Selecting levels for factors for industrial process experiments

Abstract

A method is provided for defining a minimally sized set of industrial process experiments which are sufficient to identify optimal levels for factors which go into the process. The method defines levels for the factors for the experiments in terms of a symmetric orthogonal array, which represents a valid Galois field for a number of levels for each factor equal to a prime number. The factors are divided into first and second groups. In accordance with Galois field theory, the required number of experiments is a number sufficient to provide a complete set of permutations of levels for the first group of factors. For each experiment, the levels for the second group of factors are determined based on the levels of the first group of factors. In a preferred embodiment, level symbols which are consecutive integers ranging upward from zero are assigned to the levels for each factor. The levels for the second group of factors are computed by performing a modulo addition of the levels for the first factors, scaled by coefficients which differ for the different experiments. Interactions between factors are represented by the factors making up the interactions, and associated indices. In a second preferred embodiment, the factors which make up the interactions are assigned to the first group of factors, and the levels for the second factors are computed based on coefficients which do not correspond with the indices of the interactions.