An Analysis of the Run Sum Control Chart

Abstract

The run sum control chart is a simple but powerful procedure for monitoring the mean of a process. We analyze the run length distribution of the run sum chart using a Markov chain approach. Procedures for evaluating average run lengths for one-time shifts and linear trends in the process mean are given. Comparisons are made with the Shewhart control chart supplemented with runs rules, as well as with the cumulative sum and exponentially weighted moving average control charts. The properties of the run sum's run length distribution indicate that the run sum control chart is better than the Shewhart X̄ chart with supplementary runs rules. By adding more regions and scores, the run sum chart can be made more competitive with the cumulative sum and the exponentially weighted moving average control charts in detecting out-of-control conditions. We conclude that the run sum control chart is a simple and powerful tool for statistical process control.

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