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A distribution‐free CUSUM chart for joint monitoring of location and scale based on the combination of Wilcoxon and Mood statistics

We propose a distribution‐free cumulative sum (CUSUM) chart for joint monitoring of location and scale based on a Lepage‐type statistic that combines the Wilcoxon rank sum and the Mood statistics. Monte Carlo simulations were used to obtain control limits and examine the in‐control and out‐of‐control performance of the new chart. A direct comparison of the new chart was made with the original CUSUM Lepage based on Wilcoxon rank sum and Ansari‐Bradley statistics. The result is a more powerful chart in most of the considered scenarios and thus a more useful CUSUM chart. An example using real data illustrates how the proposed control chart can be implemented.