Robustification of Cumulative Sum Charts by Winsorization

Cumulative sum control charts are particularly effective for detecting special causes that lead to a persistent change in the process parameters. Like the traditional Shewhart charts (though to a much smaller degree) they are affected by the underlying distribution of data, in particular, to occasional outliers that might be a natural part of the process rather than a special cause. In processes where the process measurements are prone to outliers, it is advisable to make the cusum robust to these outliers. One good way of doing this is by winsorizing, which does not eliminate outliers, but limits their effect. This paper shows how the cusum parameters should be altered to reflect the use of winsorization and that doing so makes the cusum much more robust to outliers with little effect on its out-of-control performance. Some implications of winsorization on parameter estimation are also discussed.