Optimal Imperfect Periodic Preventive Maintenance for Systems in Time-Varying Environments

Abstract

Manufacturing systems run in time-varying environmental and operational conditions. For the effective manager to make a long-term preventive maintenance decision, it is necessary to integrate the time-varying environment into preventive maintenance (PM) policies. This paper considers PM for systems running in the time-varying environment, modeled as a two-state homogeneous Markov process, where one state represents a typical condition, and the other represents a severe condition. Environmental conditions affect the hazard rate function through a proportional hazard model. To avoid sudden failures in a system due to either minor failures or catastrophic failures, an extended periodic imperfect preventive maintenance model is carried out, and the maintenance effect is modeled with an age reduction factor, and a hazard improvement factor. We prove the discontinuity of the hazard rate function of the system in a time-varying environment through a Markov additive process. We also give a method to compute the probability density function of failure at any time. Further, the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$s$</tex></formula> -expected cost rate of the system in the time-varying environment is compared with the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$s$</tex></formula> -expected cost rates of the system always working in typical, and severe conditions. Finally, numerical examples fully verify our main results.