A geometric process warranty model using a combination policy

This paper proposes a geometric process warranty model. Assume that a combination policy (W, T) is applied after selling a product, so that a free warranty is offered in [0, W), followed by a pro-rata warranty in [W, T). Assume further the successive operating times (repair times) of the product form a decreasing (increasing) geometric process. The average cost rate of the product to the manufacturer and a consumer can be derived respectively. For exponential distribution case, the explicit formulas of the average cost rate are obtained, and an finite algorithm for determination of an optimal combination policy is suggested.