The effects of a free-repair warranty on the discrete-time periodic replacement policy

Abstract

This paper presents the effects of a free-repair warranty on a periodic replacement policy with a discrete time process. Considering a repairable product that should be operational at the time over an indefinitely long operation cycle n ( n =1, 2, …), under the discrete-time periodic replacement policy, a product is preventively replaced at pre-specified operation cycles N , 2 N , 3 N , … ( N =1, 2, …). 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 customers' perspectives 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 impact of a free-repair warranty on the optimal periodic replacement policies is investigated analytically. The optimal N * for a warranted product should be adjusted toward the end of the warranty period. Finally, numerical examples are demonstrated for the optimal policy illustration and verification. The observations from the numerical results provide valuable information for a buyer (user) to adjust the optimal periodic replacement policy if a product is operating in discrete time under a free-repair warranty.