(adsbygoogle = window.adsbygoogle || []).push({}); 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Stochastic process (renewal process)

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**