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

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

Posted: 5 Mar 2016

See all articles by Aili Cheng

Aili Cheng

Independent

Pallavi Chitturi

Temple University - Department of Statisitcs

Date Written: 2011

Abstract

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.

Keywords: robust parameter design, noise variables, control variables

Suggested Citation

Cheng, Aili and Chitturi, Pallavi, A Confidence Region for Zero-Gradient Solutions for Robust Parameter Design Experiments (2011). International Journal of Quality, Statistics, and Reliability Volume 2011, Article ID 537543, 11 pages , Available at SSRN: https://ssrn.com/abstract=2741959

Aili Cheng

Independent ( email )

Pallavi Chitturi (Contact Author)

Temple University - Department of Statisitcs ( email )

Philadelphia, PA 19027
United States

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