Optimal random inspection policy with two types of failures

This paper considers an optimal random inspection policy with two types of failures. The system is checked at, periodic and random times. The failures are classified into two types: Type-1 failure is detected by periodic inspection or random inspection. On the other hand, type-2 failure is detected only by random inspection. However, the cost for one check of random inspection is higher than that of periodic inspection. For example, random inspections are done when the system has finished the successive tasks. Introducing the loss cost elapsed between a, failure and its detection, we obtain the expected cost, and derive analytically optimal interval of periodic inspection which minimizes the expected cost. Numerical examples are given when the times to failure and between random inspections are exponential distribution.