Optimal burn-in and warranty for a product with post-warranty failure penalty

This paper develops an optimization model to investigate the lengths of the optimal burn-in and warranty period, so that the mean of total product servicing cost is minimised. It is assumed that the cost of a minimal repair to a component at age t is a continuous non-decreasing function of t. Moreover, we model the customer dissatisfaction with product failures after the warranty within the product useful lifetime by introducing a post-warranty failure penalty cost to the manufacturer. The properties of the optimal burn-in time and optimal warranty policy are also analysed. Finally, under different product lifetime distributions, numerical examples and sensitivity analysis with respects to the values of the model parameters are provided.