A note on the efficiency of Taguchi signal-to noise ratio

Use of Taguchi Signal-to-Noise (SN) ratio is often advocated for the analysis of robust parameter design when a cross array format is employed for the experiment. Theoretical studies, however, have shown that such use should be limited to the special case in which the population standard deviation is proportional to the mean. In other circumstances, performance measures other than the SN ratio need to be used. For example, when the standard deviation is not dependent on the mean, the familiar variance should be employed instead of the SN ratio. This particular situation is explored in this paper to show that SN ratio is less efficient than variance, meaning that a loss of information in the available data occurs. Focusing on one specific control factors combination, two alternative significance tests are introduced to make inference on the variance and the SN ratio, respectively. Empirical power functions are then calculated and utilized to assess the loss of efficiency associated with the use of SN ratio.