Optimum Component Redundancy for Maximum System Reliability

Abstract

The method of increasing the reliability of a complex system by adding redundant components is examined using the criterion that inadvertent operation of a component (which is a possible mode of component failure) may lead to failure of the system. On this basis the use of an infinite number of redundant components leads to zero system reliability instead of 100 per cent system reliability. A simple model of a system consisting of off-on-off components is analyzed using separate probabilities for non-operation and for inadvertent operation. Considering only the effects of redundancy, it is shown that maximum system reliability occurs with a relatively small number, m , of redundant components. The value of m depends on the values of the two separate probabilities. Curves are presented which show the effect of the number of redundant elements, m , on system reliability as a function of the two separate component probabilities. The ratio, k , between failures due to non-operation and failures due to inadvertent operation permits estimation of the two separate reliabilities used in the analysis from the conventional definition of component reliability.