Optimal random and periodic inspection policies

It would be practical and useful to inspect a unit at random times in the case where it works for jobs with successive processing times. This paper considers the inspection model where a unit is checked at both random and periodic times. The total expected cost until the detection of failure is obtained. In particular, when the random times are exponential, optimal policies, which minimize the expected cost, are analytically discussed. Finally, a numerical example is given, and an optimal periodic checking time is computed.