Optimal condition-based replacement policy with unknown degradation parameters

Condition-based maintenance (CBM) has been widely applied with the development of sensor technology. A commonly used assumption of CBM models is that the degradation processes have predetermined parameters. In many practical situations, however, the parameters of degradation processes vary from system to system due to heterogeneous environments and operation habits. This paper proposes a condition-based replacement policy for a system with the degradation process unspecified. The degradation of the system conforms to a gamma process with an unknown scale parameter, whose prior distribution follows a gamma distribution. Condition monitoring is performed at equidistant time epochs to reveal the degradation level. When the degradation level exceeds a critical threshold, a system failure occurs, triggering a corrective replacement. Otherwise, a decision must be made between no replacement or preventive replacement to minimize the long-run expected average cost per unit time. A Bayesian method is used to update the probability density of the unknown scale parameter based on monitored information. The optimization problem is formulated as a Markov decision process and solved by a policy iteration algorithm. A numerical example is provided to demonstrate the efficiency of the proposed policy.