Optimal maintenance and warranty strategy for second-hand product with periodic preventive maintenance action

• Published in: Journal of the Korean Statistical Society Vol. 50; no. 3; pp. 773 - 794
• Main Authors: Park, Minjae, Jung, Ki Mun, Park, Dong Ho
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.09.2021; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Mathematics and Statistics; Research Article; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; Refund; Dealer’s perspective; Maintenance cycle; Minimal repair; Expected cost rate; Repair time threshold; Second-hand product; Preventive maintenance
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1007/s42952-021-00127-3

This paper proposes an optimal maintenance and warranty policy for the repairable second-hand product incorporating a periodic preventive maintenance strategy to slow down the deterioration of the product and derives an optimal length of non-renewing warranty period. Although a number of maintenance policies for the second-hand product have been discussed in the literature, there exist very few works dealing with the periodic preventive maintenance strategy under non-renewing warranty to obtain an optimal warranty period for the second-hand product. This work considers a non-renewing warranty policy, during which a periodic preventive maintenance is adopted to diminish the degradation process of the product and determines an optimal length of warranty period by optimizing the expected cost rate incurred to the dealer during the maintenance cycle. Since the replacement of the failed second-hand product may not be practical in general, we adopt a concept of full refund instead of replacement in this paper. By pre-setting a repair time threshold, either the refund or minimal repair is provided by the dealer depending on whether the failed second-hand product can be repaired within the repair time threshold or not. The maintenance cycle of the second-hand product starts with the purchase of the product and ends when either the refund occurs within the warranty period or the warranty expires. Given a certain cost structure charged to the dealer, we formulate the expected cost rate during the maintenance cycle of the product and determine an optimal length of warranty period minimizing the objective function. Assuming the power law process for the product’s failures and a Weibull distribution for the repair times, we present a numerical example and investigate the effects of periodic preventive maintenances and other relevant parameters on the optimal solution.