Redundancy is a basic and fundamental concept used in reliability engineering. However, the methods for analyzing the reliability of redundant systems, particularly for systems with standby redundancy, are limited. In this paper, using the concepts of counting processes, we propose a simple, accurate, and computationally efficient method to find the reliability of standby systems. The proposed method efficiently analyzes systems with non-identical components, mixed cold-warm-hot standby components, shared standby components among different subsystems operating at different conditions, switching failures, and general failure time distributions. We demonstrate the proposed method using several examples. We also provide the CPU times and a complete listing of the MATLAB code used. The examples demonstrate that the proposed method provides a practical and accurate way of evaluating the reliability of complex standby configurations that arise in a wide range of applications.