Warranty servicing with imperfect repair

A manufacturer of a product sold with warranty incurs additional costs from the servicing of warranty claims made by customers. These costs depend on several factors such as the reliability of the product, the warranty terms, the maintenance actions of the customers, and the servicing strategy used by the manufacturer. Through effective warranty servicing strategies the manufacturer can reduce the warranty costs. In the case of repairable items, several different warranty servicing strategies involving minimal repair and replace by new have been studied. For expensive products, servicing strategies involving minimal and imperfect repairs should result in lower warranty costs than strategies studied in the past. Imperfect repair results in the reliability of a repaired item being better than it was just before failure but less than that of a new item and it is much cheaper than the cost of a new item. In this paper, we look at two new warranty servicing strategies (strategies 1 and 2) involving minimal and imperfect repairs. In both strategies, a failed item is subjected to at most one imperfect repair over the warranty period. In Strategy 1, the level of improvement in reliability under imperfect repair depends on the age of the item at which imperfect repair is carried out whereas, in Strategy 2, the level of improvement does not depend on the age. As a result, Strategy 1 involves a functional optimisation to determine the optimal improvement in reliability when an imperfect repair is carried out. In contrast, Strategy 2 involves only a parameter optimisation to determine the optimal reliability improvement. In a numerical example, we compare the two new servicing strategies with two other strategies reported in the literature.