Optimal discrete - time periodic replacement policy for repairable products under free - repair warranty

This paper presents the effects of a free-repair warranty on the periodic replacement policy in discrete time process. Consider a repairable product that should be operating at the time over an indefinitely long operation cycle n (     , 2 , 1 n ); under the discrete-time periodic replacement policy, a product is preventively replaced at pre-specified operation cycles    , 3 , 2 , N N N (     , 2 , 1 N ). When the product fails, a minimal repair is performed at the time of failure and the failure rate is not disturbed by each repair. The cost models from the customer’s perspective are developed for both warranted, and non-warranted products. The corresponding optimal replacement period * N is derived such that the long-run expected cost rate is minimized. Under the assumption of the discrete time increasing failure rate, the existence and uniqueness of the optimal replacement period are shown, and the impacts of a free-repair warranty on the optimal periodic replacement policies are investigated analytically. We show that the optimal * N for a warranted product should be adjusted toward the end of the warranty period. Finally, numerical examples are provided for the optimal policy illustration and verification.