Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks

• Published in: Annals of operations research Vol. 186; no. 1; pp. 317 - 329
• Main Authors: Sheu, Shey-Huei, Chang, Chin-Chih, Chien, Yu-Hung
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.06.2011; Springer Science + Business Media; Springer; Springer Nature B.V
• Subjects: Age; Algorithms; Business and Management; Categories; Combinatorics; Cost control; Costs; Failure; Mathematical analysis; Mathematical models; Operating systems; Operations management; Operations research; Operations Research/Decision Theory; Optimization; Poisson distribution; Policies; Preventive maintenance; Random variables; Repair; Studies; Theory of Computation; Age-replacement; Replacement policy; Maintenance; Minimal repair; Cumulative repair-cost limit
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-011-0864-9

An operating system is subject to random shocks that arrive according to a non-homogeneous Poisson process and cause the system failed. System failures experience to be divided into two categories: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a replacement. An age-replacement model is studied by considering both a cumulative repair-cost limit and a system’s entire repair-cost history. Under such a policy, the system is replaced at age T , or at the k -th type-I failure at which the accumulated repair cost exceeds the pre-determined limit, or at any type-II failure, whichever occurs first. The object of this article is to study analytically the minimum-cost replacement policy for showing its existence, uniqueness, and the structural properties. The proposed model provides a general framework for analyzing the maintenance policies, and presents several numerical examples for illustration purposes.