Improvement of The Hotelling’s T 2 Charts Using Robust Location Winsorized One Step M-Estimator (WMOM)

Abstract

For product manufacturing, control charts are important tools. Different types of control charts are used to monitor different measures of product characteristics. Among the numerous charts, the popular one is the Hotelling’s T 2 chart. It is designed while taking into account the most sensitive measures such as sample covariance matrix and sample mean vector. However, the chart becomes ineffective in the presence of outliers. This work proposes a new robust chart that overcomes the problems associated with other control charts. Our chart uses robust scale estimator, Qn instead of the covariance matrix and Winsorized modified one step M-estimator (WMOM) in place of the sample mean vector. The robust chart could be removed without losing anything in the explanation. There are two main performance measurements, false alarm and probability of detection outliers. The results indicate that robust chart’s performance is superior to that of the conventional control chart.