A risk-sensitive approach to total productive maintenance

While risk-sensitive (RS) approaches for designing plans of total productive maintenance are critical in manufacturing systems, there is little in the literature by way of theoretical modeling. Developing such plans often requires the solution of a discrete-time stochastic control-optimization problem. Renewal theory and Markov decision processes (MDPs) are commonly employed tools for solving the underlying problem. The literature on preventive maintenance, for the most part, focuses on minimizing the expected net cost, and disregards issues related to minimizing risks. RS maintenance managers employ safety factors to modify the risk-neutral solution in an attempt to heuristically accommodate elements of risk in their decision making. In this paper, our efforts are directed toward developing a formal theory for developing RS preventive-maintenance plans. We employ the Markowitz paradigm in which one seeks to optimize a function of the expected cost and its variance. In particular, we present (i) a result for an RS approach in the setting of renewal processes and (ii) a result for solving an RS MDP. We also provide computational results to demonstrate the efficacy of these results. Finally, the theory developed here is of sufficiently general nature that can be applied to problems in other relevant domains.