Optimization problems of replacement first or last in reliability theory

• Published in: European journal of operational research Vol. 223; no. 1; pp. 141 - 149
• Main Authors: Zhao, Xufeng, Nakagawa, Toshio
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.11.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Age replacement; Applied sciences; Comparative analysis; Cost engineering; Cost estimates; Cumulative damage model; Electronic systems; Exact sciences and technology; Inventory control, production control. Distribution; Mathematical analysis; Mathematical models; Minimal repair; Naval; Operational research and scientific management; Operational research. Management science; Operations research; Optimization; Periodic replacement; Policies; Queuing theory. Traffic theory; Reliability theory. Replacement problems; Replacement costs; Replacement last; Studies; Working cycle; Cumulative damage model; Working cycle; Age replacement; Replacement last; Periodic replacement; Minimal repair; Costs; Replacement problem; Optimal policy; Cumulative damage; Modeling; Optimization; Repair; Age; Completion time; Execution time; Operating time; Electronic equipment; Probabilistic approach; Rupture; Reliability theory; Replacement; Maintenance; Failures; Standards; Case study; Ship
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2012.05.035

► Newly proposed notion of “replacement last” is motivated and analyzed in detail. ► Comparison methods between replacement last and the conventional replacement first are explored. ► Expected cost rate of replacement last in a standard cumulative damage model is obtained and computed. ► Replacement last in maintaining electronic systems of navy ships is applied. This paper takes up age and periodic replacement last models with working cycles, where the unit is replaced before failure at a total operating time T or at a random working cycle Y, whichever occurs last, which is called replacement last. Expected cost rates are formulated, and optimal replacement policies which minimize them are discussed analytically. Comparisons between such a replacement last and the conventional replacement first are made in detail. It is determined theoretically and numerically which policy is better than the other according to the ratios of replacement costs and how the mean time of working cycles affects the comparison results. It is also shown that the unit can be operating for a longer time and avoid unnecessary replacements when replacement last is done. For further studies, expected cost rates of modified models and their applications in a standard cumulative damage model with working cycles are obtained and computed numerically. Finally, case studies on replacement last and first in maintaining electronic systems of naval ships under battle and non-battle statuses are given.