Bivariate semiparametric control charts for simultaneous monitoring of process mean and variance

In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Weix,

Cath,

Hering

2024

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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 …”

Section: Introductionmentioning

confidence: 99%

A bivariate CUSUM control chart based on exceedance statistics

Erem

Mahmood

2023

In manufacturing systems, statistical process control (SPC) is used to detect unusual observations in the process. Most control charts are composed based on the normality assumptions of the observations. However, checking the normality assumption in multivariate control systems cannot be practical in real‐life applications. As a result, we propose a nonparametric bivariate cumulative sum control chart (CUSUM) based on exceedance statistics for detecting the shifts in location parameters. Since the proposed chart (BCUSUM‐EX) relied on exceedance statistics and is nonparametric, the use of the chart is straightforward and practical for users. Moreover, due to the nature of CUSUM charts, the proposed chart contains information about historical and current observations. The performance of the BCUSUM‐EX chart is compared with the spatial sign CUSUM (SS‐CUSUM) control chart under some well‐known bivariate distributions such as bivariate normal, t, and gamma. The BCUSUM‐EX chart's performance is better than the SS‐CUSUM control chart regarding run length characteristics. Lastly, to show the importance of the proposed control chart, the BCUSUM‐EX chart has been applied to the aluminium electrolytic capacitor manufacturing process.

“…Yen et al 15 suggested a control chart for monitoring multivariate process dispersion. Koutras and Sofikitou 16 proposed a bivariate semiparametric control chart to monitor the process mean and variance simultaneously. Sparks 17 proposed a Hotelling T 2 to monitor a highly correlated multivariate process.…”

Section: Introductionmentioning

confidence: 99%

Robust T² control chart using median‐based estimators

Maleki

Mehri

Aghaie

et al. 2020

One of the most widely used multivariate control charts is the Hotelling T 2. In order to construct a Hotelling T 2 control chart, the mean vector (μ) and the variance-covariance matrix (Σ) must be first estimated. The classical estimators of μ and Σ are usually used to design Hotelling T 2 control chart. The classical estimators are sensitive to the presence of outliers. One way to deal with outliers is to use robust estimators. In this study, a robust T 2 control chart is proposed. The mean vector is obtained from the sample median. The median absolute deviation and the comedian are used as the estimates of the elements of the variance-covariance matrix. The proposed robust estimators of the mean vector and the variance-covariance matrix are compared with the sample mean vector and the sample variance-covariance matrix, and the M estimator of these parameters, through efficiency and robustness measures. The performances of the proposed robust T 2 control chart and the classical and the M estimators are also compared by means of average run length. Simulation results reveal that the proposed robust T 2 control chart has much better performance than the traditional Hotelling T 2 and similar performance to the M estimator in detecting shifts in process mean vector. Use of other robust estimators to estimate the process parameters is an area for further research.