A Mathematical Study of Multi-Component Redundant Systems under Preventive Maintenance and Replacement Strategies

Abstract: This paper presents a mathematical model that simulates multi-component redundant systems with various types of preventive maintenance and replacement. The components of each group have different properties and follow Weibull distributions. These groups operate in series and provide the required level of redundancy. Planned corrective repairs as well as planned replacements can be applied on the individual components. The reliability, availability, and long-term expected average maintenance costs of such redundant systems are determined by applying a regenerative method. We present a numerical example to demonstrate the effectiveness of their developed mathematical model and compare the reliability and costs for several scenarios with respect to the frequency of the maintenance tasks (different maintenance cycles) and the time at which these maintenance tasks take place (different replacement times). As one could expect from an optimization problem there exists a tradeoff between the reliability of the system and its operating costs. While frequent maintenance operations improve the reliability of the system they lead to higher costs due to lost production. In contrast delayed maintenance leads to lower costs because less money will be spent on maintenance but it will increase the probability of failures. Therefore, an optimal policy has to be found that minimizes the expected average lifetime maintenance costs, i.e., it has to satisfy both the reliability and availability constraints.

Keywords: Multi-component repairable system, Redundant systems, Reliability analysis, Continuous-time Markov chain, Preventive replacement policy.