ASTM G172-02(2010)e1
(Guide)Standard Guide for Statistical Analysis of Accelerated Service Life Data
Standard Guide for Statistical Analysis of Accelerated Service Life Data
SIGNIFICANCE AND USE
4.1 The nature of accelerated service life estimation normally requires that stresses higher than those experienced during service conditions are applied to the material being evaluated. For non-constant use stress, such as experienced by time varying weather outdoors, it may in fact be useful to choose an accelerated stress fixed at a level slightly lower than (say 90 % of) the maximum experienced outdoors. By controlling all variables other than the one used for accelerating degradation, one may model the expected effect of that variable at normal, or usage conditions. If laboratory accelerated test devices are used, it is essential to provide precise control of the variables used in order to obtain useful information for service life prediction. It is assumed that the same failure mechanism operating at the higher stress is also the life determining mechanism at the usage stress. It must be noted that the validity of this assumption is crucial to the validity of 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 the effects of measurement error (typically normally distributed), combined with those unique effects which skew service life data towards early failure time (infant mortality failures) or late failure times (aging or wear-out failures). Applications of the principles in 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 on how well it fits the data and whether it leads to reasonable projections when extrapolating beyond the range of data. Further justification for selecting models should be based on theoretical considerations.Note 2—Accelerated service life or reliability data analysis packages are becoming more readily available in common computer software packages. This makes data reduction and analyses more directly a...
SCOPE
1.1 This guide briefly presents some generally accepted methods of statistical analyses that are useful in the interpretation of accelerated service life data. It is intended to produce a common terminology as well as developing a common methodology and quantitative expressions relating to service life estimation.
1.2 This guide covers the application of the Arrhenius equation to service life data. It serves as a general model for determining rates at usage conditions, such as temperature. It serves as a general guide for determining service life distribution at usage condition. It also covers applications where more than one variable act simultaneously to affect the service life. For the purposes of this guide, the acceleration model used for multiple stress variables is the Eyring Model. This model was derived from the fundamental laws of thermodynamics and has been shown to be useful for modeling some two variable accelerated service life data. 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 this guide.
1.4 The Weibull life distribution is emphasized in this guide and example calculations of situations commonly encountered in analysis 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 extrapolation from the accelerated stress levels to the usage level increases. The models and methodology used in this guide are shown for the purpose of data analysis techniques only. The fundamental requirements of proper variable selection and measurement must still be met for a meaningful model to result.
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´1
Designation: G172 − 02 (Reapproved 2010)
Standard Guide for
Statistical Analysis of Accelerated Service Life Data
This standard is issued under the fixed designation G172; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Editorially corrected designation and footnote 1 in November 2013
1. Scope 2. Referenced Documents
1.1 This guide briefly presents some generally accepted 2.1 ASTM Standards:
methods of statistical analyses that are useful in the interpre- G166Guide for Statistical Analysis of Service Life Data
tation of accelerated service life data. It is intended to produce G169Guide for Application of Basic Statistical Methods to
a common terminology as well as developing a common Weathering Tests
methodology and quantitative expressions relating to service
life estimation. 3. Terminology
1.2 This guide covers the application of the Arrhenius 3.1 Terms Commonly Used in Service Life Estimation:
equation to service life data. It serves as a general model for 3.1.1 acceleratedstress,n—thatexperimentalvariable,such
determining rates at usage conditions, such as temperature. It as temperature, which is applied to the test material at levels
serves as a general guide for determining service life distribu- higher than encountered in normal use.
tion at usage condition. It also covers applications where more
3.1.2 beginning of life, n—this is usually determined to be
than one variable act simultaneously to affect the service life.
the time of delivery to the end user or installation into field
For the purposes of this guide, the acceleration model used for
service. Exceptions may include time of manufacture, time of
multiple stress variables is the Eyring Model. This model was
repair, or other agreed upon time.
derivedfromthefundamentallawsofthermodynamicsandhas
3.1.3 cdf, n—the cumulative distribution function (cdf),
been shown to be useful for modeling some two variable
denoted by F(t), represents the probability of failure (or the
accelerated service life data. It can be extended to more than
population fraction failing) by time = (t). See 3.1.7.
two variables.
3.1.4 completedata,n—acompletedatasetisonewhereall
1.3 Only those statistical methods that have found wide
of the specimens placed on test fail by the end of the allocated
acceptance in service life data analyses have been considered
test time.
in this guide.
3.1.5 endoflife,n—occasionallythisissimpleandobvious,
1.4 TheWeibulllifedistributionisemphasizedinthisguide
such as the breaking of a chain or burning out of a light bulb
and example calculations of situations commonly encountered
filament. In other instances, the end of life may not be so
in analysis of service life data are covered in detail. It is the
catastrophic or obvious. Examples may include fading,
intentionofthisguidethatitbeusedinconjunctionwithGuide
yellowing, cracking, crazing, etc. Such cases need quantitative
G166.
measurements and agreement between evaluator and user as to
1.5 The accuracy of the model becomes more critical as the
the precise definition of failure. For example, when some
number of variables increases and/or the extent of extrapola- critical physical parameter (such as yellowing) reaches a
tion from the accelerated stress levels to the usage level
pre-defined level. It is also possible to model more than one
increases. The models and methodology used in this guide are failure mode for the same specimen (that is, the time to reach
shown for the purpose of data analysis techniques only. The
a specified level of yellowing may be measured on the same
fundamental requirements of proper variable selection and
specimen that is also tested for cracking).
measurement must still be met for a meaningful model to
3.1.6 f(t), n—the probability density function (pdf), equals
result.
the probability of failure between any two points of time t
(1)
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
Life Prediction. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
CurrenteditionapprovedJuly1,2010.PublishedJuly2010.Originallyapproved contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
in 2002. Last previous edition approved in 2002 as G172-02. DOI: 10.1520/ Standards volume information, refer to the standard’s Document Summary page on
G0172-02R10. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
G172 − 02 (2010)
dF~t!
3.1.12 Weibull distribution, n—for the purposes of this
and t ; f t 5 . For the normal distribution, the pdf is the
~ !
(2)
dt
guide, the Weibull distribution is represented by the equation:
“bell shape” curve.
t b
2S D
F~t! 51 2 e c (1)
3.1.7 F(t),n—theprobabilitythatarandomunitdrawnfrom
the population will fail by time (t). Also F(t) = the decimal
where:
fraction of units in the population that will fail by time (t).The
F(t) = probability of failure by time (t) as defined in 3.1.7,
decimal fraction multiplied by 100 is numerically equal to the
t = units of time used for service life,
percent failure by time (t).
c = scale parameter, and
b = shape parameter.
3.1.8 incomplete data, n—an incomplete data set is one
where (1) there are some specimens that are still surviving at
3.1.12.1 Discussion—The shape parameter (b), 3.1.12,isso
the expiration of the allowed test time, or (2) where one or
called because this parameter determines the overall shape of
more specimens is removed from the test prior to expiration of
the curve. Examples of the effect of this parameter on the
the allocated test time. The shape and scale parameters of the
distribution curve are shown in Fig. 1.
above distributions may be estimated even if some of the test
3.1.12.2 Discussion—The scale parameter (c), 3.1.12,isso
specimensdidnotfail.Therearethreedistinctcaseswherethis
called because it positions the distribution along the scale of
might occur.
the time axis. It is equal to the time for 63.2% failure.
3.1.8.1 multiple censored, n—specimens that were removed
prior to the end of the test without failing are referred to as left NOTE 1—This is arrived at by allowing t to equal c in Eq 1. This then
-1
reduces to Failure Probability=1− e . which further reduces to equal 1
censored or type II censored. Examples would include speci-
− 0.368 or 0.632.
mens that were lost, dropped, mishandled, damaged or broken
duetostressesnotpartofthetest.Adjustmentsoffailureorder
4. Significance and Use
can be made for those specimens actually failed.
4.1 The nature of accelerated service life estimation nor-
3.1.8.2 specimen censored, n—specimens that were still
mally requires that stresses higher than those experienced
surviving when the test was terminated after a set number of
during service conditions are applied to the material being
failures are considered to be specimen censored. This is
evaluated. For non-constant use stress, such as experienced by
another case of right censored or type I censoring. See 3.1.8.3.
time varying weather outdoors, it may in fact be useful to
3.1.8.3 time censored, n—specimens that were still surviv-
choose an accelerated stress fixed at a level slightly lower than
ing when the test was terminated after elapse of a set time are
(say 90% of) the maximum experienced outdoors. By control-
considered to be time censored. Examples would include
ling all variables other than the one used for accelerating
experiments where exposures are conducted for a predeter-
degradation,onemaymodeltheexpectedeffectofthatvariable
mined length of time.At the end of the predetermined time, all
at normal, or usage conditions. If laboratory accelerated test
specimens are removed from the test. Those that are still
devicesareused,itisessentialtoprovideprecisecontrolofthe
surviving are said to be censored. This is also referred to as
variables used in order to obtain useful information for service
rightcensoredortypeIcensoring.Graphicalsolutionscanstill
life prediction. It is assumed that the same failure mechanism
be used for parameter estimation.Aminimum of ten observed
operating at the higher stress is also the life determining
failuresshouldbeusedforestimatingparameters(thatis,slope
mechanismattheusagestress.Itmustbenotedthatthevalidity
and intercept, shape and scale, etc.).
ofthisassumptioniscrucialtothevalidityofthefinalestimate.
3.1.9 material property, n—customarily, service life is con-
4.2 Accelerated service life test data often show different
sidered to be the period of time during which a system meets
distribution shapes than many other types of data. This is due
critical specifications. Correct measurements are essential to
to the effects of measurement error (typically normally
produce meaningful and accurate service life estimates.
distributed), combined with those unique effects which skew
3.1.9.1 Discussion—There exists many ASTM recognized
service life data towards early failure time (infant mortality
and standardized measurement procedures for determining
failures) or late failure times (aging or wear-out failures).
material properties. These practices have been developed
Applications of the principles in this guide can be helpful in
within committees having appropriate expertise, therefore, no
allowing investigators to interpret such data.
further elaboration will be provided.
4.3 The choice and use of a particular acceleration model
3.1.10 R(t), n—the probability that a random unit drawn
and life distribution model should be based primarily on how
fromthepopulationwillsurviveatleastuntiltime(t).AlsoR(t)
=thefractionofunitsinthepopulationthatwillsurviveatleast well it fits the data and whether it leads to reasonable
projections when extrapolating beyond the range of data.
until time (t); R(t)=1− F(t).
Further justification for selecting models should be based on
3.1.11 usage stress, n—the level of the experimental vari-
theoretical considerations.
able that is considered to represent the stress occurring in
NOTE 2—Accelerated service life or reliability data analysis packages
normal use. This value must be determined quantitatively for
are becoming more readily available in common computer software
accurate estimates to be made. In actual practice, usage stress
packages.Thismakesdatareductionandanalysesmoredirectlyaccessible
may be highly variable, such as those encountered in outdoor
to a growing number of investigators.This is not necessarily a good thing
environments. as the ability to perform the mathematical calculation, without the
´1
G172 − 02 (2010)
FIG. 1 Effect of the Shape Parameter (b) on the Weibull Probability Density
fundamental understanding of the mechanics may produce some serious
service life might lead to a normal, or gaussian, distribution.
errors. See Ref (1).
Such distributions are symmetrical about a central tendency,
usually the mean.
5. Data Analysis
5.2.1 Some non-random factors act to skew service life
5.1 Overview—It is critical to the accuracy of Service Life
distributions. Defects are generally thought of as factors that
Prediction estimates based on accelerated tests that the failure
can only decrease service life (that is, monotonically decreas-
mechanism operating at the accelerated stress be the same as
ing performance). Thin spots in protective coatings, nicks in
that acting at usage stress. Increasing stress(es), such as
extruded wires, chemical contamination in thin metallic films
temperature, to high levels may introduce errors due to several
are examples of such defects that can cause an overall failure
factors. These include, but are not limited to, a change of
even though the bulk of the material is far from failure. These
failure mechanism, changes in physical state, such as change
factors skew the service life distribution towards early failure
from the solid to glassy state, separation of homogenous
times.
materials into two or more components, migration of stabiliz-
5.2.2 Factors that skew service life towards greater times
ers or plasticisers within the material, thermal decomposition
also exist. Preventive maintenance on a test material, high
of unstable components and formation of new materials which
quality raw materials, reduced impurities, and inhibitors or
may react differently from the original material.
other additives are such factors.These factors produce lifetime
5.2 A variety of factors act to produce deviations from the
distributions shifted towards increased longevity and are those
expected values. These factors may be of purely a random
typically found in products having a relatively long production
nature and act to either increase or decrease service life
history.
depending on the magnitude and nature of the effect of the
5.3 Failure Distribution—There are two main elements to
factor. The purity of a lubricant is an example of one such
the data analysis forAccelerated Service Life Predictions. The
factor. An oil clean and free of abrasives and corrosive
first element is determining a mathematical description of the
materials would be expected to prolong the service life of a
life time distribution as a function of time. The Weibull
movingpartsubjecttowear.Acontaminatedoilmightproveto
distribution has been found to be the most generally useful.As
be harmful and thereby shorten service life. Purely random
Weibull parameter estimations are treated in some detail in
variation in an aging factor that can either help or harm a
Guide G166, they will not be covered in depth here. It is the
intentionofthisguidethatitbeusedinconjunctionwithGuide
G166.Themethodologypresentedhereindemonstrateshowto
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this standard. integrate the information from Guide G166 with accelerated
´1
G172 − 02 (2010)
testdata.Thisintegrationpermitsestimatesofservicelifetobe in terms of time rather than rate.As time and rate are inversely
made with greater precision and accuracy as well as in less related, the new expression is formed by changing the sign of
time than would be required if the effect of stress were not the exponent so that the time, t, is:
accelerated. Confirmation of the accelerated model should be ∆H/kT
Time 5 A'e (3)
made from field data or data collected at typical usage
5.4.5 The time element used in the Eq 3 is arbitrary. It can
conditions.
be the time for th
...
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. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: G172 − 03 (Reapproved 2010) G172 − 02 (Reapproved 2010)
Standard Guide for
Statistical Analysis of Accelerated Service Life Data
This standard is issued under the fixed designation G172; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Editorially corrected designation and footnote 1 in November 2013
1. Scope
1.1 This guide briefly presents some generally accepted methods of statistical analyses that are useful in the interpretation of
accelerated service life data. It is intended to produce a common terminology as well as developing a common methodology and
quantitative expressions relating to service life estimation.
1.2 This guide covers the application of the Arrhenius equation to service life data. It serves as a general model for determining
rates at usage conditions, such as temperature. It serves as a general guide for determining service life distribution at usage
condition. It also covers applications where more than one variable act simultaneously to affect the service life. For the purposes
of this guide, the acceleration model used for multiple stress variables is the Eyring Model. This model was derived from the
fundamental laws of thermodynamics and has been shown to be useful for modeling some two variable accelerated service life
data. 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 this
guide.
1.4 The Weibull life distribution is emphasized in this guide and example calculations of situations commonly encountered in
analysis 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 extrapolation
from the accelerated stress levels to the usage level increases. The models and methodology used in this guide are shown for the
purpose of data analysis techniques only. The fundamental requirements of proper variable selection and measurement must still
be met for a meaningful model to result.
2. Referenced Documents
2.1 ASTM Standards:
G166 Guide for Statistical Analysis of Service Life Data
G169 Guide for Application of Basic Statistical Methods to Weathering Tests
3. Terminology
3.1 Terms Commonly Used in Service Life Estimation:
3.1.1 accelerated stress, n—that experimental variable, such as temperature, which is applied to the test material at levels higher
than encountered in normal use.
3.1.2 beginning of life, n—this 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 cdf, n—the cumulative distribution function (cdf), denoted by F(t), represents the probability of failure (or the population
fraction failing) by time = (t). See 3.1.7.
3.1.4 complete data, n—a complete data set is one where all of the specimens placed on test fail by the end of the allocated test
time.
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 Life
Prediction.
Current edition approved July 1, 2010. Published July 2010. Originally approved in 2002. Last previous edition approved in 2002 as G172 - 03.G172 - 02. DOI:
10.1520/G0172-03R10.10.1520/G0172-02R10.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
G172 − 02 (2010)
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 bulb
filament. 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 evaluator and user as to the precise
definition of failure. For example, when some critical physical parameter (such as yellowing) reaches a pre-defined level. It is also
possible to model more than one failure mode for the same specimen (that is, the time to reach a specified level of yellowing may
be measured on the same specimen that is also tested for cracking).
3.1.6 f(t), n—the probability density function (pdf), equals the probability of failure between any two points of time t and t ;
(1) (2)
dF t
~ !
f~t!5 . For the normal distribution, the pdf is the “bell shape” curve.
dt
3.1.7 F(t), n—the probability that a random unit drawn from the population will fail by time (t). Also F(t) = the decimal fraction
of units in the population that will fail by time (t). The decimal fraction multiplied by 100 is numerically equal to the percent failure
by time (t).
3.1.8 incomplete data, n—an incomplete data set is one where (1) there are some specimens that are still surviving at the
expiration of the allowed test time, or (2) where one or more specimens is removed from the test prior to expiration of the allocated
test time. The shape and scale parameters of the above distributions may be estimated even if some of the test specimens did not
fail. There are three distinct cases where this might occur.
3.1.8.1 multiple censored, n—specimens that were removed prior to the end of the test without failing are referred to as left
censored or type II censored. Examples would include specimens that were lost, dropped, mishandled, damaged or broken due to
stresses not part of the test. Adjustments of failure order can be made for those specimens actually failed.
3.1.8.2 specimen censored, n—specimens that were still surviving when the test was terminated after a set number of failures
are considered to be specimen censored. This is another case of right censored or type I censoring. See 3.1.8.3.
3.1.8.3 time censored, n—specimens that were still surviving when the test was terminated after elapse of a set time are
considered to be time censored. Examples would include experiments where exposures are conducted for a predetermined length
of time. At the end of the predetermined time, all specimens are removed from the test. Those that are still surviving are said to
be censored. This is also referred to as right censored or type I censoring. Graphical solutions can still be used for parameter
estimation. A minimum of ten observed failures should be used for estimating parameters (that is, slope and intercept, shape and
scale, etc.).
3.1.9 material property, n—customarily, service life is considered to be the period of time during which a system meets critical
specifications. Correct measurements are essential to produce meaningful and accurate service life estimates.
3.1.9.1 Discussion—
There exists many ASTM recognized and standardized measurement procedures for determining material properties. These
practices have been developed within committees having appropriate expertise, therefore, no further elaboration will be provided.
3.1.10 R(t), n—the probability that a random unit drawn from the population will survive at least until time (t). Also R(t) = the
fraction of units in the population that will survive at least until time (t); R(t) = 1 − F(t).
3.1.11 usage stress, n—the level of the experimental variable that 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 highly
variable, such as those encountered in outdoor environments.
3.1.12 Weibull distribution, n—for the purposes of this guide, the Weibull distribution is represented by the equation:
t b
S D
F t 5 12 e c (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, and
b = shape parameter.
3.1.12.1 Discussion—
The shape parameter (b), 3.1.12, is so called because this parameter determines the overall shape of the curve. Examples of the
effect of this parameter on the distribution curve are shown in Fig. 1.
3.1.12.2 Discussion—
´1
G172 − 02 (2010)
FIG. 1 Effect of the Shape Parameter (b) on the Weibull Probability Density
The scale parameter (c), 3.1.12, is so called because it positions the distribution along the scale of the time axis. It is equal to the
time for 63.2 % failure.
-1
NOTE 1—This is arrived at by allowing t to equal c in Eq 1. This then reduces to Failure Probability = 1 − e . which further reduces to equal 1 − 0.368
or 0.632.
4. Significance and Use
4.1 The nature of accelerated service life estimation normally requires that stresses higher than those experienced during service
conditions are applied to the material being evaluated. For non-constant use stress, such as experienced by time varying weather
outdoors, it may in fact be useful to choose an accelerated stress fixed at a level slightly lower than (say 90 % of) the maximum
experienced outdoors. By controlling all variables other than the one used for accelerating degradation, one may model the
expected effect of that variable at normal, or usage conditions. If laboratory accelerated test devices are used, it is essential to
provide precise control of the variables used in order to obtain useful information for service life prediction. It is assumed that the
same failure mechanism operating at the higher stress is also the life determining mechanism at the usage stress. It must be noted
that the validity of this assumption is crucial to the validity of 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 the
effects of measurement error (typically normally distributed), combined with those unique effects which skew service life data
towards early failure time (infant mortality failures) or late failure times (aging or wear-out failures). Applications of the principles
in 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 on how well
it fits the data and whether it leads to reasonable projections when extrapolating beyond the range of data. Further justification for
selecting models should be based on theoretical considerations.
NOTE 2—Accelerated service life or reliability data analysis packages are becoming more readily 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 ability
to perform the mathematical calculation, without the fundamental understanding of the mechanics may produce some serious errors. See Ref (1).
5. Data Analysis
5.1 Overview—It is critical to the accuracy of Service Life Prediction estimates based on accelerated tests that the failure
mechanism operating at the accelerated stress be the same as that acting at usage stress. Increasing stress(es), such as temperature,
The boldface numbers in parentheses refer to the list of references at the end of this standard.
´1
G172 − 02 (2010)
to high levels may introduce errors due to several factors. These include, but are not limited 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 more
components, migration of stabilizers or plasticisers within the material, thermal decomposition of unstable components and
formation of new 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 nature
and act to either increase or decrease service life depending on the magnitude and nature of the effect of the factor. The purity of
a lubricant is an example of one such factor. An oil clean and free of abrasives and corrosive materials would be expected to
prolong the service life of a moving part subject to wear. A contaminated oil might prove to be harmful and thereby shorten service
life. Purely random variation 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 factors that can only
decrease 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 bulk
of the material is 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 raw
materials, reduced impurities, and inhibitors or other additives are such factors. These factors produce lifetime distributions shifted
towards increased longevity and are those typically found in products having a relatively long production history.
5.3 Failure Distribution—There are two main elements to the data analysis for Accelerated Service Life Predictions. The first
element is determining a mathematical description of the life time distribution as a function of time. The Weibull distribution has
been found to be the most generally useful. As Weibull parameter estimations are treated in some detail in Guide G166, they will
not be covered in depth here. It is the intention of this guide that it be used in conjunction with Guide G166. The methodology
presented herein demonstrates how to integrate the information from Guide G166 with accelerated test
...
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