Probabilistic analysis of two reliability models of a single-unit system with preventive maintenance beyond warranty and degradation

Abstract

This paper presents two reliability models of a single-unit system with the concept of preventive maintenance (PM) beyond warranty and degradation. In both the models, repair of any failure during warranty is cost-free to the users, provided failures are not due to the negligence of users. There is a single repairman who always remains with the system. Beyond warranty, the unit goes under PM and works as new after PM (in both models). In model-1, the unit works as new after its repair beyond warranty whereas; in model-2, the unit becomes degraded. After failure, the degraded unit is replaced by a new one. The failure time of the system follows negative exponential distribution while PM, replacement and repair time distributions are taken as arbitrary with different probability density functions. Supplementary variable technique is adopted to derive the expressions for some economic measures such as reliability, mean time to system failure (MTSF), availability and profit function. Using Abel's lemma, the behaviour of the system in steady-state has been examined. To highlight the behaviour of reliability and profit function, numerical results are considered for particular values of various parameters and repair cost. Profit comparison of both the models is also made to see the usefulness of the concept of degradation.