Optimisation of preventive maintenance policies with replacement first and last for systems subject to shocks

摘要

This paper addresses preventive replacement policies for operating systems subject to non-homogeneous Poisson process shocks. A shock causes two types of system failures with number-dependent probability: type-Ⅰ (repairable or minor) failures can be rectified by minimal repair; type-Ⅱ (non-repairable or catastrophic) failures must be removed by corrective replacement. A preventive replacement model is designed to replace the system before a type-Ⅱ failure occurs. Similar to conventional replacement models, our model bases replacement on type-Ⅱ failures at age T or number of working times N; however, contrary to conventional models, our model replaces the system at the last occurring age or working time. Thus, we refer to our model as a preventive replacement last model and existing methods as conventional replacement first models. Comparisons between these models are discussed in detail. The optimal schedule that minimises the mean cost rate of each preventive replacement model is derived analytically and computed numerically. The proposed model provides a general framework for analysing policies and other special cases of previous models.