A renewal process model with failure based PM and imperfect CM for unavailability exploration

Abstract

Purpose The paper aims to explore unavailability of dormant systems that are under both preventive and corrective maintenance. Preventive maintenance is considered as a failure based maintenance model, where full renew is realized at the occurrence of every nth failure. It proposes the imperfect corrective maintenance model, where each restoration process deteriorates the system lifetime, probability distribution of which is gradually changed via increasing failure rate. Design/methodology/approach Basic reliability mathematics necessary for unavailability quantification of a system which undergoes a real aging process with maintenance has been derived proceeding from renewal theory. New renewal cycle was defined to cover the real aging process and the expectation of its length was determined. All events resulting in the failure of studied system were explored to determine their probabilities. An integral equation where the unavailability function characterizing studied system is its solution was derived. Findings Preventive maintenance is closely connected with the occurrence of the nth failure, which starts its renew. The number n can be considered as a parameter which significantly influences the unavailability course. The paper shows that the real aging process characterized by imperfect repairs can significantly increase the unavailability courses in contrast with theoretical aging. This is true for both monitored and dormant systems. Originality/value Although mathematical methods used in this article were inspired and influenced by the work of reference (van der Weide and Pandey, 2015), derivation of final formulas for unavailability quantification considering the new renewal cycle is original. Idea of the real aging process is new as well. This paper fulfils an identified need to manage the maintenance of realistically aging systems.