Application and Simulation Study of the Hotelling's T 2 Control Chart to Monitor a Wastewater Treatment Process

The purpose of this paper is to study the application of the Hotelling's T² statistic to assess the performance of a wastewater treatment process. Standard control charts are widely used in engineering for quality improvement through the detection of special causes of variability. These methods assume that the observations are independent. In wastewater treatment processes the data are frequently autocorrelated. One possible way to apply control charts to autocorrelated observations is to monitor the one-step ahead forecast errors after estimating the process time series model. In this paper the application of control charts to individual forecast errors of the multivariate time series model from a wastewater process is discussed. Hotelling's T² statistics are computed using the sample covariance matrix, the successive differences estimator and the minimum volume ellipsoid estimator. A Monte Carlo simulation study shows that the application of these charts to the time series model residuals is quite effective in detecting the mean changes. However, the multivariate T² charts are more powerful when applied to independent observations. The simulation study also indicates that the autocorrelation affects the properties of the T² control chart giving a large false alarm rate when using the successive difference estimator, or affecting its power to detect level shifts when using the sample covariance matrix or the minimum volume ellipsoid estimator. These two charts have essentially no power to detect the simulated shifts.