A machine is made up of two components that operate independently. The lifetime Xi (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}.