Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2011, Article ID 537543, 11 pages
Research Article

A Confidence Region for Zero-Gradient Solutions for Robust Parameter Design Experiments

1Department of Statistics, Temple University, 1810 North 13th Street, Philadelphia, PA 19122, USA
2Quantitative Sciences, GlaxoSmithKline Pharmaceuticals, 1250 South Collegeville Road, Collegeville, PA 19426, USA

Received 11 March 2011; Accepted 28 June 2011

Academic Editor: Myong (MK) Jeong

Copyright © 2011 Aili Cheng et al. 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.


One of the key issues in robust parameter design is to configure the controllable factors to minimize the variance due to noise variables. However, it can sometimes happen that the number of control variables is greater than the number of noise variables. When this occurs, two important situations arise. One is that the variance due to noise variables can be brought down to zero The second is that multiple optimal control variable settings become available to the experimenter. A simultaneous confidence region for such a locus of points not only provides a region of uncertainty about such a solution, but also provides a statistical test of whether or not such points lie within the region of experimentation or a feasible region of operation. However, this situation requires a confidence region for the multiple-solution factor levels that provides proper simultaneous coverage. This requirement has not been previously recognized in the literature. In the case where the number of control variables is greater than the number of noise variables, we show how to construct critical values needed to maintain the simultaneous coverage rate. Two examples are provided as a demonstration of the practical need to adjust the critical values for simultaneous coverage.