This paper presents the effects of a free minimal repair warranty (FMRW) on the periodic replacement policy under discrete operating circumstance. For the discrete-time periodic replacement policy, a product is preventively replaced at pre-specified operation cycles N, 2N, 3N, … (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. From the customer's perspective, the cost models are developed for both a warranted and a nonwarranted product, and the corresponding optimal periodic replacement policies are derived such that the long-run expected cost rates are minimized. Under the assumption of the discrete time increasing failure rate (IFR), the existence and uniqueness of the optimal N* are shown, and the impacts of a FMRW on the optimal replacement policies are investigated analytically. We found that the optimal N* for a warranted product should be adjusted toward the end of the warranty period.
One-dimensional discrete-time quantum walks on random environments