Assessment of the effect of imputation of missing values on the performance of Phase II multivariate control charts

Observations with missing data are a typical predicament in the context of multivariate statistical process control (MSPC). When process control is performed using a T-2 control chart of the principal components (PCs), several score imputation methods have been proposed. Some of these lead to estimators with good properties. However, there are no detailed studies pertaining the performance of Phase II Hotelling's T-2 and squared prediction error (SPE) charts when such imputation methods are used. In this paper, a simulation study was conducted to assess the consequences of the estimation of incomplete observations using score imputation methods on T-2 and SPE control charts. The study involves several scenarios that combine different correlation structures for the PCA model, methods of score estimation, percentages of missing data and patterns of incomplete information. Results show that the charts' standard control limits are adequate only for small percentages of missing values and that their average run lengths (ARLs) tend to be larger than expected in out-of-control situations. To illustrate the conclusions of the study, we present two examples. Our findings lead us to suggest a modification that may result in an improvement in the performance of the T-2 and SPE control charts.