A study of two-dimensional warranty policies with preventive maintenance

In dealing with the effects of product deterioration in the context of reliability analysis, it may not be satisfactory to consider only the effects of time or age because usage is often another essential factor that accounts for deterioration. A two-dimensional warranty with consideration of both time and usage for deteriorating products would be more advantageous for manufacturers. In this paper, a two-dimensional warranty model in which the customer is expected to perform appropriate preventive maintenance is analyzed and the warranty policy that maximizes the manufacturers' profits is determined. The proposed approach provides manufacturers with guidelines on how to offer customers two-dimensional warranty programs with proper time and usage limits. A numerical example shows the effectiveness of the proposed approach. Sensitivity analyses are conducted to investigate the robustness of the derived optimal warranty policy.