A New Approach to Maintenance Optimization by Modeling Intensity Control

In this paper, we present an optimal-control-based framework for deteriorating systems that are subject to repair and inspection. The model is based on two common assumptions that include the maintenance process is adapted to partial information including history of inspection events, and inspections do not impact on the failure characteristics of components. The latter means, at inspection times the system is repaired minimally that brings the system back to the operating condition just previous to inspection (as-bad-as-old) otherwise the operating system with slight overhaul is left to continue to operate. To model the unobservable damage (state) process which measures the effect of operating environment on the system, non-homogeneous Markov process with state space S = {1, 2} is applied. By projection on the observed history, the partial information control problem is converted into a complete information problem. To put the maintenance model in an intensity control framework, the transition rate of Markov process driven by control process u is addressed as a measure to control not only intensity of inspection, but also the flow of revenue associated with the damage process. To solve optimal inspection problem, and to optimally adjust the state of the process over inter-arrival time of inspections (repair), an evolution of optimal control process which is solution of Hamilton-Jacobi equations is derived. To tackle the maintenance optimization problem numerically, an example is given. Provided optimal control process, a sequence of optimal inspection times and corresponding inspection intensity and conditional survival function of the system are obtained. Also, to predict the system failure, conditional mean times to failure (CMTTF) of the system indexed by inspection events are derived. Finally, a failure intensity based optimal stopping rule to replace the system is proposed.