Preventive maintenance for the constrained multi-attempt minimal repair

Cha, Ji Hwan and Finkelstein, Maxim (2024) Preventive maintenance for the constrained multi-attempt minimal repair. Reliability Engineering and System Safety, 243. 109899. ISSN 0951-8320 (

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In practice, at some instances, the repair of a failed item can be unsuccessful and should be repeated due to various reasons. This can happen in practice with a minimal repair when a failed part of a system is replaced, e.g., by the faulty spare. The corresponding stochastic model that takes into account this possibility can be described probabilistically in terms of the Polya-Aeppli process, which is a generalization of the Poisson process to the case of multiple occurrences of events. Some useful properties for considering optimal preventive maintenance problems are derived. The optimal replacement policy for a system with the multi-attempt minimal repairs is defined and analysed. The characteristic feature of this policy is that the system is replaced not only on reaching the predetermined age but also after a fixed number of unsuccessful minimal repairs. The detailed numerical examples illustrate our findings.