Robust Point M-Scale Estimators for Monitoring the Mean of EWMA Control Chart under the Normal Process

Abstract

The Exponentially Weighted Moving Average (EWMA) control chart is well known in statistical process control (SPC) for identifying small shifts in process parameters. In general, the EWMA control chart is focused on data set estimates of the process characteristics under study. In this research, for observing the process mean, we modify the control limits of the EWMA control chart by using robust point M-scale estimators under the normal process. We compare five robust point M-scale estimators proposed in SPC literature, namely Sn, Qn, MAD, Tauτ^ and FQn. The traditional control limits are evaluated and distinctions are also made based on true process control limits. The control charts performances under study are estimated via a Monte-Carlo simulation analysis by calculating the interval widths (IWs) and optimal out-of-control average run length (ARL1). From the simulation studies results, it is seen that although all proposed and traditional control limits are closely approximating the true limits of the process but the proposed control limits based on robust FQn, Tauτ^ and MAD estimators are comparatively more stringent for detecting the small shifts in process mean. Moreover the results demonstrates that at optimal size of interval L, the control charts based on MAD, Tauτ^ as well as FQn estimators demonstrate higher sensitivity in comparison to the traditional control chart based on sample standard deviation (S) and proposed control charts based on QnandSn estimators in terms of having smaller ARL1 values. The OC curves of ARL1 indicate similar findings. For the purposes of illustration, a real-life data set is analyzed that also confirms our conclusions from the simulation analysis to a certain degree.

Keywords

• Normal process
• EWMA control chart
• Statistical Process Control (SPC)
• Robust M-Scale estimators
• Monte-Carlo Simulation Study
• Interval Width (IW)