Enhanced univariate and multivariate control charts via outliers’ screening technique, robust estimators and varying sample size schemes

Abstract

The ability to monitor processes using control charts for contaminated environments is vital. Typical control charts may not serve the purpose because of violations in the underlined assumptions or the presence of outliers in such environments. Fixed sample size (FSS) based control charts are not only less efficient as compared to varying sample size (VSS) but are sometimes more expensive to administer. Therefore, this study has developed new control charts to improve the statistical process control for contaminated processes. The goals are to design univariate and multivariate control charts that are more sensitive, efficient, and robust in the presence of outliers and violation of the model's assumptions. The study enhances the Shewhart, the exponentially weighted moving average, and exponentially and homogenously double-weighted moving average charts, with outliers’ screening techniques to improve the sensitivity of the charts in the estimation and monitoring processes. Next, robust multivariate location estimators were applied to Hotelling T2 and multivariate cumulative sum (MCUSUM) charts, to retain their efficiency when underlying assumptions are violated in contaminated process environments. In addition, this research proposes a new adaptive homogenous weighted moving average features (HWMA) chart with VSS, for location monitoring. This study also employed Monte-Carlo simulations to evaluate the effectiveness of the proposed control charts, using the run length properties to measure the performance of the control charts. The results show that the enhanced control charts for outlier detection are more sensitive and efficient than their counterparts at detecting anomalies. The efficiency of the multivariate Shewhart and CUSUM charts is improved when the robust multivariate estimators were employed in contaminated settings. The results also indicate that the adaptive VSS-HWMA charts outperform their counterparts. In conclusion, the proposed control charts incorporating an outlier detection model and employing robust estimators could be used to monitor processes adequately for contaminated environments.