A Study on the Cost of Two-Dimensional Product Warranty Based on Imperfect Repair

The cost from the servicing of warranty depends on the reliability of the product, the maintenance actions, and the warranty strategy. In this paper, we focus on a repair strategy based on imperfect repair for two-dimensional (2D) warranty. We consider a rectangular warranty region with two measures (age and usage) and divide it into three disjoint sub-regions. Only the first failure in the second interval is rectified by imperfect repair while all the other failures are repaired minimally. We modeled the 2D product warranty cost for this warranty strategy, and then used a two-stage process to minimize the total expected warranty cost. At last, we give an illustrative numerical example and compute the expected warranty cost, as the proportional hazard rate reduction factor varies from 0 to 0.8 and usage rat varies from 0 to 10. We can find for the numerical example that the imperfect repair strategy can save significant cost for manufacturer, especially when the usage rate is high.