Despite the rich body of research on reliability analysis and optimization of warm standby systems, the existing works have mostly failed to consider the practical storage component of such systems. This paper advances the state of the art by modeling and optimizing the reliability of a 1-out-of-n warm standby system with product storage, characterized by a maximum capacity, and specific uploading and downloading paces constraints. The storage may accumulate surplus product when the performance of the operating element exceeds the demand and compensate product deficiency otherwise. A numerical algorithm based on the probabilistic model is first proposed to evaluate the reliability or success probability of the system mission (MSP) that must satisfy a pre-specified demand during a required mission time. As a further contribution, the optimal element activation sequence problem is formulated and solved to maximize the mission success probability. Influences of several model parameters (storage capacity, demand, mission time, element reliability, and storage uploading/downloading pace constraints) on the MSP and optimization solutions are investigated through an example of a power system.