Response Surface Equations Research Articles

Mixture Designs for Three Factors

Summary Scheffé, in two recent papers (1958, 1963), has given designs for experimenting with mixtures. The basis of these designs is the choice of symmetrical arrangements of points in the factor space and the fitting of carefully chosen models which have exactly as many coefficients as there are data points. The designs are such that some of the experiments do not contain any of one or more ingredients of the mixture. This may or may not be a disadvantage depending on the problem involved. Here an alternative form of design selection is made for the case of mixtures of three factors. (The method has also been extended to four factors.) This involves the premise that, in the absence of specialist knowledge about the form of the true response function, it is desired to fit a response surface equation of first or second order over the factor space of possible mixtures, and experimental runs are needed which, in a certain sense, ensure the best surface fit possible. The principles used in the choice of appropriate designs will be those originally introduced by Box and Draper (1959).

The Effect of Sulfur on the Absorption and Utilization of Molybdenum by Peas

AbstractAn experiment including a factorial combination of 4 rates of S and 3 rates of Mo fertilization was conducted on a low‐S, low‐Mo soil to evaluate the effects of soil S level on the absorption and utilization of Mo by peas. The uptake of soil and fertilizer Mo was markedly reduced by applications of sulfate fertilizer. The higher rates of S fertilization also reduced the apparent efficiency of utilization of Mo by the plant. Higher plant Mo levels were required for maximum yield and N fixation as the SO4‐S content of the plant tissue was increased by S fertilization. Correlation coefficients of 0.78 and 0.94 were obtained with response surface equations for seed yield and vine N content as functions of the Mo and SO4‐S contents of the plant tissues. Maximum pea yields were associated with plant tissue Mo contents of 0.3 to 1.0 ppm. and 200 to 600 ppm. of SO4‐S.