A distribution-free phase I control chart for subgroup scale. - Jones-Farmer, L. Allison (Journal of Quality Technology)
Most Phase I control chart methods are based on the often untested and unreasonable assumption of normally distributed process observations. While there has been some work on distribution-free Phase I procedures for process location, at present, we found no distribution free Phase I methods for evaluating process scale. We propose a Phase I control chart that is distribution free when the process is in-control. This method can be used to define the in-control state of the process variability and to aid in identifying an in-control reference sample. The proposed scale charting method is compared with the traditional R and S-charts using Monte Carlo simulation. We show that the in control performance of the R and S charts is poor in Phase I, both when the process data follow a normal distribution and when the distribution deviates from the normal model. Our proposed method achieves desired in control performance when used with both normal and nonnormal data and is sensitive to subgroup differences in process scale. We offer advice for combining this method with an existing distribution free Phase I chart for studying process location.