| Summary: | This article investigates uncertainty analysis for system with aleatory and epistemic uncertainties and defines a sensitivity analysis indicator to measure the effect of imprecise parameter with epistemic uncertainty on system output, and an efficient numerical simulation methodology is proposed to evaluate the uncertainty analysis and sensitivity analysis indicator. System inputs have aleatory uncertainties defined by probability density functions, and distribution parameters of probability density functions are imprecise due to epistemic uncertainties and are defined by fuzzy sets with membership functions. System will fail to operate when output is less than or equal to zero, and we define membership function of reliability index as system output for uncertainty analysis, and sensitivity analysis indicator associated with an imprecise parameter is defined by absolute difference between original membership function and conditional membership function of reliability index when eliminating epistemic uncertainty relevant to the parameter of interest. Direct evaluation is a time-consuming coupled several-loop Monte Carlo sampling procedure. Thus, we propose an improved importance sampling method for efficient evaluation of uncertainty analysis and sensitivity analysis indicator. Using the proposed improved importance sampling method, only one importance sampling run with a set of input–output importance sampling samples is required to solve uncertainty analysis and sensitivity analysis indicator. Three examples are employed to demonstrate computational efficiency of the proposed method.
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