Infant mortality failures have critical effects on the reliability of items and result in considerable expenses to both producer and customer. In the electronic industry, two types of reliability testing to decrease these risks are common : Environmental Stress Screening(ESS) and Bum-in. In this study, 2-level program where perform ESS at part level and bum-in at unit level is employed. The effective screening durations to satisfy the failure rate of system immediately after burn-in or mission reliability at specified time after shipment are determined. Also, two optimal screening durations are obtained by minimizing the life-cycle cost with a failure rate or mission reliability constraint. Numerical experiments to investigate effects on optimal screening times of input parameter values are conducted.