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QM ZG528 L-5

Reliability EngineeringGajanand Gupta

Department of Mechanical Engineering

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Time-Dependent Failre M!del"Chapter - 4

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One of the most proailit! distriution in reliailit!

engineering is "eiull#

$t is characteri%ed ! ha%ard rate function of the form

&or mathematical con'enience is e(pressed as-

T#e $eibll Di"tribti!n

)

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*hape Parameter $f +1 *hape of PD& is similar to e(ponential

$f .) /large 'alues0- *hape is somehat s!mmetrical

li2e normal distriution

$f PD& shape is s2eed $f .1, 0constant - PD& is identical to e(ponential ith(

.13

- *cale Parameter

$nfluences mean and spread of distriution#/4#40

5ariance /4#60

T#e $eibll Di"tribti!n

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Gi'en a desired reliailit! 7,

8hen design life #/4#90

"hen 7.:#;; is referred as

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&or a s!stem comprised of n seriall! related componentsha'ing n independent failure modes, each ha'ing eiull

failure distriution then s!stem failure rate function can

e determined as-

Failre M!de"

1:

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$f s!stem consist of nindependent, seriall! related

components ha'ing identical ha%ard rate functions

8hen the s!stem ha%ard rate is

And

Identi'al $eibll (!mp!nent"

1B

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"hen there is minimum life such that 8, the threeparameter eiull ma! e appropriate#

8he parameter is called as location parameter#

8he 'ariance of distriution is same as to parameter,

hoe'er

8he design life corresponding to reliailit! 7 is-

T#ree )arameter $eibll Di"tribti!n

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Redndan'y *it# $eibll Failre"

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T#an+"

B1