The variability of system failure probability

Abstract

The failure probability of a system of components is a function of the component failure probabilities. When the latter are random variables owing to the distribution among the components of a property on which failure depends, the system failure probability is also a random variable. To assess the implications of this, it is necessary to obtain the corresponding probability density function. In this paper, an expression is derived relating the probability density functions for system and component failure probabilities, assuming that system failure is defined as failure of at least one component. An example is described in which the expression is evaluated for a system of seven components, using an assumed form for the component failure probability distributions. The density function obtained in this way is compared with the results of an experiment in which the function was simulated from sets of randomly selected numbers.