Journal of the Operations Research Society of Japan · 1981 · 77 citations · 6 references
EngineeringIndustrial EngineeringOperations ManagementMaintenance EngineeringOperations ResearchOptimizationCost FunctionsMaintenance Cost ManagementMaintenance CostsMaintenance OptimizationReliability ModelingReplacement DecisionsExpected Cost MinimizationExpected Loss CostMaintenance Engineering EconomicsOptimal Replacement PolicyRepair Cost AllocationRepairable Systems ModelsReplacement Cost ApproachStochastic Replacement Models
The study builds on Makabe and Morimura’s basic model where a unit is replaced at the k‑th failure. It extends this framework to two generalized models: one with two failure types and replacement at type‑2 or k‑th type‑I failure, and another with two unit types and replacement at unit‑2 or k‑th unit‑I failure. Expected cost rates for each model are derived analytically using probability calculus. Optimal replacement thresholds k* that minimize cost rates are uniquely determined by solving specific equations under stated conditions.
This paper summarizes the results of the basic model of Makabe and Morimura, in which a unit is replaced at k-th failure. The two generalized models are considered: A) A unit has two types of failures and is replaced at type 2 failure or k-th type I failure. B) A system has two types of units and is replaced at unit 2 failure or k-th unit I failure. The expected cost rates for each model are obtained, using the calculus method of probability. It is shown that the optimal numbers k* which minimize the cost rates are given by unique solutions of equations under certain conditions.
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Mathematical Theory of Reliability
A. P. Basu, Richard E. Barlow, Frank Proschan · Econometrica · 1966 · 2.7K citations
Optimum Preventive Maintenance Policies
Richard Barlow, Larry C. Hunter · Operations Research · 1960 · 1.4K citations
Engineering, Industrial Engineering, Continuous Improvement +13