A Markov Regenerative Process Model for the Dependability and Performance of a Two-Unit Multi-State System under Maintenance

Preventive maintenance (PM) is a key aspect for industrial, production and generally technological systems, since it can prevent unexpected breakdowns and their consequences. However, PM incurs additional cost and thus system designers should carefully examine how and when to implement it. Beyond this, modeling correctively the structure and the evolution of the system is of critical significance when designing the appropriate PM strategy. In this paper, a two-unit multi-state parallel system with one repair facility, which can model various industrial systems like power generation or pump systems, production systems or even computing systems, is considered, in which PM is enabled to prevent failures and improve system's dependability and performance. Given some specific system characteristics, a Markov Regenerative Process is proposed to be used to accurately model the evolution of the system in time. The asymptotic availability, the expected downtime and the expected operational cost are evaluated as measures for the system dependability and performance correspondingly. The aim is to determine the PM policies that optimize these measures either separately or jointly, through formulating and solving the appropriate optimization problem. The theoretical framework is illustrated through a numerical example for a pumping station consisting of two centrifugal pumps working in parallel.