Abstract
The reverse engineering of a valid algebraic inequality often leads to a novel physical reality characterized by a distinct signature: the algebraic inequality itself. This paper uses reverse engineering of valid algebraic inequalities for generating new knowledge and substantially improving the reliability of common series-parallel systems. Our study emphasizes that in the case of series-parallel systems with interchangeable redundant components, the asymmetric arrangement of redundancies always leads to higher system reliability than a symmetric arrangement. This finding remains valid, irrespective of the particular reliabilities characterizing the components. Next, the paper also presents algebraic inequalities whose reverse engineering enabled significant enhancement of the reliability of series-parallel systems with asymmetric arrangements of redundant components, irrespective of the component reliabilities. Lastly, the paper presents a new technique for validating complex algebraic inequalities associated with reliability of series-parallel systems. This technique relies on a permutation of variable values and the method of segmentation.
