This dissertation has three chapters related to the maintenance optimization.
In the first chapter, we examine the problem of adaptively scheduling perfect
inspections and preventive replacement for a multi-state, Markovian deterioration
system with silent failures, such that total expected discounted cost is minimized.
We model this problem as a partially observed Markov decision process for which
three actions - replace, do nothing, perfectly inspect - are available at each decision epoch, and establish structural properties of the optimal policy for certain nonextreme sample paths.
The second chapter also considers discrete -time, Markovian deterioration system.
However, while in the first chapter, we consider maintenance action with
perfect outcome, that is, as a result of replacement, the system transits to “as good as new state”, in the second chapter, we explore optimal policy structure for
such a system in the case of stochastic repair.
In the third chapter, we consider discrete-time, nonstationary Markovian deterioration system with the same set of actions as in the first chapter. We investigate the structure of the optimal maintenance policy for such a system by minimizing the expected total discounted cost over an infinite horizon.