A minimal repair replacement model with two types of failure and a safety constraint

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,C-m and C-2,C-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 omega. 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. (c) 2007 Elsevier B.V. All rights reserved.