Methods for the Construction of SOGDRD

Abstract

Since the introduction of second order rotatable designs (SORD) by Box and Hunter (1957) some authors have proposed to get new series of second order response surface designs. One such attempt was made by Das and Dey (1967) to get an alternative series of response surface designs by modifying the restrictions imposed on the levels of the factors in a second order rotatable design. Such designs are termed as second order group divisible rotatable designs (SOGDRD). They also proposed some methods for the construction of SOGDRD.  In this paper, a remark on Das and Dey (1967) SOGDRD is noted and some modifications are made in the methods of Das and Dey (1967) to derive the SOGDRD.  A new method of construction of CCD type SOGDRD is also derived. In addition to these methods, general formula for A- and D- optimality for SOGDRD are also deduced.