Continuous Pure Risk Modeling with Triple Integral Structure and Entropy-Driven Uncertainty Quantification

نویسندگان

1 Department of Industrial Engineering, Kish International Campus, University of Tehran, Kish Island, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

3 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.

doi
10.5829/ije.2026.39.11b.22
چکیده

This paper proposes a continuous four-parameter framework for the quantitative assessment of pure risk in gas transmission pipelines. Unlike conventional static probability–consequence models, the proposed approach integrates probability of occurrence, consequence severity, accessibility difficulty, and detectability within a space–time–uncertainty structure. Explosion probability is mapped to the continuous interval [0,1] using a cumulative normal distribution, while epistemic uncertainty is quantified via normalized Shannon entropy, emphasizing maximum risk under mid-probability conditions (P≈0.5). Consequences are modeled through combined financial and non-financial components, and operational constraints are incorporated as continuous coefficients. Overall risk is computed using a triple integral over the spatial, temporal, and uncertainty domains, numerically approximated via a weighted Riemann scheme. At the same time, Monte Carlo simulation is employed separately for uncertainty propagation. Cost-component weights are determined using the Fuzzy Bayesian Best–Worst Method. An application to five zones of an aging gas transmission pipeline in northern Iran shows that, contrary to conventional assessments that rank zone 3 as most critical, the entropy-based model identifies zone 4 as the highest-risk zone and highlights elevated risk in zone 5, consistent with observed incidents.