An Imprecise Fault Tree Approach To Quantifying Reliability Bounds For Corrosion-Induced System Failures

Abstract In high-risk sectors such as oil and gas, time-dependent corrosion can significantly undermine system integrity, leading to unexpected failures and severe incidents. This paper examines why imprecise analysis is used strategically in risk and reliability assessment, the practical barriers to its adoption, and how integrating confidence intervals can overcome these barriers to enhance results. In response, we propose an imprecise approach based on a new unavailability formula to improve conventional fault tree analysis (CFTA) and better account for dependencies among uncertain parameters. In a representative case study, we first apply CFTA with precise inputs, then use interval arithmetic-based FTA with imprecise inputs implemented in MATLAB® through adaptive interval parameterization to quantify uncertainty and reduce over-conservatism caused by neglected variable dependencies. We also develop an affine arithmetic-based FTA in MATLAB®, which preserves first-order dependencies through shared noise symbols. The proposed approach narrows the system unavailability interval by 22.7% compared with IA-based FTA. A subsequent robustness analysis, performed on a different model structure and parameter configuration, demonstrates an even greater reduction of 28.7%, highlighting the method's effectiveness and adaptability. These results confirm that affine arithmetic is an effective method for managing uncertainty in risk and reliability assessment of real engineering systems, as it reduces overestimation, retains computational efficiency, and facilitates decision-maker updates to safe and reliable control actions.