Using Algebraic Inequalities to Reduce Uncertainty and Risk

The paper discusses applications of the domain-independent method of algebraic inequalities, for reducing uncertainty and risk. Algebraic inequalities have been used for revealing the intrinsic reliability of competing systems and ranking the systems in terms of reliability in the absence of knowledge related to the reliabilities of their components. An algebraic inequality has also been used to establish the principle of the well-ordered parallel-series systems which, in turn, has been applied to maximize the reliability of common parallel-series systems. The paper introduces linking an abstract inequality to a real process by a meaningful interpretation of the variables entering the inequality and its left- and right-hand parts. The meaningful interpretation of a simple algebraic inequality led to a counterintuitive result. If two varieties of items are present in a large batch, the probability of selecting randomly two items of different variety is smaller than the probability of selecting randomly two items of the same variety. This article is available in the ASME Digital Collection at https://doi.org/10.1115/1.4048403.