Exploring the optimal condition-based maintenance policy under the gamma degradation process

As an industry-wide ongoing effort of the system health management (SHM), condition-based maintenance (CBM) utilizes the modern sensor technology for periodic inspections of a system, and the maintenance actions are made based on the inspection of working conditions of the system unlike traditional methods. It is an effective method to reduce unexpected failures as well as the operations and maintenance costs. Among various stochastic processes to describe degradation paths, the gamma process is characterized by a monotonic degradation evolution, suitable for modeling crack growth and wears for example. Its flexibility and mathematical tractability also ensure the analytical properties of the degradation model. In this work, we discuss the condition-based maintenance/replacement policy with the optimal inspection points under the gamma degradation process. A random effect parameter is used to account for the potential population/environmental heterogeneities and its distribution is continuously updated at each inspection epoch. The observed degradation level along with the system age is utilized for making the optimal maintenance decision. Aiming to minimize the total discounted operational costs, we investigate the structural properties of the optimal policy and determine the optimal inspection intervals. It was realized that the optimal maintenance policy that minimizes the total discounted operational costs is a monotone control limit policy, similar to the cases of Wiener process and inverse Gaussian process.