Reliability improvement and risk reduction by inequalities and segmentation

The article introduces new domain-independent methods for improving reliability and reducing risk based on algebraic inequalities and chain-rule segmentation. Two major advantages of algebraic inequalities for reducing risk have been demonstrated: (1) ranking risky prospects in the absence of any knowledge related to the individual building parts and (2) reducing the variability of a risk-critical output parameter. The article demonstrates a highly counter-intuitive result derived using inequalities. If no information about the component reliability characterising the individual suppliers is available, purchasing components from a single supplier or from the smallest possible number of suppliers maximises the probability of a high-reliability assembly. The article also demonstrates the benefits from combining domain-independent methods and domain-specific knowledge for achieving risk reduction in several unrelated domains, decision-making, manufacturing, strength of components and kinematic analysis of complex mechanisms. In this respect, the article introduces the chain-rule segmentation method and applies it to reduce the risk of computational errors in kinematic analysis of complex mechanisms. Finally, the article demonstrates that combining the domain-independent method of segmentation and domain-specific knowledge in stress analysis leads to a significant reduction of the internal stresses and reduction of the risk of overstress failure.