Earlier Switch Research Articles

Optimal maintenance policies under deterministic deterioration and stochastic failure

AbstractThompson1 considers a linear control model to ascertain the optimal preventive maintenance policy for production equipment and, simultaneously, its optimal sale date. He assumes age‐dependent deterministic continuous deterioration, production rate and linear efficiency of maintenance expenditures. In the present paper we first consider a linear maintenance model under a budget constraint. The impact of such a restriction is an earlier switch in the optimal bang‐bang policy. Then a non‐linear, non‐autonomous generalization of Thompson's model is analysed by the maximum principle. The optimal maintenance policy is shown to be downward sloping provided that in each time period the production rate is greater than the sum of interest and deterioration rate. The monotonicity of the optimal rate of preventive maintenance holds also under the additional possibility of random machine failure provided the production rate is greater than the sum of the rate of interest, the rate of deterioration and the rate of stochastic failure at each age. Moreover, it is shown that the higher the failure rate the smaller the optimal expenditures for preventive maintenance at any fixed age of the machine. In particular, the optimal maintenance rate at age t in a model without random failure is greater than those in any case including stochastic failure at the same age.