A Domain-Independent Method for Risk Reduction Based on Reverse Engineering of Sub-Additive Algebraic Inequalities

Source abstract

This paper introduces a novel, domain-independent methodology for risk reduction based on the reverse engineering of sub-additive inequalities. The proposed approach establishes a robust and unifying theoretical framework for risk reduction that is applicable across a broad range of otherwise unrelated domains. As part of the methodology, a general sub-additive inequality is formulated and rigorously proved, together with sufficient conditions for its validity. The analysis demonstrates that, for the inequality to be reverse engineered, both the risk-controlling parameter and the measure of risk must be additive quantities. Several important special cases of general inequality are derived, and the influence of segmentation on risk reduction has been examined. The practical applicability of the proposed framework is demonstrated through diverse examples, including the reduction in expected failures through optimized inspection, mitigation of corrosion damage and environmental pollution, prevention of runaway reactions, enhancement of cutting tool reliability, and optimization of dose distribution to reduce health risks.