A MEASURE OF ROTATABILITY FOR SECOND ORDER RESPONSE SURFACE DESIGNS

SUNG H. PARK^{1}, JUN H. LIM^{1} AND YASUMASA BABA^{2}

1Department of Computer Science and Statistics, Seoul National University, San 56-1, Shinrim-Dong, Kwanak-ku, Seoul 151-742, Korea

2The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan

(Received March 28, 1991; revised November 16, 1992)

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.

Key words and phrases: Rotatability, measure, response surface design, factorial design, central composite design.