A measure of rotatability for second order response surface designs

Abstract

Abstract. The concept of rotatability introduced by Box and Hunter (1957, Ann. Math. Statist., 28, 195-241) is an important design criterion for response surface design. Recently, a few measures of rotatability that enable us to assess the degree of rotatability for a given response surface design have been introduced. In this paper, a new measure of rotatability for second order response surface designs is suggested, and illustrated for 3 k factorial design and central composite design. Also a short comparison is made between the proposed measure with the previously suggested measures.

A measure of robust slope-rotatability for second-order response surface experimental designs

“…The degree of rotatability for a design that is not rotatable under ordinary (i.e. with uncorrelated and homoscedastic errors) regression models was assessed by Draper and Guttman [10], Khuri [15], Draper and Pukelsheim [11] and Park et al [27]. Many authors have studied rotatable designs and slope-rotatable designs assuming errors to be uncorrelated and homoscedastic.…”

Statistical Measure of Second Order Response Surface Rotatability Using an Infinite Class of Supplementary Difference Sets

“…Further research was done by Mutiso, Kerich and Ng'eno [3,4] where they constructed five level rotatable designs using an infinite class of supplementary difference sets. Park et al [5,6] developed a measure of rotatability that is invariant under rotation and Ng'eno [7] developed a measure of modified rotatability using an infinite class of supplementary difference sets by fixing c=5. This article presents a measure of Box-Hunter [1] rotatability by fixing c = 3.…”

George Box and the design of experiments: statistics and discovery

“…Subsequent research has explored a number of metrics that can be useful for describing designs when rotatability cannot be achieved. These include variance dispersion graphs [17] and some indices of rotatability [18][19][20][21].…”