Residual-Based Multivariate Exponentially Weighted Moving Average Control Chart for Statistical Process Control of Water Quality in Surabaya City Utilizing Generative Adversarial Network

Abstract

This study investigates the water quality characteristics of pH, turbidity, and KMnO4. Initial Phase I and II analyses revealed that while the examined water quality parameters adhered to established regulatory limits, significant autocorrelation within the time-series data compromised the statistical independence assumption, potentially affecting subsequent analyses' reliability. To address this methodological limitation, a Generative Adversarial Network (GAN) model was developed and rigorously optimized to generate residual time series exhibiting reduced autocorrelation. The efficacy of the GAN model in decorrelating the data was quantitatively evaluated using standard error metrics, including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). The generated residual series was subsequently subjected to statistical process control monitoring using a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart, employing a smoothing parameter λ =0.4. In Phase I, following the identification and removal of statistically significant outliers, indicated a process operating under statistical control. However, subsequent Phase II online monitoring detected statistically significant out-of-control signals, suggesting a potential loss of process stability over time. The findings of this research underscore the potential utility of GAN-based residual analysis as a strategy for mitigating the impact of autocorrelation in environmental water quality.

Keywords: forecasting, Generative Adversarial Network, Control Chart, MEWMA