23working_repair

# 23working_repair - Supplement for Repairable System...

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Supplement for Repairable System Reliability PDF = probability_density_function = ft () Reference: Probability and Reliability for Engineers, Miller, TA340.M648 1985 t primarily chapter 15 CDF = cumulative_distribution_function = = () NIST e-book Engineering Statistics Handbook, Ft fx dx 0 sections labelled 8.1.2.2 Reliability or Survival function Reliability_function = probability_unit_survives_beyond_t Rt = 1 = 1 R t or . .. 8.1.2.3 Failure (or Hazard) rate ht ( ) = failure_rate = = conditional probability 1 F t () Rt therefore . .. = R t ()ht now . .. = 1 d = d = dt dt d = = dt = d ( () ln R t ) dt t integrate from 0 to t hx dx = ( ()) ln R t 0 t hx dx exponentiate . . = e 0 t dx therefore . .. = R t = ()e 0 now . . if assume (observe) failure rate h(t) = constant = λ := λ λ t dx := 0 h t ) t t ( − λ ) t := t λ⋅ e ( − λ ) x dx e ( − λ + 1 := 1 e − λ e 0 have exponential assumption of probability of failure times 1 11/27/2006

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exponential pdf and cdf example
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## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.611 taught by Professor Davidburke during the Fall '06 term at MIT.

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23working_repair - Supplement for Repairable System...

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