Optimisation of nominal-the-best type quality characteristic in the absence of scaling factor: an empirical method

For a nominal-the-best type of response variable, Taguchi's two-step optimisation process uses signal-to-noise (SN) ratio for minimising the variability in the first stage and then adjusts the mean to the target by changing the levels of some scaling factor that affect only the mean and not the variability. In reality, the input variables often affect both the variability and mean value. In such situations, Taguchi's SN ratio-based optimisation approach is not truly applicable. There prevail some response surface methodology-based approaches which can tackle the above situations. However, fitting well-explained response surfaces for mean and variance is not quite an easy task for many quality practitioners, particularly those who do not have a strong background in mathematics/statistics. In this paper, a simple empirical method is proposed, which requires neither a scaling factor nor response surfaces for mean and variance. The performance of the proposed method is compared with other methods using three case studies. The results show that the proposed method results in optimal or very close to optimal solution.