A New Algorithm Based Orthogonal Arrays for Design of Experiment on Nonlinear Functions

Abstract

A new algorithm based orthogonal arrays was developed to determine the optimal solution amid all the optional settings for a new initiated device. The proposed algorithm begins with several successive orthogonal arrays and ends with a full factorial array. After each orthogonal array is accomplished, the algorithm employs variance analyses to screen the dominating variable from among all the current variables and then determines the best level of the dominating variable. Here, after successive orthogonal arrays were completed, the number of unfixed variables was gradually reduced to a number that was small enough to feasibly conduct a full factorial array, resulting in the final selection of the problem’s optimum setting. We verified the proposed algorithm by first applying it to the Rosenbrock function.To distinguish the superior performance of the proposed algorithm in comparison with other design of experiments approaches, we experimented with three different problems with non-interactive or interactive variables. The results show that the proposed method not only provides a final solution that is identical to the problem’s exact solution but also that the computation time in comparison with that required by a full factorial array drops drastically as the number of variables increases.