A simple case of preventive maintenance decision making with limited historical data

When the operating time until failure of a piece of equipment is a random variable it often makes sense to undertake preventive maintenance at regular intervals. Mathematical models have been available for choosing the optimal preventive maintenance interval given that one assumes no uncertainty about the probability distribution of the operating time until failure, i.e., the distribution is assumed known. This is a questionable assumption, particularly with the recent rapid advances in technology, hence limited historical data on operating times. To provide an initial perspective as to the effects of relaxing this assumption, the authors treat the simplest case of just two possible lifetimes. A dynamic programming formulation is developed together with two much simpler heuristic approaches. The behaviour of the optimal policy, as a function of the parameters involved, provides considerable insight. Moreover, one of the heuristic methods performs in an excellent fashion.