app8_hazard_func

app8_hazard_func - Application Example 8 (hazard function)...

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Application Example 8 (hazard function) OLD BETTER THAN NEW, NEW BETTER THAN OLD. .. If a component or a system is subjected to a random environment, its reliability can be defined in terms of the random variable T = time to failure. In fact, the reliability of the system at any given time t is simply Reliability at t = P[no failure before t] = P[T > t] = 1 - F T (t) (1) where F T is the cumulative distribution function (CDF) of T. An alternative characterization of component or system reliability is through the so-called hazard function h(t), which is defined such that h(t)dt is the probability that failure occurs in the time interval (t, t+dt), given that no failure occurred prior to t. First we show how h(t) is related to the CDF F T (t) and the PDF f T (t) of T and then comment on other properties of the function h(t). • h(t) can be obtained from F T (t) and f T (t) as h(t) = f T (t) (2) 1 F T (t) In fact, using the definition of conditional probability,
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h(t)dt = P failure in (t,t + dt) no failure prior to t ] = Pt < T t + dt [ T > t ] [ ( [ Pt < T t + dt ) ( T > t ) ] (3) = PT > t ] [ Pt < T t + dt ) ] [ ( = PT > t ] [ f
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This note was uploaded on 02/27/2008 for the course PTE 461 taught by Professor Donhill during the Fall '07 term at USC.

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app8_hazard_func - Application Example 8 (hazard function)...

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