Sensitivity Analysis in Quantified Interval Constraint Satisfaction Problems

Interval is an alternative to probability distribution in quantifying epistemic uncertainty for reliability analysis when there is a lack of data to fit a distribution with good confidence. It only requires the information of lower and upper bounds. The propagation of uncertainty is analyzed by solving interval-valued constraint satisfaction problems (CSPs). By introducing logic quantifiers, quantified constraint satisfaction problems (QCSPs) can capture more semantics and engineering intent than CSPs. Sensitivity analysis (SA) takes into account of variations associated with the structure and parameters of interval constraints to study to which extent they affect the output. In this paper, a global SA method is developed for QCSPs, where the effects of quantifiers and interval ranges on the constraints are analyzed based on several proposed metrics, which indicate the levels of indeterminacy for inputs and outputs as well as unsatisfiability of constraints. Two vehicle design problems are used to demonstrate the proposed approach.