Multi‐response optimisation using Taguchi method and super ranking concept

Abstract

Purpose

The purpose of this paper is to propose a simple methodology in solving multi‐response optimisation problems by employing Taguchi methods and a non‐parametric statistical technique.

Design/methodology/approach

There is a continuous interest in developing effective and statistically sound multi‐response optimisation methods such that they will provide a firm framework in global product and process improvement. A non‐parametric approach is proposed for the first time in a five‐step methodology that exploits Taguchi's fractional factorial designs and the concept of signal‐to‐noise ratio in data consolidation. The distinct feature of this method is the transformation of each response variable to a single rank variable. The subsequent incorporation of the squared ranks for each of the investigated responses issues a single master‐rank response suitably referred to conveniently as a “Super Rank” (SR) response, thus collapsing all dependent product characteristic information into a single non‐dimensional variable. This SR variable is handled by standard non‐parametric methods such as Wilcoxon's two‐sample, rank sum test or Mann‐Whitney's test eliminating at the same time multi‐distribution effects and small‐sample complications expected for this type of experimentation.

Findings

The proposed methodology is tested on already published data pertaining a design problem in the electronic assembly technology field. The case study requires six‐factor simultaneous optimisation of three response variables. A second example is analyzed by the proposed method focusing on the optimisation of a submerged arc‐welding process problem due to a group of five factors. The Mann‐Whitney's test contrasts the effects of factor settings one‐to‐one on the SR response in order to assign statistical significance to the optimal factor settings.

Research limitations/implications

The application of this methodology is tested at the same time in a real three‐response optimisation case study where each response belongs to different optimisation category.

Practical implications

The methodology outlined in this work eliminates the need for sophisticated multi‐response data handling. In addition, small‐sample considerations and multi‐distribution effects that may be inherent do not restrict the applicability of the method presented herein by this type of experimentation.

Originality/value

This investigation provides a new angle to the published methods of multi‐response optimisation by supporting Taguchi's design of experiments methods through a multi‐ranking scheme that leads to non‐parametric factor resolution.

Citation

Besseris, G.J. (2008), "Multi‐response optimisation using Taguchi method and super ranking concept", Journal of Manufacturing Technology Management, Vol. 19 No. 8, pp. 1015-1029. https://doi.org/10.1108/17410380810911763