Probabilistic interpretation of algebraic inequalities related to reliability and risk.

The paper explores the probabilistic interpretations of algebraic inequalities and presents several findings. First, the inequality of the additive ratios can be used to increase the probability of an event occurring within a set of mutually exclusive and exhaustive events. The interpretation of this inequality produced a counter‐intuitive result, that for suppliers delivering the same quantity of reliable products alongside unknown numbers of unreliable products, the probability of purchasing a reliable product from a randomly selected supplier is higher than the probability of purchasing a reliable product from the market formed by all suppliers. Next, the paper discusses how averaging the reliabilities of components from different varieties can lead to a significant overestimation of the calculated system reliability, as demonstrated by another algebraic inequality interpretation. Finally, the paper derives tight bounds for the reliability of demand in a load‐strength interference model by interpreting the Hayashi's inequality. Notably, these bounds do not depend on the shape of the load distribution and only require the strength distribution to be known in relatively small vicinities of the lower and upper bound of the load. [ABSTRACT FROM AUTHOR]