Extensions and characterization of optimal maintenance policies for multistate partially observed Markovian systems

This research aims at modeling and characterizing optimal maintenance policies for complex deteriorating systems. Such systems widely exist in manufacturing enterprises where it has been gaining the interest of researchers for many decades. Representing complex systems as multi-state systems has been the trend in the literature (Derman, 1962), (Hopp and Wu, 1990) and (Maillart, 2006). Markov Decision Process (MDP) and Partially Observed Markov Decision Process (POMDP) have been used as the general frame to model and represent such systems.;The main objective of this work is to characterize optimal maintenance policies for multistate systems over the systems state occupancy vectors ordered by the first order stochastic dominance. New set of conditions to guarantee the existence of optimal threshold-type maintenance policies are provided. The main advantage of the developed conditions is ensuring the first order stochastic dominance to survive conditioning. As a new approach, this is achieved by developing new relations with other useful partial orders which were not considered for this problem before, namely, the reverse hazard rate and the component wise dominance partial orders. For the sake of illustration, a two-state model is provided first, and then it is extended to the case of n-states.;In order to link maintenance, operation and quality, a new model within the POMDP framework is formulated. The model uses Overall Systems Effectiveness (OSE) as a criterion. OSE combines systems availability, process rate and quality rate in a composite criterion. This provides a mechanism that ties maintenance and operation through the process rate. In such situation the optimal action will be a maintenance action coupled with a specific system speed that reflects the process rate.;Condition-based maintenance is usually based on measuring or observing systems conditions; however, measurements are not error free. The impact of measurement errors on the POMDP optimal maintenance polices is formulated and studied. A new Bayesian update for a three layers hidden Markov model is provided and proved to be a sufficient statistic. Also, the objective function for the POMDP problem is shown to be piecewise linear convex one. The relation between observations quality and the impact of measurement errors is discussed.;For the case where an expert opinion better relates observed signals to the true underlying state of the system is considered. A POMDP with fuzzy observations is assumed. A fuzzy membership function is provided and utilized to fuzzify the state observations matrix. The application of the fuzzy membership function and the significance of this scenario are illustrated by examples. Finally, the dissertation is concluded by a summary of the contributions and suggestions for future research.