Multidimensional Risk Analysis in Conditions of Stochastic Data Heterogeneity

In a broad sense, risk is understood as the possible danger of any adverse outcome. When assessing the reliability of systems, it is often necessary to consider many risk factors that may be correlated. When conducting risk analysis, situations often arise when data samples are stochastically heterogeneous. Such situations include non-Gaussian distributions of risk factors, heterogeneity of data, the presence of outliers and small samples. This imposes requirements on risk analysis methods. In this case, risk analysis is fraught with difficulties. The paper considers the basic model of multidimensional risk, in which set risk factors are represented as a Gaussian vector with correlated components. This model assumes a known range of adverse outcomes. Stochastic heterogeneity of data leads to instability of risk analysis based on this model. Various ways of accounting for data heterogeneity are considered. An approach based on the preliminary identification of outliers for each of the risk factors and subsequent adjustment of the covariance matrix of the data is proposed. The analysis on test cases showed acceptable stability of risk analysis in conditions of contamination data.

Keywords: Risk, random vector, model, system, robustness, Gaussian distribution, heterogeneity of data.