JSM 2005 - Toronto

Abstract #303823

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Activity Number: 125
Type: Topic Contributed
Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
Sponsor: Section on Quality and Productivity
Abstract - #303823
Title: Partially Rotatable Split-plot Response Surface Design
Author(s): Li Wang*+ and G. Geoffrey Vining
Companies: Virginia Polytechnic Institute and State University and Virginia Polytechnic Institute and State University
Address: 810 University City Blvd Apt.17, Blacksburg, VA, 24060, United States
Keywords: split plot ; response surface design ; rotatable
Abstract:

Box and Hunter (1957) derived the conditions for the rotatable completely randomized design. In cases when some factors are hard to change while others are easy to change, a split-plot experiment is formed. We find that exact rotatability for a split-plot central composite design (CCD) cannot be achieved. As an alternative, we propose the partially rotatable split-plot design that uses two distance measures for the whole-plot factors and subplot factors. The resulting prediction variance is a function of the separate distances, instead of their sum. The resulting design has separate alpha values for the whole-plot and subplot axial runs. In the special case where the whole-plot variance component is zero, the partially rotatable split-plot CCD becomes the standard rotatable CCD. When the design is balanced and meets the conditions for the ordinary least-squares estimates to be equivalent to the generalized least-squares estimates and if the subplot quadratic terms are not whole-plot effects, the choice of the two alpha values for a partially rotatable split-plot CCD does not depend on the specific values for the two variance components.

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Revised March 2005