Distribution-free Mixed CUSUM-MA Control Chart to Detect Mean Shifts

Control charts are an important statistical tool for controlling, monitoring and improving production processes. Herein, we proposed the Tukey cumulative sum-moving average (MCM-TCC) control chart for detecting changes in the process mean when the observations are symmetrically and asymmetrically distributed. We compared its efficacy with those of the cumulative sum (CUSUM), moving average (MA), mixed cumulative sum-moving average (MCM), mixed moving average-cumulative sum (MMC), mixed cumulative sum-Tukey (CUSUM-TCC) and mixed moving average-Tukey (MA-TCC) control charts with various change levels of the process mean. The criteria to measure the efficacy were the average run length (ARL) and median run length (MRL), which were evaluated by using Monte Carlo simulation (MC). When the observations followed an exponential distribution, the MCM-TCC control chart had the highest efficacy for detecting a change in the process mean for change level \(0.05\leq\delta\leq 0.25\) whereas the MA-TCC control chart was the most efficacious for \(\delta\geq 0.5\) . In addition, when applying the control charts to two processes with real datasets of observations, we found that the MCM-TCC control chart could detect a change in the process mean earlier than the others.