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
Date Written: 2011
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: Suggested Citation