(untitled) (Journal of the College of Basic Education, 2026)
This paper focuses on calculating the allocation and optimal reliability distribution for each component of a complex system by estimating a polynomial reliability function using the shortest path method and applying matrices to find the most successful path for the device. Most studies, with their development, rely on increasing closed-loop functions to link cost and its direct relationship to reliability that is, a direct relationship between reliability and cost, meaning that the cost of a component increases with its reliability. However, these relationships can sometimes be complex, ambiguous, or difficult to construct. In this study, the reliability function of the complex system was extracted using MATLAB version R2020a, and the correlation between cost and reliability was examined across several datasets. In addition to determining the overall cost and reliability of the system, the Harmonic Search (HSA) algorithm was used to determine the cost and reliability of each individual component. The performance of this algorithm was optimized, and an optimal reliability distribution was achieved, by applying the Behavior model (cost function).