The Computer Search For The Optimal Settings Of A Multi-Factorial Experiment Using Response Surfaces D-Optimality Design Criterion

ABSTRACT

Most experimental situations call for standard designs that can be constructed

with many statistical software packages. In some situations, however, standard designs

are not appropriate or practicable.

Computer-aided designs are experimental designs that are generated based on a

particular optimality criterion and are generally optimal only for a specified model.

In this work designs are generated for non-standard multifactor experiment using

D-optimality criterion.

The experiment involves four factors, Nitrogen, Phosphorus, Sulphur, and

Potassium each varied at 5, 5, 3, and 2 levels respectively. The total treatment

combinations are 150, out of which only the best 21 treatment combinations are required.

The factors were tested on maize, sorghum and millet.

The D-optimality criterion, which seeks to maximize the determinant of the

information matrix of a design, was used to search for the best 21 treatment combinations

(optimal settings). The interaction, quadratic and purequadratic models were used as

prespecified models while generating the optimal settings. Also, control and without

control levels of the factors were considered.

The spread of points and the number of design points generated by each model

was studied. The quadratic model was found to be the most suitable and recommended

for this type of experiment. A measure of rotatability was computed for the quadratic

model and it was found that the design generated by the model is 83.55% rotatable,

indicating that the design is near rotatable.