Random inspection schedules with non-decreasing intensity

The problem of minimizing expected cost until detection of failure is addressed here, using random checking (inspection) schedules. Non-homogeneous Poisson checking processes with continuous non-decreasing intensity are investigated. An approximation of the original problem, in the form of an optimal control problem, is discussed. An optimal solution is proved to exist and then it is characterized, using Pontryagin’s Maximum Principle.