Robust Control Charts for Monitoring Process Mean of Phase-I Multivariate Individual Observations

Hoteling's control charts are widely used in industries to monitor multivariate processes. The classical estimators, sample mean, and the sample covariance used in control charts are highly sensitive to the outliers in the data. In Phase-I monitoring, control limits are arrived at using historical data after identifying and removing the multivariate outliers. We propose Hoteling's control charts with high-breakdown robust estimators based on the reweighted minimum covariance determinant (RMCD) and the reweighted minimum volume ellipsoid (RMVE) to monitor multivariate observations in Phase-I data. We assessed the performance of these robust control charts based on a large number of Monte Carlo simulations by considering different data scenarios and found that the proposed control charts have better performance compared to existing methods. 1. Introduction Control charts are widely used in industries to monitor/control processes. Generally, the construction of a control chart is carried out in two phases. The Phase-I data is analyzed to determine whether the data indicates a stable (or in-control) process and to estimate the process parameters and thereby the construction of control limits. The Phase-II data analysis consists of monitoring future observations based on control limits derived from the Phase-I estimates to determine whether the process continues to be in control or not. But trends, step changes, outliers, and other unusual data points in the Phase-I data can have an adverse effect on the estimation of parameters and the resulting control limits. That is, any deviation from the main assumption (in our case, identically and independently distributed from normal distribution) may lead to an out-of-control situation. Therefore, it becomes very important to identify and eliminate these data points prior to calculating the control limits. In this paper, all these unusual data points are referred to as “outliers.” Multivariate quality characteristics are often correlated, and to monitor the multivariate process mean Hoteling’s control chart [1, 2] is widely used. To implement Hoteling's control chart for individual observations in Phase-I, for each observation we calculate where = is the th -variate observation, ( ) and the sample mean , sample covariance matrix are based on Phase-I observations. In Phase-I monitoring, the values are compared with the control limit derived by assuming that the ’s are multivariate normal so that the control limits are based on the beta distribution with the parameters and . However, the classical estimators, sample