Sequential robust response surface strategy

• Main Author: DeFeo, Patrick A.
• Other Authors: Statistics
• Format: Others
• Language: en_US
• Published: Virginia Polytechnic Institute and State University 2015
• Subjects: LD5655.V856 1988.D433; Linear models (Statistics); Response surfaces (Statistics)
• Online Access: http://hdl.handle.net/10919/53687

General Response Surface Methodology involves the exploration of some response variable which is a function of other controllable variables. Many criteria exist for selecting an experimental design for the controllable variables. A good choice of a design is one that may not be optimal in a single sense, but rather near optimal with respect to several criteria. This robust approach can lend well to strategies that involve sequential or two stage experimental designs. An experimenter that fits a first order regression model for the response often fears the presence of curvature in the system. Experimental designs can be chosen such that the experimenter who fits a first order model will have a high degree of protection against potential model bias from the presence of curvature. In addition, designs can also be selected such that the experimenter will have a high chance for detection of curvature in the system. A lack of fit test is usually performed for detection of curvature in the system. Ideally, an experimenter desires good detection capabilities along with good protection capabilities. An experimental design criterion that incorporates both detection and protection capabilities is the A₂* criterion. This criterion is used to select the designs which maximize the average noncentrality parameter of the lack of fit test among designs with a fixed bias. The first order rotated design class is a new class of designs that offers an improvement in terms of the A₂* criterion over standard first order factorial designs. In conjunction with a sequential experimental strategy, a class of second order rotated designs are easily constructed by augmenting the first order rotated designs. These designs allow for estimation of second order model terms when a significant lack of fit is observed. Two other design criteria, that are closely related, and incorporate both detection and protection capabilities are the J_PCA, and J_PCMAX criterion. J_PCA, considers the average mean squared error of prediction for a first order model over a region where the detection capabilities of the lack of fit test are not strong. J_PCMAX considers the maximum mean squared error of prediction over the region where the detection capabilities are not strong. The J_PCA and J_PCMAX criteria are used within a sequential strategy to select first order experimental designs that perform well in terms of the mean squared error of prediction when it is likely that a first order model will be employed. These two criteria are also adopted for nonsequential experiments for the evaluation of first order model prediction performance. For these nonsequential experiments, second order designs are used and constructed based upon J_PCA and J_PCMAX for first order model properties and D₂ -efficiency and D-efficiency for second order model properties. === Ph. D.