Answer:[tex]\frac{1}{\mu }+\frac{1}{\lambda }[/tex]
Step-by-step explanation:
If a machine is replaced at some time t, then the expected time until next failure is [tex]\frac{1}{\mu }[/tex]
and the time between the checks is exponentially distributed with rate \lambda, the expected time until next failure is [tex]\frac{1}{\lambda }[/tex]
Because of memory less property of the exponential The answer is
[tex]\frac{1}{\mu }+\frac{1}{\lambda }[/tex]
