%0 Journal Article
%T An Optimization-Based Approach to Calculate Confidence Interval on Mean Value with Interval Data
%A Kais Zaman
%A Saraf Anika Kritee
%J Journal of Optimization
%D 2014
%R 10.1155/2014/768932
%X 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. 1. 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. Uncertainty in engineering analysis and design arises from several different sources and must be quantified with accuracy for further analysis. Sources of uncertainty may be divided into two types: aleatory and epistemic. Aleatory uncertainty is irreducible. Examples include phenomena that exhibit natural variation like environmental conditions (temperature, wind speed, etc.). Manufacturing variations due to limited precision in tools and processes also result in this type of uncertainty. In contrast, epistemic uncertainty results from a lack of knowledge about the system, or due to approximations in the system behavior models, or due to limited or subjective (e.g., expert opinion that results in interval data) data; it can be reduced as more information about the system or the variables is obtained. Epistemic uncertainty can be viewed in two ways. It can be defined with reference to a stochastic but poorly known quantity [1] or with reference to a fixed but poorly known physical quantity [2]. The
%U http://www.hindawi.com/journals/jopti/2014/768932/