Construction of confidence interval on mean value with interval data

In this paper, we propose a methodology for construction of confidence interval on mean values with interval data for input variable in uncertainty analysis problems. Confidence interval on mean values depends on the values of moments of the sampled data. For construction of confidence interval with point data, well-established methods are available in the literature. However, unlike point data where single estimates for the moments of data can be calculated, moments of interval data can only be computed in terms of upper and lower bounds implying that with interval data every moment will be an interval itself. This suggests that the construction of confidence interval with interval data is an optimization problem. In this paper, we present efficient algorithms based on continuous optimization to find the confidence interval on mean values with interval data. Several sets of interval data with different numbers of intervals and type of overlap are presented to demonstrate the proposed methods. As against the current practice for the design optimization with interval data that typically implements the constraints on interval variables through the computation of bounds on mean values from the sampled data, the proposed approach of construction of confidence interval enables more complete implementation of design optimization under interval uncertainty.