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.

Long-Term Statistical Process Monitoring of an Ultrafiltration Water Treatment Process

“…Then, model residuals are obtained, which are the differences between the model predicted values and the actual values of the monitoring variable. Some work has been done using multiple regression to detrend monitoring variables prior to monitoring. , It is also common to monitor the residuals from ML or time series models, but these methods do not distinguish between explanatory and monitoring variables in the process. − Instead, they predict each monitoring variable using previous values or other process variables as predictors. Separating process variables into “explanatory” or “monitoring” reduces the number of variables being monitored directly and leads to a more straightforward interpretation of any OC signals as attributable to changes in the process that are not predicted by the explanatory variables.…”

A bivariate CUSUM control chart based on exceedance statistics

“…Also, according to the simulation results, the performance of SS-CUSUM and DD-CUSUM control charts is better than traditional CUSUM charts. For more research on nonparametric multivariate control charts, we cite Koutras and Sofikitou, 30 Koutras and Triantafyllou, 31 Mahmood and Erem, 32 Xie and Qiu, 33 and Zhou and Qiu. 34 This study proposes a CUSUM control chart relying on bivariate exceedance statistics for observing the shifts in location parameters in bivariate manufacturing processes.…”

“…Also, according to the simulation results, the performance of SS‐CUSUM and DD‐CUSUM control charts is better than traditional CUSUM charts. For more research on nonparametric multivariate control charts, we cite Koutras and Sofikitou, 30 Koutras and Triantafyllou, 31 Mahmood and Erem, 32 Xie and Qiu, 33 and Zhou and Qiu 34 …”