Optimal age replacement policies for k-out-of-n systems considering mission durations

In order to provide the required reliability of k-out-of-n systems during mission executing process, mission durations are integrated into age replacement policies for k-out-of-n systems. Then, the simple replacement, replacement first and replacement last are proposed respectively. In each replacement policy, optimum parameters are discussed analytically and numerical examples are given to demonstrate the accuracy of derivations. Via comparing with traditional replacement policies, the effectiveness of our suggested replacement policies is verified. Finally, the proposed policies are illustrated in maintaining the engine system of an unmanned copter, which aims to guide engineers to determine the best replacement policy in three situations.