Warranty Cost Modeling and Warranty Length Optimization under Two Types of Failure and Combination Free Replacement and Pro-Rata Warranty

The product warranty has become an indispensable facet of business operations. Burn-in is effective at eliminating infant mortality and improving operational reliability levels for consumers. This paper considers the influence of different failure states and different phases of product reliability and warranty policies on warranty costs from predelivery inspection to the end of the warranty period. We then propose a comprehensive warranty cost model that considers burn-in, free replacement warranty and pro-rata warranty as three phases for repairable products presenting two types of failure (minimal and catastrophic failure) that involve minimal repair and replacement, respectively. Warranty costs are the result of a combination of the three phases, where two types of failure occur individually or simultaneously. Moreover, we developed a framework for the modeling process of warranty costs, and the effects of various parameters, such as the burn-in time, warranty period, and distribution function on warranty costs, were analyzed. Finally, a practical case was examined by using a warranty cost model, and through an after-sales service data analysis, we obtained the failure rate distribution and optimal warranty length by minimizing the average warranty cost, which can serve as a reference for manufacturers when developing warranty policies.