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Unformatted text preview: 1 Slide #1 ECE 4001 L10 2011 Lecture 10 Reliability measures and prediction System reliability Slide #2 ECE 4001 L10 2011 Solve this problem: Your company has developed a new microcontroller. A lot of 1000 units are tested for 2000 hours, after which 500 good units remain. What is the is the probability that one unit will have failed after in the first 100 hours of operation? Slide #3 ECE 4001 L10 2011 Probability of Failure Let F(t) be the define the probability of failure probability fa f(t) as: ilure den ( ) sity ( ) d f t F t dt = It follows that: ( ) ( ) t F t f d = Slide #4 ECE 4001 L10 2011 Define R(t) as: R(t) = 1  F(t), or R(t) reliabilit + F(t y ) = 1 ( ) ( ) ( ) ( ) Differentiating gives d d R t F t dt dt d d R t F t dt dt + = =  2 Slide #5 ECE 4001 L10 2011 O F S F O S number of failures per unit time t Total failed survived number of units at time t=0 Number of units at time t Number of units at time t Define h per unit failure ra (t) a te s : ( ) = N N N N N + N h t = = = = otal units remaining Slide #6 ECE 4001 L10 2011 number of failures per unit time ( ) total units remaining [ ] [ ( / )] / [ ] 1 ( ) ( ) ( ) O S F S S S O S O h t d dt N N d dt N d dt N N N N d dt N N R R h t h t h t = = = = =  Slide #7 ECE 4001 L10 2011 [ ] ( ) ( ) ( ) ln d dt h t dt R R h t h t dt R A R Ae = = + = ( ) 1, since 1 at h t dt A R t R e = = = = Slide #8 ECE 4001 L10 2011 Bath Tub Model for h(t) (Hyman) 3 Slide #9 ECE 4001 L10 2011 ( ) Suppose failure rate ( ) = = constant / then, system reliability = 1/ mean time to failure h t dt h t t t R e e e  = = = = = = O O O / good units...
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 Spring '09
 FRAZIER

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