Unformatted text preview: Example 24.6 (Derivation of Density Functions from Failure Rates) TRtfbe the density function for a continuous random variable t 2 0 and let F be the correspondingstribution function. Think of the random variable t axenoting the lifetime of a mechanical or electrical component. Then, s&) = R(t) = 1  F(t) = Pr{T > t}, the probability that the component lasts at least t tiine units, is called the reliability function. Given f, F, and R, the failure rate or hazard function Z is defined as The function Z can be thought of as the probability that the.component will fail in 'the next At time units, given that it has not failed up to time t, because the latter conditional probability is equal to Pr(t < T 5 t + At) P r ( t < T < t + A t I T > t ) = P(T > t ) = Z(t) At....
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 Spring '10
 Kutler
 Differential Equations, Microeconomics, Derivative, ORDINARY DIFFERENTIAL EQUATIONS

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