A New Nonparametric Tukey CUSUM-MA Control Chart for Detecting Mean Shifts

Abstract

This research aims to create a new non-parametric control chart, called Tukey cumulative sum-moving average control chart (MCM-TCC) used for detecting parameter changes in asymmetrical process mean. The proposed control chart efficiency was compared with that of the cumulative sum (CUSUM), moving average (MA), mixed cumulative sum-moving average (MCM), mixed moving average-cumulative sum (MMC), mixed cumulative sum-Tukey’s (CUSUM-TCC) and mixed moving average-Tukey’s (MA-TCC) control charts at different levels of parameter changes by using average run length (ARL) and median run length (MRL), via Monte Carlo simulation (MC). The results of the study found that the MCM-TCC chart was efficiency more than other control charts, when the small parameter changes, and if the moderate-to-large parameter changes the MA-TCC had more efficiency, for the case of exponential distribution. In the case of the gamma distribution, the MMC control chart had more efficiency to detect the small-to-moderate parameter changes, if the large parameter changes the MA-TCC had more efficiency. For the application of the MCM-TCC chart to two datasets. It was found that the proposed control chart was almost as fast as the CUSUM-TCC chart, when the observations had an exponential distribution.