Robust T2 control chart using median‐based estimators

Abstract

AbstractOne of the most widely used multivariate control charts is the Hotelling T2. In order to construct a Hotelling T2 control chart, the mean vector (μ) and the variance–covariance matrix (Σ) must be first estimated. The classical estimators of μ and Σ are usually used to design Hotelling T2 control chart. The classical estimators are sensitive to the presence of outliers. One way to deal with outliers is to use robust estimators. In this study, a robust T2 control chart is proposed. The mean vector is obtained from the sample median. The median absolute deviation and the comedian are used as the estimates of the elements of the variance–covariance matrix. The proposed robust estimators of the mean vector and the variance–covariance matrix are compared with the sample mean vector and the sample variance–covariance matrix, and the M estimator of these parameters, through efficiency and robustness measures. The performances of the proposed robust T2 control chart and the classical and the M estimators are also compared by means of average run length. Simulation results reveal that the proposed robust T2 control chart has much better performance than the traditional Hotelling T2 and similar performance to the M estimator in detecting shifts in process mean vector. Use of other robust estimators to estimate the process parameters is an area for further research.