The performance of treatments in single-factor experiments using Six Sigma metrics

Whether the specification of a process parameter of interest (response) is available or not, experimenters always try to optimise the process by moving the mean close to the target value and simultaneously reducing the variance. The Analysis of Variance (ANOVA) is a powerful method and is useful to know whether the treatment means are significantly different or not. As a part of post-ANOVA analysis, when the hypothesis of equal means is rejected, various types of Multiple Comparison Tests (MCTs) are available to classify the means into different homogeneous groups. Also, in order to identify the significant treatment levels, the Analysis of Means (ANOM), a graphical approach, is found to be useful as it serves as an alternative to ANOVA. This paper concentrates on the analysis of the actual performance of the treatment means from the Six Sigma practitioners' point of view. Therefore, a new Six Sigma-based approach is proposed to study the performance of the treatment levels in single-factor experiments using Six Sigma performance metrics such as 'mean shifts' and 'sigma quality levels'. A new graphical display that uses mean shifts and sigma quality levels is also developed for easy interpretation. This approach will help the experimenters, particularly Six Sigma practitioners, decide on the treatment level(s) that can give the most efficient response. A number of examples are considered for illustration.