Optimal scheduling of fallible inspections

This paper gives the exact optimal solution to the problem of designing inspection schedules with fallible and time-consuming test procedures. The optimality criterion is designed to achieve a balance between the cost of inspections and the cost of undetected failure. The solution is derived in continuous time, with arbitrary failure distribution, and is based on infinite-horizon dynamic programming with time-dependent utilities, and with an additional optimization with respect to initial conditions. Results include uniqueness and monotonicity properties of the optimal solution, as well as computational algorithms.