ABSTRACT
This chapter provides an overview of research related to the applications of algebraic inequalities and fundamental concepts related to risk and uncertainty reduction by using algebraic inequalities. Among the introduced concepts are the concepts of risk, uncertainty and domain-independent methods for reliability improvement and risk and uncertainty reduction. The chapter argues that the reliability and risk science provides primarily methods for measuring and assessing the reliability and risk, not domain-independent methods for improving the reliability and reducing risk which could provide direct input to the design process. The chapter analyses the drawbacks of the data-driven approach and the physics-of-failure approach to reliability improvement and risk reduction and summarizes the advantages of the domain-independent approach. The chapter also introduces a new domain-independent method for risk and uncertainty reduction based on algebraic inequalities which can be used for: (i) revealing the intrinsic reliability of systems and processes and their ranking, in the absence of knowledge related to the reliabilities of their building parts; (ii) reducing aleatory and epistemic uncertainty; (iii) obtaining tight upper and lower bounds of risk-critical parameters and mechanical properties; (iv) supporting risk-critical decisions and (v) optimisation to achieve maximum reliability, performance and robust design.
The advantages of the new domain-independent methods are also spelled out. A formidable advantage of algebraic inequalities is that they do not require knowledge related to the distributions of the variables entering the inequalities. This makes the method of algebraic inequalities ideal for handling deep uncertainty associated with components, properties and control parameters and for ranking designs in the absence of reliability data related to the separate components.
Finally, a classification is proposed of techniques based on algebraic inequalities for reliability improvement and risk and uncertainty reduction.
