An Efficient Method for Reliability Analysis of Systems Under Epistemic Uncertainty Using Belief Function Theory

We present an efficient method based on the inclusion-exclusion principle to compute the reliability of systems in the presence of epistemic uncertainty. A known drawback of belief functions and other imprecise probabilistic theories is that their manipulation is computationally demanding. Therefore, we investigate some conditions under which the measures of belief function theory are additive. If this property is met, the application of belief functions is more computationally efficient. It is shown that these conditions hold for minimal cuts and paths in reliability theory. A direct implication of this result is that the credal state (state of beliefs) about the failing (working) behavior of components does not affect the credal state about the working (failing) behavior of the system. This result is proven using a reliability analysis approach based on belief function theory. This result implies that the bounding interval of the system's reliability can be obtained with two simple calculations using methods similar to those of classical probabilistic approaches. A discussion about the applicability of the discussed theorems for non-coherent systems is also proposed.