Proper Formulation of π-Equation and a Comparison With Regressive Orthogonal Rotating Experimental Design

It is more often than not that prediction precision of an empirical equation is low, which is obtained through the π-equation, the component equations and the corresponding experiments. This paper revealed that “The component equations must have the same form”, advanced by G. Murphy and the lower correlation coefficient of regression model are the major sources of the predictions error. Based on the experiment of “Settling Time of a Sphere in a Fluid” containing 7 variables, author explicitly suggested that the component equations may have different forms from each other and advanced that the prediction may be carried out in a set of separated areas on the curved surface in the factorial space. Each area has its own P-equation which is form ulated by corresponding component equations. A comparison with the regressive orthogonal rotating experimental design was briefly made.