<p>Designing systems for optimal reliability at minimal cost presents a significant challenge. In this work, we consider a standby system consisting of a main unit, which can be fully repaired every time it fails, and a standby unit activated only during the main unit’s repair. The main unit is given priority, ensuring that it resumes operation immediately after completing its repair. Additionally, we incorporate a rejuvenation process for the standby unit, restoring it to a “good as new” condition while inactive. This rejuvenation process is critical for mitigating the aging effects that accumulate during prolonged standby periods, thereby enhancing overall system reliability. We first compute the reliability in the time domain for arbitrary distributions of the lifetimes of the main and standby units, as well as arbitrary distribution of repair and rejuvenation durations. Then we utilize the Interior-Point Method for Nonlinear Optimization to determine the optimal configuration in terms of component lifetimes, repair time (either fixed or distributed in random), and rejuvenation time distributions. The objective is to minimize the cost needed to achieve a target level of reliability within a specified time frame. The proposed optimization framework helps designers and decision-makers identify the best trade-offs for optimal resource allocation for reliability in standby systems, considering both the benefits and the risks introduced by rejuvenation.</p>