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Homework Help: Stochastic process (renewal process)

  1. Nov 19, 2008 #1
    A component in a manufacturing process breaks down regulary and needs to be replaced by a new component. Assume that the lifetimes of components are i.i.d. random variables. The company adopts this policy: a component is replaced when it breaks down or after it has operated for time "a", whichever comes first. "a" is a fixed positive parameter.

    Question> Assume the lifetime of the component is exponentially distributed with rate "alpha". Compute the mean time between replacements. Let B(t) be the forward recurrence time so that P{B(t)>x} is the probability that there will be no replacement for another x time units. Find the lim P{B(t)>x} when t goes to infinity.

    I thought that this would be solved by inspection paradox. Right?
  2. jcsd
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