Many industrial experiments are conducted under various conditions which do not facilitate complete randomization of all the experimental factors. In response surface methodology whenever there are restrictions on randomization the experimental procedure usually follows the split plot design approach. Split plot designs are used when there are factors which are difficult or costly to change or adjust during an experiment. Split plot designs are currently generating renewed interest because of their usefulness and practical application in industrial settings. Despite the work accomplished through various research efforts, there is still a need to understand the optimality properties of these designs for second-order response surface models. This dissertation provides the development of an analytical approach for the computation of various optimality properties for the assessment of second-order split plot designs. The approach involves a thorough investigation of the impact of restricted randomization on the information matrix, which characterizes much of the relationship between the design points and the proposed response surface model for split plot designs. Several important insights are presented for the construction of second-order split plot designs. In addition, the analytical equations reported compute exact design optimality values and are more efficient than currently available methods. A particular feature of these analytical equations is that they are functions of the design parameters, radius and variance ratio. Further, a significant result is the ability to efficiently compute the exact value of the integrated prediction variance for both split plot designs and completely randomized designs. The functionality of the computational procedures presented provides easy evaluation of the impact of changes in the design structure and variance ratio on the optimality properties of second-order split plot designs. / A Dissertation Submitted to the Department of Industrial Engineering in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy. / Summer Semester, 2006. / July 6, 2006. / Integrated Variance G-optimality, Information Matrix, Split Plots, Design Optimality, Response Surface Designs / Includes bibliographical references. / James R. Simpson, Professor Directing Dissertation; Anuj Srivastava, Outside Committee Member; Peter A. Parker, Outside Committee Member; Joseph J. Pignatiello, Jr., Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_175739 |
| Contributors | Wesley, Wayne R. (authoraut), Simpson, James R. (professor directing dissertation), Srivastava, Anuj (outside committee member), Parker, Peter A. (outside committee member), Pignatiello, Joseph J. (committee member), Department of Industrial and Manufacturing Engineering (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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