Joint reliability-importance of components

Hong & Lie (1993) defined joint reliability importance (JRI) as a measure of how two components in a system interact in contributing to system reliability. Their definition and theorems regarding JRI were limited to statistically independent component states. This paper removes the statistical independence restriction by showing that similar results hold in the more general case where component failures can be statistically dependent; however, the calculation of actual values becomes more difficult, because covariance terms can appear in the JRI formula. Despite this, the essential determination and interpretation of the signs of the JRI remain unchanged. Thus analysts who wish to use JRI (e.g., as a design heuristic) can do so in working with real systems where statistical independence is not valid. It is further shown that JRI is always nonzero for some classes of systems