The Effects of a Pro Rata Rebate Warranty on the Discrete Age Replacement Policy with Salvage Value Consideration

Abstract

Consider a system that should be operating over an indefinitely long operation cycle n ( n = 1,2,... ). Under the discrete time age-replacement policy, a system is replaced at the completion of cycle N ( N = 1,2,... ) or at failure, whichever occurs first. For the pro rata rebate warranty (PRRW), the customer will be refunded a proportion of the purchasing cost if the system fails within the warranty period. When the system is preventive replaced, a salvage value that proportional to its expected residual lifetime is gained. Cost models from the customer’s perspective are developed for both warranted, and non-warranted systems. The corresponding optimal replacement age 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 N* are shown, and the impacts of a PRRW on the optimal replacement policies are investigated analytically. Finally, a numerical example is demonstrated for the optimal policy illustration and verification. The observations from the technical analysis and numerical results provide valuable information for a buyer (user) to adjust their optimal preventive replacement policy when the system is operating in discrete time and under a PRRW.