A general equation and optimal design for a 2-factor restricted region

Economic, practical, or physical constraints sometimes prevent the factor space of a designed experiment from being a regular p-dimensional hypercube or hypersphere. Since standard designs may not be the best choice, it is desirable to be able to find best designs under these restrictions. This paper extends the work of Zahran et al. (J. Quality Tech. 35 (4)) using a more general equation to define the boundary of a modifying 22 factorial design and considers optimality criteria for the best of the designs.