From taguchi’s orthogonal arrays to full factorial designs and back

Abstract

BACKGROUND Experimentation by means of Taguchi’s orthogonal arrays is frequently used both in exploration and industrial practice, as the way of application of Taguchi’s off-line quality control. In addition, traditional factorial designs are in use for the same purpose. Both approaches have certain advantages and disadvantages in their application. It is commonly accepted that Taguchi’s orthogonal arrays are fractional factorial designs, for two-, three-, four- and five-level factorials. The main advantage of Taguchi’s orthogonal arrays is that they are based on the matrix approach in experimentation. There are no differences between Taguchi’s orthogonal arrays and traditional factorial designs with two-level factors, and, sometimes, with three-level factors, but, until now, it has not been proved that they are unique for more than three level factors. FROM TAGUCHI… In the first part of this chapter, designs are viewed as full factorial designs, Taguchi’s orthogonal arrays as a closed design and traditional arrays as an open factorial design. The process of development procedures and corresponding equations for the allocation of factorial effects in matrix columns are presented, and they are common for both approaches. The procedure consists of the identification of columns for the main effect factors, i.e., basic columns. This is followed by the placement of interactions. It is especially important in cases with more than two-level factors, where there are partitions for all interactions. This methodology has been developed for any number of factor levels, i.e., for sk designs where s = 2…, k also = 2…. The examples of allocations of factorial effects are also presented.. .. AND BACK The second part of the chapter discusses some methods of Taguchi’s post-analysis of experimental results, which the authors consider as the most useful in practical applications. Those post-analyses include the determination of the optimal factor settings for the obtained results, as well as the contribution ratio, followed by Pareto analysis. All described methods are presented by the examples from two case studies, and they are applicable to both approaches.