An extended geometric process and its application in replacement policy

In this article, we develop an extended geometric process model with a recovery factor and propose a two-dimensional evaluation function for each maintenance effect. The developed model can describe the mean inter-failure time which can be improved by the first or several former repairs in some repairable systems. We also propose parameter estimation methods for the developed geometric process model and use some real failure datum to prove the model’s application. Focused on the developed geometric process model, two novel replacement policies and their optimizations are also presented in detail. Then, two real case studies are discussed to illustrate the modelling and optimizing process. Modelling results show that each recovery factor is related to the effect of each repair, and the developed geometric process model has a good-fitting property for some real cases. Optimization results display that the optimal (N, m) replacement policy is applicable for some small-sized manufacturing systems, whereas the proposed (N) replacement policy is suitable for some expensive systems.