogenous materials into two or morecomponents, migration of stabilizers or plasticisers within the material, thermal decomposition of unstable components andformation of new
42、materials which may react differently from the original material.5.2 A variety of factors act to produce deviations from the expected values. These factors may be of purely a random natureand act to either increase or decrease service life depending on the magnitude and nature of the effect of the f
43、actor. The purity ofa lubricant is an example of one such factor. An oil clean and free of abrasives and corrosive materials would be expected toprolong the service life of a moving part subject to wear.Acontaminated oil might prove to be harmful and thereby shorten servicelife. Purely random variat
44、ion in an aging factor that can either help or harm a service 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 life distributions. Defects are generally thought of as
45、 factors that can onlydecrease service life (that is, monotonically decreasing performance). Thin spots in protective coatings, nicks in extruded wires,chemical contamination in thin metallic films are examples of such defects that can cause an overall failure even though the bulkof the material is
46、far from failure. These factors skew the service life distribution towards early failure times.5.2.2 Factors that skew service life towards greater times also exist. Preventive maintenance on a test material, high quality rawmaterials, reduced impurities, and inhibitors or other additives are such f
47、actors. These factors produce lifetime distributions shiftedtowards increased longevity and are those typically found in products having a relatively long production history.5.3 Failure DistributionThere are two main elements to the data analysis for Accelerated Service Life Predictions. The firstel
48、ement is determining a mathematical description of the life time distribution as a function of time. The Weibull distribution hasbeen found to be the most generally useful. As Weibull parameter estimations are treated in some detail in Guide G166, they willnot be covered in depth here. It is the int
49、ention of this guide that it be used in conjunction with Guide G166. The methodologypresented herein demonstrates how to integrate the information from Guide G166 with accelerated test data. This integrationpermits estimates of service life to be made with greater precision and accuracy as well as in less time than would be required ifthe effect of stress were not accelerated. Confirmation of the accelerated model should be made from field data or data collectedat typical usage conditions.5.3.1 Establishing, in an accelerated time frame, a descr
