A sensitivity analysis method to evaluate the impacts of random and interval variables on the probability box

Sensitivity analysis (SA) has been widely used in engineering analyses and designs because it provides information about the importance of input variables to a model response. In practical engineering problems, random and interval variables often coexist. Although some existing SA methods are applicable for the mixture of random and interval variables, most of them do not deal with the epistemic uncertainty of the model response and cannot be performed over a partial range of the response distribution, making it difficult to assist engineers effectively reduce the uncertain scope of the model response. In this paper, a new SA method that evaluates the impacts of parameters of input variables to the entire range or a partial range of the probability box (p-box) is developed. First, the area between the lower and upper bounds of the entire range or a partial range of the p-box is used to measure the uncertain scope of the model response. Three global sensitivity indices are then defined for the sensitivity of the area with respect to the parameters of interval and random variables. To efficiently and accurately calculate these indices, a predictive model based uncertainty analysis method is developed to determine the most probable points and values of the interval variables. The effectiveness of the proposed method is verified by two engineering examples.