Estimating the reliability of complex systems using various bounds methods

The precise two-terminal reliability calculation becomes more difficult when the numeral of components of the complex system increases. The accuracy of approximation methods is often adequate for expansive coverage of practical applications, while the algorithms and computation time are typically simplified. As a result, the reliability bounds of two-terminal systems and estimation methods have been established. Our method for determining a complex system's reliability lower and upper bounds employs a set of minimal paths and cuts. This paper aims to present a modern assessment of reliability bounds for coherent binary systems and a comparison of various reliability bounds in terms of subjective, mathematical, and efficiency factors. We performed the suggested methods in Mathematica and approximated their interpretation with existing ones. The observed results illustrate that the proposed Linear and Quadratic bounds (LQb) constraint is superior to Esary-Proschan (EPb), Spross (Sb), and Edge-Packing (EDb) bounds in the lower bond, and the EDb bound is preferable to other methods above in the upper bond. This modification is attributed to sidestepping certain duplicative estimations that are part of the current methods. Given component test data, the new measure supplies close point bounds for the system reliability estimation. The Safety–Critical-System (SCS) uses an illustrative model to show the reliability designer when to implement certain constraints. The numerical results demonstrate that the proposed methods are computationally feasible, reasonably precise, and considerably speedier than the previous algorithm version. Extensive testing on real-world networks revealed that it is impossible to enumerate all minimal paths or cuts, allowing one to derive precise bounds.