Optimal preventive and opportunistic maintenance policy for a two-unit system

Abstract

This paper presents a new optimal opportunistic and preventive maintenance policy for a two-unit model with economic dependency applicable to the electric power distribution systems. Unlike the previous optimal maintenance policies which considered mainly single unit systems or no opportunistic maintenance for two-unit systems, we consider a two-unit system with economic dependency, where unit 1 is subject to condition monitoring and soft failure and unit 2 is subject to hard failure. Unit 1 is gradually deteriorating and unit 2 has a general life time distribution. Condition of unit 1 is monitored periodically and it is considered as failed when its deterioration level reaches a critical level N. At the failure time of unit 2 system is considered as failed, although unit 1 is working, and unit 2 will be correctively replaced by the next inspection epoch. Units 1 or 2 are preventively replaced when deterioration level of unit 1 or age of unit 2 reaches or exceeds the related PM levels. At the time of corrective or preventive replacement of a unit, there is an opportunity to replace also the other unit. A mathematical model is derived to find the preventive and opportunistic replacement levels for units 1 and 2 that minimize the long run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. Numerical example is provided to illustrate the performance of the proposed model and a comparison of the proposed model with other policies is carried out.