A study on the effects of a skewed distribution on the EWMA and MA charts

Abstract

The control chart is the most powerful tool in statistical process control. A control chart is a graphical display used to determine the presence of assignable causes so that prompt corrective actions can be taken to remove such causes before many nonconforming products are produced. The exponentially weighted moving average (EWMA) and moving average (MA) charts are very effective in detecting small and moderate shifts in the process mean. These two charts are constructed based on the properties of the normal distribution. In many practical applications, the validity of the normality assumption is always doubted as the process distribution could be skewed. A skewed distribution can result in a higher incidence of false alarms. This is due to the inconsistencies between the spread of a skewed distribution and the normality assumption employed in setting up a control chart. This paper studies the effects of a skewed distribution on the performances of the EWMA and MA charts, in terms of the charts' false alarm rates. We compare the in-control average run length (ARL0) performance of these two charts when the underlying distributions are normal and skewed. The gamma distribution is selected to represent the skewed distribution. A Monte Carlo simulation using the Statistical Analysis System (SAS) software is carried out to compute the necessary ARL0s. The findings of this study show that the ARL 0 performance of the EWMA and MA charts is substantially affected by the skewed distribution. However, the MA chart is not as robust as the EWMA chart, in terms of the ARL0, when the distribution is skewed. © 2014 AIP Publishing LLC.