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    CONFIDENCE REGIONS FOR OPTIMAL CONTROLLABLE VARIABLES FOR THE ROBUST PARAMETER DESIGN PROBLEM

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    Genre
    Thesis/Dissertation
    Date
    2012
    Author
    Cheng, Aili
    Advisor
    Chitturi, Pallavi
    Committee member
    Raghavarao, Damaraju
    Sobel, Marc J.
    Peterson, John
    Viswanathan, Krupa S.
    Department
    Statistics
    Subject
    Statistics
    Confidence Region
    Noise Variables
    Response Surface
    Robust Parameter Design
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/959
    
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    DOI
    http://dx.doi.org/10.34944/dspace/941
    Abstract
    In robust parameter design it is often possible to set the levels of the controllable factors to produce a zero gradient for the transmission of variability from the noise variables. If the number of control variables is greater than the number of noise variables, a continuum of zero-gradient solutions exists. This situation is useful as it provides the experimenter with multiple conditions under which to configure a zero gradient for noise variable transmission. 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. The zero-gradient confidence region only focuses on the variance, and there are in fact many such situations in which focus is or could be placed entirely on the process variance. In the situation where both mean and variance need to be considered, a general confidence region in control variables is developed by minimizing weighted mean square error. This general method is applicable to many situations including mixture experiments which have an inherit constraint on the control factors. It also gives the user the flexibility to put different weights on the mean and variance parts for simultaneous optimization. It turns out that the same computational algorithm can be used to compute the dual confidence region in both control factors and the response variable.
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