A Distribution-Free Phase I Control Chart for Subgroup Scale

Abstract

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.

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