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Journal of Optimization
Volume 2014, Article ID 768932, 8 pages
Research Article

An Optimization-Based Approach to Calculate Confidence Interval on Mean Value with Interval Data

Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh

Received 5 February 2014; Revised 28 June 2014; Accepted 29 June 2014; Published 13 July 2014

Academic Editor: Ferrante Neri

Copyright © 2014 Kais Zaman and Saraf Anika Kritee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.