The performance of control charts for monitoring process variation

The Shewhart R–and S–charts are often used to monitor the variability of a quality characteristic of interest. In order to improve the sensitivity of these charting procedures to detecting small shifts in the process standard deviation, runs rules have been suggested. We evaluate the properties of the run length distributions of these charting procedures using a Markov chain approach. We show that the rules commonly used in practice based on the Western Electric Handbook do not have the statistical performance one might expect. Alternative runs rules are provided that provide the same in-control ARL's as the usual X-chart with runs rules. Average run length comparisons are made among various charts for monitoring variability, including cumulative sum charts and exponentially weighted moving average charts. It is shown that detection of decreases in variability is problematic with all of these methods.