ISBIS4 Abstract

Contact Author's Name: Sung Hyun Park(last name)
Title of Abstract: Slope-rotatable designs for response surface experiments and their statistical properties
Author(s): Sung Hyun Park
Affiliation: Seoul National University, Seoul, South Korea

The concept of rotatability which is very important in response surface second order designs was proposed by Box and Hunter(1957). A design is said to be rotatable if the variance of the response estimate is a function only of the distance of the point from the design center. However, if differences at points close together are involved, estimation of the local slopes (the rate of change) of the response surface is of interest. In this context \'slope-rotatability\' which is analogue to rotatability was proposed. This paper reviews the proposed concepts of slope-rotatability for second order response surfaces.
Two basic design concepts of slope-rotatability were reviewed, and two more modified concepts of slope-rotatability were also reviewed. The basic concepts are slope-rotatable design over axial directions (Hader and Park(1978)), and slope-rotatable design over all directions(Park(1987)). The modified concepts are slope-rotatable design with equal maximum directional variance(Park and Kwon(1998)), and slope-rotatable minimax design(Park and Kwon(1998)).
Also two measures to assess the slope-rotatability were reviewed. One measure is to assess the slope-rotatability over axial directions (Park and Kim(1992)), and another measure is to assess the slope-rotatabiity over all directions (Jang and Park(1993)).
Future possible directions for further research with regard to these matters were elaborated.