The redundancy allocation to original system components is a common technique to improve the system reliability and its performance. This paper considers a coherent system consisting of n independent components equipped with m independent redundant components. Both common schemes for allocating the redundant components to the system, called active and standby redundancies are considered. The essential problem which is of great importance in redundancy allocation problem of systems is how to find the optimal allocation strategy such that the performance of the system be optimal in the sense of some stochastic orders. In view of the usual stochastic order and in order to maximize the system reliability, an algorithm is proposed to find the optimal redundancy allocation. We first introduce a new measure of component importance which is useful to find the best allocation for adding m = 1 redundant component and then use it to propose our algorithm when m > 1. This algorithm solves the optimal redundancy allocation problem and extends the most existing results in literature for particular structures such as series, parallel, k-out-of-n and those systems with m = 1 redundant component.

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