Optimising batch withdrawal strategies for non-safety-related defects under risk sensitivity

A significant challenge in warranty-protected products is determining the appropriate strategy for removing batches that are vulnerable to non-safety-related failures. Two main approaches exist for handling such failures: an active strategy that compensates customers for current faulty units but preemptively withdraws remaining batch units to prevent future warranty claims, and a passive strategy that compensates customers throughout the warranty window without removing the batch. Under two different risk quantification methods, we examine the connection between a product's warranty configuration and the optimal timing strategy for withdrawing a batch that is susceptible to non-safety-related defects. The first method reveals a deterministic optimal withdrawal strategy, and we identify conditions where a passive strategy is optimal, irrespective of warranty length or batch size. In contrast, the optimal strategy under the second method is a probabilistic decision rule that depends on a random event's outcome. We also derive the maximum likelihood estimator for the parameters governing the product's failure probability, and use numerical analysis to explore the performance cost of dynamically learning these parameters. The results suggest that maximum likelihood estimation is a robust method for identifying the parameters of the failure probability function when these parameters are initially unknown during the warranty period.