Improving system reliability and the probability of selecting reliable components by interpreting algebraic inequalities

Abstract

New results related to the reliability of common systems with interchangeable redundancies at a component level have been obtained by deriving and interpreting a new algebraic inequality. It is shown that for systems with interchangeable redundant components, the system reliability can be increased by asymmetrical arrangement of the redundant components. Maximum system reliability is obtained by arranging the main components in ascending order of their probabilities of failure while the redundant components are arranged in descending order of their probabilities of failure. For the inequality of the additive ratios, a novel probabilistic interpretation is provided which resulted in a powerful strategy for improving the probability of an event occurring with mutually exclusive events. Using this result, a counter-intuitive strategy has been developed for improving the probability of purchasing a reliable product from a set of suppliers.