This paper considers an optimal replacement model for a system subject to two types of failure. If the failure is of type 1, the system is minimally repaired. In the case of type 2 failure, the system is minimally repaired with probability p and replaced with probability 1 qp . A modified random and age replacement model is considered in which the system is replaced at a planned time T, at a random working time Y, or at the first non repairable type 2 failure whichever occurs first. Explicit expression for the expected total cost and the optimal replacement time T, minimizing the expected total cost are derived analytically. Finally, numerical example is considered to highlight the characteristics of the policy.
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