Robust monitoring of multivariate processes with short‐ranged serial data correlation

Abstract Control charts are commonly used in practice for detecting distributional shifts of sequential processes. Traditional statistical process control (SPC) charts are based on the assumptions that process observations are independent and identically distributed and follow a parametric distribution when the process is in‐control (IC). In practice, these assumptions are rarely valid, and it has been well demonstrated that these traditional control charts are unreliable to use when their model assumptions are invalid. To overcome this limitation, nonparametric SPC has become an active research area, and some nonparametric control charts have been developed. But, most existing nonparametric control charts are based on data ordering and/or data categorization of the original process observations, which would result in information loss in the observed data and consequently reduce the effectiveness of the related control charts. In this paper, we suggest a new multivariate online monitoring scheme, in which process observations are first sequentially decorrelated, the decorrelated data of each quality variable are then transformed using their estimated IC distribution so that the IC distribution of the transformed data would be roughly N(0, 1), and finally the conventional multivariate exponentially weighted moving average (MEWMA) chart is applied to the transformed data of all quality variables for online process monitoring. This chart is self‐starting in the sense that estimates of all related IC quantities are updated recursively over time. It can well accommodate stationary short‐range serial data correlation, and its design is relatively simple since its control limit can be determined in advance by a Monte Carlo simulation. Because information loss due to data ordering and/or data categorization is avoided in this approach, numerical studies show that it is reliable to use and effective for process monitoring in various cases considered.