A MEASURE OF ROTATABILITY FOR
SECOND ORDER RESPONSE SURFACE DESIGNS

SUNG H. PARK1, JUN H. LIM1 AND YASUMASA BABA2

1 Department of Computer Science and Statistics, Seoul National University,
San 56-1, Shinrim-Dong, Kwanak-ku, Seoul 151-742, Korea
2 The 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 3k 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.

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