Two-state optimal maintenance planning of repairable systems with covariate effects

Abstract

Optimal maintenance planning for repairable systems plays a critical role in ensuring an appropriate level of system reliability and availability. An important class of optimal maintenance planning decisions are those in which one must determine whether to implement a repair or a renewal (replacement) upon system failure. Most existing models within this class are based on a single-state framework, wherein the system age is utilized as the unique measure to determine whether to repair or renew. Extended models have also appeared in the literature which utilize both the system age and the number of failures/repairs since last replacement to provide a two-dimensional characterization of the system state thereby providing more flexibility and improving the quality of maintenance planning. The existing two-state optimal maintenance planning models, however, only work for a single system. They cannot handle situations where multiple systems are involved, especially when multiple systems operate in different environments (treated as covariate effects) leading to heterogeneity in failure processes of those systems. Ignoring the covariate effects can result in a non-optimal (i.e., more costly) maintenance planning. In this article, we propose a two-state covariate-dependent optimal maintenance planning model for multiple systems. Specifically, we develop a covariate-dependent trend renewal process model to formulate the heterogeneous failure processes of multiple systems. A maximum likelihood estimation method is developed for model parameter estimation. Based on the proposed model, we develop a two-state covariate-dependent optimal maintenance planning by utilizing a discrete semi-Markov decision process. The optimal covariate-dependent control-limit maintenance policy is derived based on a numerical search algorithm. A simulation study and a real-world case study are conducted to illustrate the proposed approach.