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. In [N. Jack, F. Van der Duyn Schouten, Optimal repair-replacement strategies for a warranted product, Int. J. Prod. Econ. 67 (2000) 95–100] a conjecture is made 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.