A Bivariate Post-Warranty Maintenance Model for the Product under a 2D Warranty

In this study, by integrating preventive maintenance (PM) into a two-dimensional warranty region, a two-dimensional warranty with customized PM (2D warranty with customized PM) is proposed from the manufacturer's perspective to reduce the warranty cost. The warranty cost of a 2D warranty with customized PM is derived. The manufacturer's tradeoff between PM cost and minimal repair cost saving is obtained by choosing the proper reliability threshold and the number of customized PMs, and the advantage of a 2D warranty with customized PM is illustrated. Second, by integrating PM into the post-warranty period, a bivariate post-warranty maintenance (BPWM) policy is proposed from the consumer's perspective to ensure the reliability of the product through the 2D warranty with customized PM. The expected cost rate model of BPWM is derived. Optimal BPWM is obtained in the numerical experiments. It is shown that a 2D warranty with customized PM is beneficial for both the manufacturer and the consumer, since both the manufacturer's warranty cost and the consumer's total cost are reduced.