Analytical fault detection algorithms have the potential to reduce the size, power and weight of fault tolerant safety-critical aerospace systems. One obstacle is the need for appropriate tools to certify the reliability of these systems. To complement high fidelity Monte Carlo simulations, this paper presents a theoretical method to assess the probabilistic performance of analytically redundant systems. Specifically, this paper considers a dual-redundant fault tolerant system that uses a fault detection algorithm to switch between the hardware components. The exact system failure rate per hour is computed using the law of total probability. The analysis assumes known failure models for the hardware components as well as knowledge of the probabilistic performance of the fault detection logic. A numerical example is provided to demonstrate the proposed method.