Extended composite importance measures for multi-state systems with epistemic uncertainty of state assignment

Model-based reliability analysis may not be practically useful if reliability estimation contains uncontrollable errors. This paper addresses potential reliability estimation errors from model bias together with model parameters. Given three representative scenarios, reliability analysis strategies with representative methods are proposed. The pros and cons of these strategies are discussed and demonstrated using a tank storage problem based on the finite element model with different fidelity levels. It is found in this paper that the confidence-based reliability analysis considering epistemic uncertainty modeling for both model bias and model parameters can make reliability estimation errors controllable with less conservativeness compared to the direct reliability modeling using the Bayesian approach.

Model-Based Reliability Analysis with Both Model Uncertainty and Parameter Uncertainty

The fault tree analysis has been extensively implemented in failure analysis of engineered systems. In most cases, the probabilities of basic events, e.g. components’ failures, are represented by c...

Evidential network-based failure analysis for systems suffering common cause failure and model parameter uncertainty:

Reliability assessment of systems subject to interval-valued probabilistic common cause failure by evidential networks

Extended LK heuristics for the optimization of linear consecutive-k-out-of-n: F systems considering parametric uncertainty and model uncertainty

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.

Felipe Aguirre Martinez

Papers

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