04_Constant+Failure+Rates_Problems.doc

1 1 iii design life for a system reliability of 099

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1 1 (iii). Design life for a system reliability of 0.99, 99 . 0 ) ( des s t e t R days t des 09 . 1 00921 . 0 ) 99 . 0 ln( 2. Failure on demand, with CFR Operating time, . min 20 o t Idle time, . min 40 i t Operating failure rate, 01 . 0 o Idle failure rate, 0002 . 0 i Failure on demand, 03 . 0 p hour t t p t t t t t t i o o i o o i i o i eff / 033467 . 0 1 03 . 0 01 . 0 * 60 20 0002 . 0 * 60 40 2
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Reliability for 24 hrs of operation, t eff e t R * ) ( 4479 . 0 ) 24 ( 24 * 033467 . 0 e R 3. (i). CFR System, hrs MTTF 5 1 5 1 1 1 1 MTTF and 5 1 1 2 2 MTTF 40 . 0 5 / 2 2 1 s Reliability for first 2 hrs of operation, t s e R ) 2 ( 4493 . 0 ) 2 ( 2 * 40 . 0 e R Therefore, failure probability, ) 2 ( 1 ) 2 ( R F 5506 . 0 4493 . 0 1 ) 2 ( F (ii). If the failed batteries are immediately replaced, then the failure follows a Poisson distribution. Therefore, 2642 . 0 ! 1 ) 5 * 2 . 0 ( ! 0 ) 5 * 2 . 0 ( 1 ! ) ( 1 )] 1 ( ) 0 ( [ 1 ) 2 ( 1 0 5 * 2 . 0 1 1 e i t e P P F i i t 4. Active redundant system with: 00034 . 0 1 and, 00034 . 0 2 t t t t t e e t R e e e t R 00068 . 0 00034 . 0 2 2 2 ) ( 2 ) 1 ( 1 ) ( Reliability over 30 days (30*24=720hrs), 95285 . 0 2 ) 720 ( 720 * 00068 . 0 720 * 00034 . 0 e e R hrs MTTF 7 . 4411 00034 . 0 5 . 1 5 . 1 For a single component, 7828 . 0 ) 720 ( 720 * 00034 . 0 1 e R , 22% increase in reliability due to redundancy. 3 1 2
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Hazard rate function, ) ( 1 . ) ( ) ( ) ( ) ( t R dt t dR t R t f t ) 50 . 0 1 ( ) 1 ( 00034 . 0
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