In the face of increasing awareness among customers and today's competitive market, the warranty of a product has become an added feature in marketing strategy. A reliable product causes less warranty support cost. However, a more reliable product costs more to manufacture. Thus, a suitable trade-off between the cost and the benefit of a development and testing program is essential to optimize the performance measure, e. g., minimize total expected cost. Renewal theoretic models of sequences of failures over the burn-in and warranty periods and their costs are developed. Contrary to the usual asymptotic assumptions, transient behaviors of the renewal processes are considered. The expected costs associated with in-plant and field failures are balanced against the costs of implementing a burn-in program. A multi-component series system with different Weibull distributions for the components are considered. Burn-in is performed at the assembly level and the components are assumed to have different age accelerations under a common stress regimen. Models based on analyses both at the component and the system level are constructed. Two different burn-in policies are considered. These are "fixed duration" bum-in and "failure freell burn-in. A free replacement warranty for the components with policies of both fixed warranty period and renewed warranty period after each failure is considered in the models. The profit functions under different models are optimized with respect to burn-in period, stress parameters and warranty period. The models are extended to include reliability growth over the warranty period. Finally I solution procedures for optimizing the profit functions for all cases are given. / Ph. D.