On a class of optimal preventive replacement policies of systems subject to shocks

A system subject to a conditioned Poisson stream of shocks is proposed in which the intensity is a Markov chain (representing the cumulative damage level) assuming the values α1, α2 and α3 with α1 < α2 < α3. The conditioned Poisson stream of shocks is specified by assuming that a shock results in the intensity making a transition to the next higher value. In the absence of shocks the intensity representing the damage level, which is a process by itself, has a propensity to move down in its state space (representing the repair facility in operation), the residence time in any state i being exponentially distributed with parameter vi. Each shock weakens the system, making it more expensive to run. The system is replaced at a fixed time T. The optimal period T* is obtained, minimizing the expected cost per unit time. Higher order characteristics of the process and certain other variations of interest are spelt out. © 1988.