Optimal two-dimensional warranty repair strategy

For repairable products, the warrantor has options in choosing the type of repair performed to an item that fails within the warranty period. The focus is on a particular warranty repair strategy, related to the degree of the warranty repair, under a non-renewing two-dimensional warranty policy that is free of charge to the consumer. A rectangular warranty region, as in the automotive industry, is considered and partitioned into disjoint subregions. Each of these subregions has a preassigned degree of repair for a faulty item. First, for a partition of size n, an expression is derived for the associated expected warranty servicing cost per item sold. Second, using an example, for a given discretization of the warranty period, the way in which the number of subregions and their shape can be determined, so that the expected warranty servicing cost per item sold is minimum, is demonstrated.