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QM ZG528 L-3

Reliability EngineeringGajanand Gupta

Department of Mechanical Engineering

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Constant Failre Rate Mo!elChapter - 3

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Models useful in describing failure process

-Eponential

- !eibull

-"ormal -#ognormal

$ailure distribution ha%ing constant failure rate is called

exponential probability distribution

Intro!"tion

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&ne of the most common failure distribution in reliabilit'

engineering is eponential or C$( )Constant $ailure

(ate*model+

ssume )t*., t /. 0, /0

hen .222)3+1*

E#$onential Reliability Fn"tion

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222222+)3+4*

5ariance

. 222)3+3*

6tandard de%iation . . M$ 7t implies that %ariabilit' of failure increases as the

reliabilit')M$* increases

E#$onential Reliability Fn"tion

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. . 0+39:

7t means component ha%ing C$( has slightl' better than

one-third chance of sur%i%ing to its mean time to failure

Design life of component ha%ing eponentiall' distributedfailure time can be obtained as-

. (

;ence 222+)3+*

!hen (.0+8 median of distribution is obtained as i+e+.0+9

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micro=a%e transmitter has ehibited a constant failure

rate of 0+0003 failure per operating hour+ $ind out the

reliabilit' o%er a 30 da' continuous operating period+

lso find the M$, med and design life for a reliabilit'

of 0+

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Comple s'stem =ill fail through %arious means

useful anal'sis approach is to separate these failures

according to mechanism or component causing failure

7f is reliabilit' function of ith failure mode then s'stemreliabilit' R(t) is

.(3.6)

Failre Mo!es

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7f failure ne%er occurs prior to some time then is

threshold time or called as guaranteed lifetime+

his is e@ui%alent to re=riting densit' function b'

replacing t=ith t-

$or this probabilit' densit' function becomes

(eliabilit' function =ill be-

T&o (ara%eter E#$onential )istribtion

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$ailure (ate but mean is no longer but is shifted

distance along t ais+

Bsing integration b' parts

he design life

( can be found as-

T&o (ara%eter E#$onential )istribtion

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