L10_ECE4001_Fall_2008

L10_ECE4001_Fall_2008 - Solve this problem: Lecture 10...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Slide #1 ECE 4001 L10 © 2008 Lecture 10 Reliability measures and prediction System reliability Slide #2 ECE 4001 L10 © 2008 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 © 2008 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 = 0 It follows that: ( ) ( ) t F t f d τ = Slide #4 ECE 4001 L10 © 2008 Define R(t) as: R(t) = 1 - F(t), or R(t) reliabilit + F(t y ) = 1 ( ) ( ) 0 ( ) ( ) Differentiating gives d d R t F t dt dt d d R t F t dt dt + = = -
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Slide #5 ECE 4001 L10 © 2008 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 © 2008 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 © 2008 [ ] ( ) ( ) ( ) ln d dt h t dt R R h t h t dt R A R Ae - - = - = + = ( ) 1, since 1 at 0 h t dt A R t R e - = = = = Slide #8 ECE 4001 L10 © 2008 Bath Tub Model for h(t) (Hyman)
Background image of page 2
Slide #9 ECE 4001 L10 © 2008 ( ) Suppose failure rate ( ) = λ = constant / then, system reliability = 1/ mean time to failure h t dt h t t t R e e e λ τ - = - - = = = = = O O O / good units unit will Thus, if have N 0 then N remain N = N N at time where: at t t t t e e - - = =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

L10_ECE4001_Fall_2008 - Solve this problem: Lecture 10...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online