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 w0, where w0ow, from the time of purchase with a new product at no cost to the buyer; meanwhile, any failure in the time interval from w0 to w results in a pro-rata replacement, i.e., any product is replaced with a new item at pro-rata cost to the buyer. Numerical examples are provided given that the failure time of the product follows either the mixed exponential distribution or the mixed Weibull distribution and four warranty policies are examined. Based on the results of analysis, it is noted that the fully renewing combination FRW/PRW is always better than the fully renewing policy in terms of cost.