Some third-order rotatable designs in three dimensions

Abstract

SummarySome new third-order rotatable designs in three dimensions are derived from some of the available third-order rotatable designs in two dimensions. When these designs are used the results of the experiments performed according to the two-dimentional designs need not be discarded. Some of these designs may be performed sequentially in all three factors, starting with a one-dimensional design. Further, these third-order rotatable designs require a smaller number of points than most of the available three-dimensional third-order rotatable designs.

On third order rotatability

“…It is often hard to select a design with a suitably small number of points due to the several moment conditions that must be satisfied simultaneously. Specific discussions are given by Adhikary and Panda (1984, 1986, Arap Koske and Patel (1989), Bagchi (1986), Draper (1960a,b;1961), Gardiner, Grandage and Hader (1959), Herzberg (1964Herzberg ( , 1967, Huda (1981Huda ( , 1982a1983, 1984, 1987a1988, Mukerjee and Huda (1985), Narasimham and Rao (1980), Nigam (1967), Panda (1982), Panda and Das Roy (1990b), Thaker and Das (1961), and Tyagi (1964).…”