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Abstract
In this study we model the problem of maintaining a stochastically deteriorating system as both a completely observable and a partially observable Markovian decision process with deterministic and stochastic maintenance actions and finite state and action spaces. The feature of these models that distinguishes them from previous maintenance/replacement models is the inclusion of multiple maintenance actions that reverse system deterioration but may not restore the system to as good as new. These models are used to derive structural results concerning the optimal maintenance policy under various sets of assumptions.
Under the assumptions of deterministic maintenance actions and complete state observation, we show that if the reward functions are separable then the optimal maintenance can be characterized as a monotonic control limit policy. If maintenance costs are linear in the number of states improved, a "monotonic 3-zone" policy is shown to be optimal. Under the assumptions of stochastic, state independent maintenance actions, and complete state observation the optimal policy has a monotonic control limit structure under certain reasonable conditions. If the effect of stochastic maintenance actions is state independent then a constant maintenance control limit policy is shown to be optimal.
Several maintenance models with incomplete state observation are considered. If maintenance actions are deterministic and state dependent, then the optimal maintenance policy is shown to be finitely computable under mild conditions. Furthermore, a mild control limit result is demonstrated for this case. If maintenance actions are deterministic and state independent, the optimal policy is shown to have a specific structure consisting of monotonic waiting times and constant maintenance actions. The results for both the state dependent and state independent maintenance cases are extended to the case where the effect of maintenance actions is stochastic.
Alternate modeling assumptions, such as non-preventive maintenance, shutdown maintenance and instantaneous maintenance are examined as extensions to the basic maintenance models. Applications of the various models to practical maintenance problems are given and the reasonableness of the modeling assumptions are discussed in the context of these applications.
