Kronecker Product Analytical Approach to ANOVA of Surface Roughness Optimization

Abstract

The Fishers-Yates algorithm has remained the most widely used statistical approach that involves the use of sum of squares of treatments or blocks in the determination of mean square errors (MSEs) needful for the computation of F-statistic prior to the decision making based on the acceptance or rejection of the null hypothesis. A review of literature on design of experiments shows a trend away from uncritical acceptance of the approach, thus confirming that sustained effort is being made to develop a new method. As part of this effort, this paper attempts to develop a novel approach for determining the MSEs in designed experiment. Using the new method, the combination of controllable variables that optimized most the surface finish of machined workpiece materials was determined with Kronecker product analysis which was enhanced by the use of MATLAB software package. The response value for the surface roughness, X_ijklmn, obtained from the model developed was 1.5368μm. Residual analysis carried out indicates that the model output was adequate. The analytical method explored can be used to develop a statistical software package that will be helpful in the computation of sums of squares of observation as well as make decision on the null hypothesis without recourse to Fisher’s table.

Keywords: Kronecker product, Sum of Squares, Mean sum of squares, Optimization.