Distribution-free mixed cumulative sum-exponentially weighted moving average control charts for detecting mean shifts

In this paper, we propose distribution-free mixed cumulative sum-exponentially weighted moving average (CUSUM-EWMA) and exponentially weighted moving average-cumulative sum (EWMA-CUSUM) control charts based on the Wilcoxon rank-sum test for detecting process mean shifts without any distributional assumption of the underlying quality process. The performances of the proposed charts are measured through the average run-length, relative mean index, average extra quadratic loss, and average ratio of the average run-length and performance comparison index. It is found that the proposed charts perform better than its counterparts considered in this paper under non-normal distributions and outperform the classical mixed CUSUM-EWMA and EWMA-CUSUM charts in many cases under the normal distribution. The effect of the phase I sample size is also investigated on the phase II performance of the proposed charts. A numerical illustration is given to demonstrate the implementation and simplicity of the proposed charts.