A dependency bounds analysis method for reliability assessment of complex system with hybrid uncertainty

In reliability assessment, a difficulty is to handle a complex system with hybrid uncertainty (aleatory and epistemic uncertainty) and dependency problem. Probability-box is a general model to represent hybrid uncertainty. Arithmetic rules on the structure are mostly used between independent random variables. However, in practice, dependency problems are also common in reliability assessment. In addition, in most real applications, there is some prior information on the dependency of components, but the available information may be not enough to determine dependent parameters. The issue is named non-deterministic dependency problem in the paper. Affine arithmetic is hence used to produce dependent interval estimates. The arithmetic sometimes has a better effect than probability-box arithmetic (interval arithmetic) in dealing with dependency problem. Bayesian network is a commonly used model in reliability assessment. Under Bayesian network framework, this paper proposes a dependency bounds analysis method that combines affine arithmetic and probability-box method to handle hybrid uncertainty and non-deterministic dependency. For the sake of illustration, this method is applied to two real systems. To show the advantages of the proposed method, the proposed method is compared with the Frechet inequalities and 2-stage Monte Carlo method in the second case study.