Developing robust design: determining critical limits for signal-to-noise ratio based on process capability index

In design of experiments (DOE), the higher the ratio of signal‐to‐noise (S/N) is, the better the experiment would be. However, there might be cases in which, process capability is not desirable, while the S/N ratio is high. To resolve such problem, in this study an approach has been proposed to control the ratio. For this purpose, the process capability indices, i.e., Cp and CPK ratios have been integrated with S/N ratio, and critical ratios have been determined for the two mentioned indices. The determined ratios not only have been used in measuring the value of S/N ratio, but also have been compared with the critical ratio. In this comparison, the changes of denominator has been studied and it has been found that selecting the experiment with highest S/N ratio is done in respect of controlling its undesirable changes within acceptable limits.