GAN-based statistical process control for the time series data

The cumulative sum (CUSUM) control chart and the multivariate anomaly detection with the generative adversarial network (MAD-GAN) were compared for monitoring the time series data. However, the control boundaries constructed in terms of the one-class classification with only the normal data for the training phase are inappropriate for the test phase because the normal data and the abnormal data should be classified for the test phase. In this regard, we first propose this GAN-based statistical process control (SPC) framework to compare them in terms of detecting the process mean shift based on the perspective of SPC. Second, we propose the residual MAD-GAN in order to improve the detection performance. Third, we develop the loss function of the MAD-GAN. Finally, we find that the maximum mean discrepancy (MMD) as well as the nash equilibrium is useful for the MAD-GAN. Our experiments demonstrate that the residual MAD-GAN is more effective than the residual CUSUM control chart in terms of the run lengths for the time series data. Therefore, we propose SPC practitioners to consider the residual MAD-GAN for detecting the process mean shift in time series data.