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Introduction If a machine fails during operation, it is repaired or replaced by new one. A typical maintenance policy for a repairable machine is the minimal repair policy. By the minimal repair policy, a machine is minimally repaired upon failures, and replaced by new one at regular intervals[2, 4, 6] or the number of failures reaches to a certain amount[8, 11]. Since a minimal repair involves only that amount of work which is necessary to restore the failed machine to the average operating condition of its age, it is more appropriate to conduct at minor failures than critical failures. When a group of identical machines are under operation, which is common in many practical situations, a popular maintenance policy is a group maintenance policy. The idea of group maintenance policy is based on the set-up cost savings earned by performing maintenance all machines at a maintenance set-up. Under the classical group maintenance policy, if a machine fails during operation, it is left idle until the next group maintenance time. At the group maintenance time, failed machines are replaced by new ones and the preventive maintenance (PM) is serviced for the survivals to restore it to an as-good-as-new condition. The group maintenance is performed when a prescribed time interval elapses[7], or when the number of failed machines reaches to a certain amount[5, 1]. In the (m,T) group maintenance model of Ritchken and Wilson[9], a group maintenance is performed either when an operation time T elapses or the number of failed machines reaches to m out of N machines, whichever comes first. In the previous group maintenance policies, the failed machines are left idle until the next group maintenance set-up. Even when a minor failure occurs to a machine early in the operation, it is forced to wait to the next group maintenance time. If minimal repairs are performed immediately to minor failures during operation, the non-serious failures will not need a long wait. In this paper, the (m,T) group maintenance model of Ritchken and Wilson[9] is extended by classifying failures into two modes, critical and minor failures. The proposed policy is as follows. There are N machines of the same type under operation. If a minor failure occurs, minimal repair is performed immediately to continue its operation. When a critical failure occurs to a machine, it is left idle until the next group maintenance incurring downtime cost. Group maintenance is set up either when the operation time T elapses or the number of critical failures reaches to m, , whichever comes first. At the group maintenance, the critically failed machines are replaced by new ones, and PM is serviced for the survivals to restore it to an as-good-as-new condition. Then a new cycle begins. d