On Monitoring High-Dimensional Processes with Individual Observations

Abstract: Modern data collecting methods and computation tools have made it possible to monitor high-dimensional processes. In this article, Phase II monitoring of high-dimensional processes is investigated when the available number of samples collected in Phase I is limitted 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 a unified procedure for Phase I and II by employing a self-starting control chart is proposed. 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 through average run length (ARL) criterion in the absence and presence of outliers and reveals that the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Finally, we illustrate the applicability of our proposed method via a real-world example.