Diagnostic Results Concerning a Measure of Rotatability
研究了Khuri提出的旋转性度量，用于判断预测方差在球面上的恒定性，给出了预测方差范围的上界，帮助理解响应曲面设计的近似旋转性，并通过四个设计实例说明。
SUMMARY The measure of rotatability introduced by Khuri is utilized to determine the closeness of the prediction variance to being constant on a sphere S(r) of radius r centred at the origin. In particular, several upper bounds on the range of the prediction variances on S(r) are obtained. These upper bounds provide information about the amount of dispersion that can exist in the prediction variances on all spheres inside a region of interest. Such information gives added insight into the nature of ‘near rotatability’ of a given response surface design. This is illustrated in an example involving four designs: the 32 factorial and three hybrid designs described by Roquemore, namely the 310, 311A and 311B designs.