Multivariate auto‐correlated process control by a residual‐based mixed CUSUM‐EWMA model

Abstract

Multivariate auto-correlated process control issues in industrial systems are a concern for statistical process monitoring (SPM). Traditional control charts produce large false alarms and/or miss timely detections of quality deterioration because they are unable to recognize the signals from multivariate auto-correlated response variables. To track multivariate auto-correlated processes, this paper presents a new residual-based mixed multivariate control chart using cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) approaches. Using in-control data, the multi-output least square support vector regression model's optimal hyper-parameters are determined, and a bootstrap method is used to estimate the upper control limit of the proposed control chart. The suggested control chart has strong detection performance for a small magnitude mean vector shift based on the average run length (ARL) performance for a particular range of shifts. Experimental result elaborates that the proposed control chart is more sensitive to detecting the mean vector shift compared with the existing commonly used models, such as multivariate CUSUM and multivariate EWMA control charts. The proposed control chart model and corresponding computational algorithm are successfully applied to SPM in an electronic conductor production line with multivariate auto-correlated attributes.

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.…”

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

“…Riaz et al 7 . and Wang and Asrini 18 test control charts that are a linear combination of MEWMA and MCUSUM statistics for monitoring the covariance of independent observations.…”

“…However, in their simulation studies, they only generate data from a VARMA(1, 1) model. Similarly, Wang and Asrini 18 use a residual based method with a mixed CUSUM–EWMA control chart, but only consider detrending with VAR(1), VMA(1), and VARMA(1, 1) models. Thus, these methods may not perform well in complex systems that include nonlinear relationships between variables.…”

“…These MCUSUM charts assume normality, but they are not limited to bivariate data. Riaz et al 7 and Wang and Asrini 18 test control charts that are a linear combination of MEWMA and MCUSUM statistics for monitoring the covariance of independent observations. Most MSPM methods assume that observations are independent.…”