Burn-in is a quality control process used to minimize the warranty cost of a product by screening out defective products through prior operation for a period of time before sale. Two decision criteria used to determine the optimal burn-in time are the maximization of the reliability of the delivered product and the minimization of the total cost, which are composed of the cost of burn-in process and the cost of warranty claims. Because of uncertainty regarding the underlying lifetime distribution of the product, both the product reliability and the total cost are random variables. In this paper, the uncertainty in reliability and cost is quantified by use of Bayesian analysis. The joint distribution of reliability and cost is inferred from the uncertainty distribution of the parameters of the product lifetime distribution. To incorporate the uncertainty in reliability and cost as well as the tradeoff between them into the selection of optimal burn-in time, the joint utility function of reliability and cost is constructed using the joint distribution of reliability and cost. The optimal burn-in time is selected as the time that maximizes the joint utility function. Copyright (C) 2010 John Wiley & Sons, Ltd.