Optimal burn-in time and warranty length under fully renewing combination free replacement and pro-rata warranty

Warranty is an important factor of marketing products; however, warranty always involves additional costs to the seller and these costs usually depend on product reliability. Burn-in is considered as a part of the production process in which the manufactured products are operated under accelerated stresses for a short time period before their release and has been applied as a way for enhancing product reliability. In the present paper, a cost model is developed to determine the optimal burn-in time and warranty length for non-repairable products under the fully renewing combination free replacement and pro-rata warranty (FRW/PRW) policy. Denoting w as the warranty length of the product, under the FRW/PRW policy, the seller agrees to replace the product that fails prior to the time point w′, where w′