ON SECOND ORDER SURFACES ESTIMATION AND ROTABlLITY

Abstract

The design of an experiment is an important component when collecting data to gain a deeper understanding of a problem. It is from the data collected that inferential statements concerning some phenomenon have to be made; therefore, we wish to extract as much relevant infonnation as possible from the data collected. Depending on the nature of the problem, good designs may be very different. The special type of problem studied here is the estimation of second order response surfaces. This type of response sutfaces are often used to locally approximate the response in a neighborhood of its maximum. The fIrst of the three papers included in the present study provides a brief overview of one of the most co~on designs of handling this problem. This design is a fractional two-level factorial design augmented with a star. An alternative design, called the complemented simplex design, is developed and compared with the augmented fractional factorial design. It is shown that the simplex design (up tQ six dimensions) is at least as good as the fractional factorial design with respect to a defmed design criterion. The comparison is made within the class of rotatable designs. Unfortunately, it shows that the complemented simplex design cannot be made rotatable in more than six dimensions. The second paper shows how saturated designs can be constructed from the complemented simplex design. These designs are compared with improved Koshal designs (up to six dimensions). Neither design was found to be superior to the other in all dimensions. Also, which design is superior depends on the design criterion. The third paper illustrates the complexity of rotatability and the difficulties in measuring rotatability. A graphical method of presenting degree ofllack of rotatability is presented.