On monitoring high-dimensional processes with individual observations

Modern data collecting methods and computation tools have made it possible to monitor high-dimensional processes. In this article, we investigate phase II monitoring of high-dimensional processes when the available number of samples collected in phase I is limited in comparison to the number of variables. A new charting statistic for high-dimensional multivariate processes based on the diagonal elements of the underlying covariance matrix is introduced and we propose a unified procedure for phases I and II by employing a self-starting control chart. To remedy the effect of outliers, we adopt a robust procedure for parameter estimation in phase I and introduce the appropriate consistent estimators. The statistical performance of the proposed method is evaluated in phase II using the average run length (ARL) criterion in the absence and presence of outliers. Results show that the proposed control chart scheme effectively detects various kinds of shifts in the process mean vector. Finally, we illustrate the applicability of our proposed method via a manufacturing application.