Improving the Reliability of Parallel and Series–Parallel Systems by Reverse Engineering of Algebraic Inequalities

This paper presents a novel, domain-independent method for enhancing system reliability based on reverse engineering of algebraic inequalities. Although system reliability has been extensively studied, existing approaches have not addressed the challenge of improving reliability without knowing the reliability of individual components. This work fills this gap by demonstrating that the reliability of both parallel and series–parallel systems can be improved without any information about component reliability values. Specifically, this study establishes that in parallel systems, a symmetric arrangement of interchangeable components of the same type across parallel branches consistently yields higher system reliability than an asymmetric arrangement—regardless of the individual component reliabilities. This finding is derived through the reverse engineering of a new general algebraic inequality, proposed and proved for the first time. Furthermore, applying the same approach to series–parallel systems reveals that asymmetric arrangements of interchangeable redundancies offer superior system reliability compared with symmetric configurations.