Abstract: The optimal one-dimensional warranty period and sales price is designed from the perspective of the manufacturer. Considering the effects of customers' heterogeneous usage rates on filed reliability, the product's failure rate and the expected warranty cost of conducting a minimal repair strategy are proposed. The optimal one-dimensional warranty period and price are jointly designed to maximize the manufacturer's expected profit. Lastly, a case study of a central air-conditioning manufacturer is given to investigate the effects on the optimal designs. The results show that designing an optimal one-dimensional warranty period and sales price strategy is helpful to increase the products' expected profit, especially for the large equipment or system with different customers' usage rates.

Key words: product warranty, sales price, usage rate, warranty cost, demand function