A Generalized Mixed Effect Kijima Model and Application in Optimal Maintenance Planning

The Kijima model has been widely used in reliability literature to analyze repairable systems with various degrees of repair efficiency including “perfect repair,” “minimal repair,” and situations in between. Most existing studies, however, treat repair efficiency as a fixed value even though repair efficiency can vary among a series of repairs. In this paper, we propose a generalized mixed effect Kijima model to characterize the variation of repair efficiency. In particular, the newly proposed “mixed effect” model incorporates a fixed time-dependent effect and a random effect of repair efficiency, while the term “generalized” refers to the fact that the classic Kijima model is generalized to handle more maintenance situations such as “better than new” and “worse than old” situations after repair. To estimate the model parameters given a series of observed system failure times, we develop a stochastic approximation expectation maximization algorithm which is a type of maximum likelihood estimation method. Further, an optimal periodic maintenance planning is developed based on the proposed reliability model. A simulation study and a real-world case study are conducted to demonstrate the developed methods.