ABSTRACT
This chapter presents a method for improving reliability and reducing risk by proving an abstract inequality derived from a real physical system or process. It includes (i) detailed analysis of the system, (ii) conjecturing an inequality about the competing alternatives or an inequality related to the bounds of a risk-critical parameter, (iii) testing the conjectured inequality by using Monte Carlo simulation and (iv) proving the inequality rigorously.
Often, the reliabilities of the components building the system are unknown. As a result, the epistemic uncertainty associated with the reliabilities of the components building the system translates into epistemic uncertainty related to which system is superior. In many cases, the algebraic inequalities significantly reduce the epistemic uncertainty and reveal the intrinsic reliability of systems and processes. As a result, competing systems and processes can be ranked successfully in terms of reliability and risk in the absence of any knowledge related to the reliabilities of their building parts. The method is demonstrated on systems with the same topology and different components arrangements and on systems with different topologies built with the same type of components.
