Probability Bounds in Replacement Policies for Markov Systems

The precise costs of operating a stationary finite Markov system are assumed undefined. It is only known that the cost of failure is orders of magnitude higher than the cost of replacement, and that all other costs are relatively negligible. The problem considered is the maximisation of the expected length of time between replacements subject to bounds on the average hazard throughout the remaining part of the replacement cycle whenever the system is not replaced. The solution is shown to be a unique pure strategy, and a computation algorithm is presented which constitutes an extension of Howard's policy iteration principle to considerations of feasibility. A sensitivity analysis indicates the range of the cost parameters under which the same solution would be optimal for a standard minimum-cost problem. The two approaches thus appear to be essentially equivalent.