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i4" ‘4‘ L6! 3 f‘ti’f‘fhé? { cl 2 m <21; Vv«j/J' {21' [y f 4
As mentioned previously. the Vv'eibull distribution is often used to model the time until
failure of many different physical systems The parameters in the distribution provide a
great deal of ﬂexibility to model systems in which the number of failures increases with
time (bearing wear), decreases with time (some semiconductors), or remains constant with
time (failures caused by external shocks to the system) ‘ M W” l
«Eifinition l The random variable X withprobabili‘ty density function i _ _ L ‘3 x~\a'l ‘ i
,(x; 5, l = r (: Emma. forx .> O  f“ B ‘ a a) ‘ .,  (4—17) : has a Weibull distribution with scale parameter 5 > 0 and shapepararnetet ‘ i {5 > O. ‘ ‘ t
l , V A, _ ; The ﬂexibility of the W eibull distribution is illustrated by the graphs of selected probability
density functions in Fig 4—24. By inspecting the probability density function. it is seen
that when 13 = l, the Weibull distribution is identical to the exponential distribution The following result can be obtained. ’ Figure Weibull probability density functions IfX has ai‘IWeibullidisitibution ~ '  1 ii l ' ' V “ i r f
_ I ‘ I . 7 V g I I ‘ parameteisﬁ and ,thei th ‘ r
:‘_ “ distribution functionuof Xis ; u  ' i ‘ V e crud“mama” In S. inx):1‘_, gal/é)? 3 f: 4.5 Other Continuous Distributions 155 for; oz, 5) ONhOOO Figure 4.28 Graphs of WeibuH odf’s ' Integrating to obtain E(X) and quz) yields The, computation of u and 03 thus necessitates using a table of tho gamma function. Probabé WeibUT] 1M6 .188 .818 __w,w.._WijwmwmmTwmwI § .am LJX B / / g
L.LJWEZLJ~LJLJMAMLJ_1{LJWLJWLJWJWLJ_JMLWLJVAMLJWLH 8.5 7 7.5 8 8.5 S 9.5 LnﬁStress CMPaJJ be ...
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This note was uploaded on 02/01/2012 for the course M&AE 455 at Cornell University (Engineering School).
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