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The reverse engineering of a valid algebraic inequality often leads to a projection of 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 components 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 presents novel system reliability inequalities whose reverse engineering enabled significant enhancement of the reliability of series-parallel systems with asymmetric arrangements of redundant components, without knowledge of the individual component reliabilities. Lastly, the paper presents a new technique for validating complex algebraic inequalities associated with series-parallel systems. This technique relies on permutation of variable values and the method of segmentation.

Preface of 'Interpretation of Algebraic Inequalities: Practical Engineering Optimisation and Generating New Knowledge' by Michael Todinov

The paper introduces the principle of minimized rate of damage accumulation as a domain-independent principle of reliability improvement and risk reduction. A classification is proposed of methods for reducing the rate of damage accumulation. The paper introduces the method of substitution for reducing the rate of damage accumulation. The original assembly/system is substituted with assembly/system performing the same function and based on different physical principles. Such a substitution often eliminates failure modes characterised by intensive damage accumulation. One of the methods discussed is an optimal replacement resulting in the smallest rate of damage accumulation and maximum system reliability. A method for achieving the smallest rate of damage accumulation for a system with components logically arranged in series has been proposed for the first time. A dynamic programming algorithm for determining the optimal variation of multiple damage-inducing factors to minimize the rate of damage accumulation, has also been proposed for the first time. The paper shows that the necessary and sufficient condition for using the additivity rule for calculating the threshold of accumulated damage precipitating failure is the factorisation of the rate of damage accumulation into a function of the amount of damage and a function of the damage-inducing factor.