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A machine is made up of two components that operate independently. The lifetime X_i (in days) of component i has an exponential distribution with parameter , for i ~ 1,2.

Suppose that the two components are placed in series and that as soon as a component fails, it is replaced by a new one. Let N(t) be the number of replacements in the interval (0,t]. We can show that the stochastic process

Indication. If X₀ is the time between two successive replacements, then we can write that X₀ - min{X₁,X₂}.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M91887462

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