A new kind of sensitivity index for multivariate output

• A new sensitivity index for models with multivariate output is presented.
• The new index can consider both uncertainties and correlations of multivariate output.
• The mathematical properties of the new index are derived.
• The advantages of the new index with respect to the existing ones are highlighted.

Mathematical and computational models with correlated multivariate output are commonly used for risk assessment and decision support in engineering. Traditional methods for sensitivity analysis of the model with scalar output fail to provide satisfactory results for this multivariate case. In this work, we introduce a new sensitivity index which looks at the influence of input uncertainty on the entire distribution of the multivariate output without reference to a specific moment of the output. The definition of the new index is based on the multivariate probability integral transformation (PIT), which can take into account both of the uncertainties and the correlations among multivariate output. The mathematical properties of the proposed sensitivity index are discussed and its differences with the sensitivity indices previously introduced in the literature are highlighted. Two numerical examples and a rotating shaft model of an aircraft wing are employed to illustrate the validity and potential benefits of the new sensitivity index.