Logic differential calculus in time-dependent analysis of a pair of system components

An important task of reliability analysis is investigation of importance of the system components. Such an investigation allows evaluating influence of one or several system components on system operation. This evaluation is done using importance measures. A lot of measures exist for ranking importance of a single system component. In case of two components, two measures are very often used — Joint Reliability Importance (JRI) and joint failure importance. These two indices quantify interaction of two components in a system. In this paper, we propose a new measure, which allows estimating the probability that a simultaneous failure of two system components results in system failure, and we compare it with JRI. Calculation of this new measure is performed using logic differential calculus.