Abstract

In this paper, we propose a methodology for construction of confidence interval on mean values with interval data for input variable in uncertainty analysis and design optimization problems. The construction of confidence interval with interval data is known as a combinatorial optimization problem. Finding confidence bounds on the mean with interval data has been generally considered an NP hard problem, because it includes a search among the combinations of multiple values of the variables, including interval endpoints. In this paper, we present efficient algorithms based on continuous optimization to find the confidence interval on mean values with interval data. With numerical experimentation, we show that the proposed confidence bound algorithms are scalable in polynomial time with respect to increasing number of intervals. 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.

Highlights

  • Uncertainty quantification plays an increasingly important role in assessing the performance, safety, and reliability of complex physical systems, even in the absence of adequate amount of experimental data for many applications

  • Ferson et al [3] discussed the methods of computing two confidence intervals for the mean of the interval data based on the assumption that the data come from a normal population, one for the lower bound on the mean called the lower confidence limit and the other for the upper bound on mean called the upper confidence limit

  • This paper proposed several formulations and algorithms for construction of confidence interval on mean for interval data, which are illustrated through numerical examples with different numbers of intervals and type of overlap

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Summary

Introduction

Uncertainty quantification plays an increasingly important role in assessing the performance, safety, and reliability of complex physical systems, even in the absence of adequate amount of experimental data for many applications. Ferson et al [3] discussed the methods of computing two confidence intervals for the mean of the interval data based on the assumption that the data come from a normal population, one for the lower bound on the mean called the lower confidence limit and the other for the upper bound on mean called the upper confidence limit This concept of two confidence limits is useful for outlier detection problems, a single confidence interval that contains whole range of possible values for a variable described by interval data is necessary for many engineering problems (e.g., robust design optimization under interval uncertainty).

Construction of Confidence Interval with Interval Data
Numerical Examples
Conclusions
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