Optimal observation and preventive maintenance schedules for partially observed multi-state deterioration systems with obvious failures.

Abstract

We investigate a maintenance optimization problem with condition-monitoring. Condition-monitoring allows the decision maker to observe some wear-related variable throughout a system's lifetime to more accurately determine its degree of deterioration. We determine when these observations, and subsequent preventive maintenance actions, should be performed to minimize long run average cost per unit time for multi-state deterioration systems with obvious failures. Simplifying assumptions are made to provide an introductory Problem 1 that examines the task of scheduling perfect observations for 2-phase systems. We model this problem as a stochastic dynamic program and present cost rate minimizing policies, as well as satisfying policies, that determine how to efficiently allocate observation resources to a 2-phase system. Our solution approach is based on operating characteristics, which facilitate the exploration of the tradeoff between observation costs and maintenance costs. We also compare a fixed-interval observation policy to a variable-interval policy and consider a method for allocating scarce monitoring resources among a collection of 2-phase systems. The more general Problem 2 examines the problem of adaptively scheduling imperfect observations and preventive maintenance actions for a multi-state Markovian deterioration system. The observations do not reveal the deterioration level with certainty, but are probabilistically related to the deterioration level. Solving such problems can be computationally intensive, and the resulting policies can be complex and irregular. Furthermore, establishing structural results for problems with imperfect information can be difficult. For these reasons, we investigate the underlying structural properties of the analogous no observations and perfect observations policies and then adjust them for use in the imperfect observations case. We model all three of these cases as partially observed Markov decision processes (POMDP's) and provide numerical examples of optimal solutions for each case. A cost-effective heuristic policy for the imperfect observations case is developed and preliminary performance results for three heuristic methods are presented. The use of operating characteristics to represent policy performance is also discussed.