Redundancy, defined as the use of multiple independent means to accomplish a task, plays a critical role in ensuring the reliability of complex systems. This concept was exemplified in NASA's Apollo 10 mission, where redundancy allowed the mission to continue when a fuel cell malfunctioned. However, designing a complex system with redundancy presents a trade-off between achieving stringent reliability goals and managing the associated costs, weight, and size constraints. This trade-off is often challenging to optimize, as shown by Chern (1992), but some redundancy allocation models can be solved efficiently. One such model considers a system consisting of multiple independent subsystems, each built from identical components, with the objective of maximizing system reliability. These subsystems are arranged in parallel, and the system's overall reliability is the product of their individual reliabilities. The model aims to determine the number of independent components in each subsystem to achieve a specified level of system reliability. In this context, rational parameters are introduced to represent the failure probability of components and the required system reliability. When redundancy is unnecessary, the parameters are rational numbers in a specified range. This model offers a systematic approach to addressing redundancy in complex systems, ensuring their resilience while managing resource constraints.
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