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We develop a generalized block replacement model for a k-out-of-n system and determine the optimum policies of both the threshold level for the number of failed components to prevent system failures and the maintenance cycle that minimizes the expected total system cost. To overcome the existing block replacement policies' drawbacks, i.e., it is rather wasteful if a preventive replacement happens just after a failure replacement, in our developed policy, a replacement service for a failure is provided when there are a threshold number of failed components occurring. We also take into consideration the downtime period of each failed component using the order statistics for lifetime and age distributions for k-out-of-n systems. Several numerical examples are discussed to demonstrate the applicability of the methodology derived in this paper.