in-class-Reliability-sol

in-class-Reliability-sol - ESI 6321 APPLIED PROBABILITY...

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APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 March 15, 2008 IN-CLASS ASSIGNMENT - SOLUTIONS Slide 10 If the design life is 1 year, the minimum required reliability is apparently r (1) = exp ! 0.048 ( ) " 0.953. If the minimum required reliability is 90%, the design life is the solution to exp( ! 0.04 t ! 0.008 t 2 ) = 0.90 ! 0.04 t ! 0.008 t 2 = ln(0.90) 0.008 t 2 + 0.04 t + ln(0.90) = 0 i.e., the design life is t = ! 0.04 + 0.04 2 ! 4 " 0.008 " ln(0.90) 2 " 0.008 # 1.91 years. (Note that the other solution to the quadratic equation is negative and therefore meaningless.) Slide 48 The system reliability function is given by r ( t ) = r 1 ( t ) ! 1 " 1 " r 2 ( t ) ! r 3 ( t ) ( ) ! 1 " r 4 ( t ) ( ) ! 1 " r 5 ( t ) ! r 6 ( t ) ( ) { } . Slide 49 The system reliability function is given by r ( t ) = r 1 ( t ) ! 1 " 1 " r 2 ( t ) ! r 3 ( t ) + r # 3 ( t " s ) f 3 ( s ) ds 0 t $ % ( ) * + , - - . / 0 0 ! 1
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This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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in-class-Reliability-sol - ESI 6321 APPLIED PROBABILITY...

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