Optimal inspection and maintenance for stochastically deteriorating systems
This thesis concerns the optimisation of maintenance and inspection for stochastically deteriorating systems. The motivation for this thesis is the problem of determining condition based maintenance policies, for systems whose degradation may be modelled by a continuous time stochastic process. Our emphasis is mainly on using the information gained from inspecting the degradation to determine efficient maintenance and inspection policies. The system we shall consider is one in which the degradation is modelled by a Levy process, and in which failure is defined to occur when the degradation reaches a critical level. It is assumed that the system may be inspected or repaired at any time, and that the costs of inspections and repairs may depend on the level of system degradation. Initially we look at determining optimal inspection policies for systems whose degradation may be directly and perfectly observed, before extending this analysis to the case where the degradation is unobservable, and a related covariate process is used to determine maintenance decisions. In both cases it is assumed the replacement policy is fixed and known in advance. Finally we consider the case of joint optimisation of maintenance and inspection, for cases in which the maintenance action has either deterministic or random effect on the degradation level. In all of these cases we use the properties of the Levy process degradation model to form a recursive relationship which allows us to determine integral and functional equations for the maintenance cost of the system. Solutions to these determine optimal periodic and non-periodic inspection and maintenance policies. Throughout the thesis we use the gamma process degradation model as an example. For this model we determine optimal perfect inspection policies for the cases when inspections are periodic and non-periodic. As a special case of a covariate process we consider the optimal imperfect periodic inspection policy. Finally we obtain jointly optimal deterministic-maintenance and periodic-inspection policies.