An unpunctual preventive maintenance policy under two-dimensional warranty

In the business-to-consumer context, e.g., the automobile industry, preventive maintenance (PM) of warranted items usually relies upon customers to return their items to authorized maintenance centers according to prescribed schedules. However, item owners may be unpunctual, causing actual maintenance instants deviating from scheduled instants. This paper studies the impact of customer unpunctuality on the optimization of PM policy and the resultant warranty expenses. An unpunctual imperfect PM policy, which allows customers to advance or postpone scheduled PM activities in a tolerated range, is proposed for repairable items sold with a two-dimensional warranty. The expected total warranty costs of the unpunctual (and punctual) PM policies are derived under the assumption that customer unpunctuality is governed by a specific probability distribution. The optimization and comparison of the two policies are investigated in different scenarios regarding the product's failure rate function. The results for two possible unpunctuality distributions—uniform and triangular—are discussed and compared. Numerical studies show that the expected total warranty cost of the unpunctual policy could be either higher or lower than that of the punctual policy, depending on customer behaviors and the shape of failure rate function. Accordingly, manufacturers could induce customers to adjust their unpunctuality behaviors by modifying PM policies or introducing penalty/bonus mechanisms.