On a conjecture of optimal repair–replacement strategies for warranted products

Under a free replacement warranty policy, the manufacturer has the option of rectifying a failure by either repairing the failed item or replacing it with a new one. Jack and van der Duyn Schouten made a conjecture on the optimality of an age-limit policy: there exists a control limit AL(t), such that a minimal repair is performed on failure with t time units remaining in the warranty period if the age of the failing unit is less than or equal to AL(t). In this paper, we prove that this conjecture is indeed correct. Moreover, we show that for a more general model where the repair cost is random, a generalized repair-cost-limit policy is optimal, and the age-limit policy becomes its degenerated form. Numerical examples are provided to illustrate the computational algorithm and to compare the performance of these policies.