Exploring the Principle of Multi-Dimensional Risk Analysis and a Case Study in Two-Dimensional Risk

By examining the significant flaws in multivariate risk analysis and integrated risk analysis, this article introduces a new approach to evaluating the total risk within complex risk systems: the principle of multi-dimensional risk (MDR) analysis. Under this framework, the scope of each individual risk is first defined, and the risk-bearing entity is identified. Each risk is then analyzed independently, and the results are subsequently integrated to provide a comprehensive view of MDR. Multivariate risk analysis becomes increasingly impractical as the number of factors grows, due to the correspondingly large sample size required—often unattainable in real-world conditions. Integrated risk analysis methods, such as weighted combinations and Copula techniques, are heavily influenced by subjective factors, which compromise the reliability of their results. In contrast, MDR analysis involves fewer variables per individual risk, reducing the sample size requirement and making data collection more feasible. Individual risks can be quantified using objective physical indicators such as economic loss or physical injury, enabling more accurate calculations of the total risk across the system. A case study involving two-dimensional risks—flood and earthquake—demonstrated that these events often have vastly different occurrence cycles. When these risks are entangled in conventional analysis, the resulting annual total risk value can be severely distorted. By analyzing individual risks separately, maintaining the focus on overall system risk, and treating the total risk as an MDR problem, a more reliable foundation for policy-making and risk management can be established. There are at least three types of MDR relationships: independent, compounding, and negatively correlated. As a result, no universal MDR analysis model exists.