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A minimal repair replacement model with two types of failure and a safety constraint. (English) Zbl 1129.90017
Summary: Consider a system subject to two types of failures. If the failure is of type 1, the system is minimally repaired, and a cost C 1 is incurred. If the failure is of type 2, the system is minimally repaired with probability p and replaced with probability 1-p. The associated costs are C 2,m and C 2,r , respectively. Failures of type 2 are safety critical and to control the risk, management has specified a requirement that the probability of at least one such failure occurring in the interval [0,A] should not exceed a fixed probability limit ω. The problem is to determine an optimal planned replacement time T, minimizing the expected discounted costs under the safety constraint. A cost C r is incurred whenever a planned replacement is performed. Conditions are established for when the safety constraint affects the optimal replacement time and causes increased costs.
90B25Reliability, availability, maintenance, inspection, etc. (optimization)