Due to the development of sensing and computer technology, measurements of many process variables are available in current manufacturing processes. It is very challenging, however, to process a large amount of information in a limited time in order to make decisions about the health of the processes and products. This paper develops a "preprocessing" procedure for multiple sets of complicated functional data in order to reduce the data size for supporting timely decision analyses. The data type studied has been used for fault detection, root-cause analysis, and quality improvement in such engineering applications as automobile and semiconductor manufacturing and nanomachining processes. The proposed vertical-energy-thresholding (VET) procedure balances the reconstruction error against data-reduction efficiency so that it is effective in capturing key patterns in the multiple data signals. The selected wavelet coefficients are treated as the "reduced-size" data in subsequent analyses for decision making. This enhances the ability of the existing statistical and machine-learning procedures to handle high-dimensional functional data. A few real-life examples demonstrate the effectiveness of our proposed procedure compared to several ad hoc techniques extended from single-curve-based data modeling and denoising procedures

The control chart is one of the most important statistical process control tools and the traditional control charts mostly require a specific probability distribution to set up their control limits. However, in modern manufacturing, the processes often have a lot of complexity and variability. Most existing control charts cannot efficiently handle situations with nonlinear or multi-modal patterns of observations. One recent trend about control charts is based on the novelty score algorithms that can effectively describe and reflect the characteristics of the monitored data. In this paper, we propose a density-sensitive novelty weight (DNW) control chart using k-nearest neighbors (kNN) algorithm that can efficiently monitor a process when the distribution of observations is unknown. More importantly, our chart can fully utilize the in-control local density information which can be regarded as the amount of in-control process knowledge. We demonstrated the usefulness of the proposed chart in experiments with simulated data in terms of average run length, and showed that the proposed chart generated proper portions of false alarms in the dense and sparse regions in Phase-I monitoring procedure in a real-life data, the E.coli dataset from the University of California, Irvine (UCI) repository.

“Normal” events are characterized as data patterns or behaviors that align with expected operational conditions, while “anomalies” are defined as deviations from these patterns, potentially signaling faults, errors, or unexpected system behaviors. The timely and accurate detection of anomalies plays a critical role in domains such as industrial manufacturing, financial transactions, and other related domains. In the context of Industry 4.0, the proliferation of sensors has resulted in a massive influx of time series data, making the anomaly detection of such multivariate time series data a popular research area. Long Short-Term Memory (LSTM) has been extensively recognized as an effective framework for modeling and processing time series data. Previous studies have combined Bi-directional Long Short-Term Memory (Bi-LSTM) architecture with Autoencoder (AE) for multivariate time series anomaly detection. However, due to the inherent limitations of LSTM, Bi-LSTM-AE still cannot overcome these drawbacks. Our study replaces the LSTM units within the Bi-LSTM-AE architecture of existing research with Working Memory Connections for LSTM units and demonstrates that this architecture performs better in the field of multivariate time series anomaly detection compared to using standard LSTM units. The model we proposed not only outperforms the baseline models but also demonstrates greater robustness across various scenarios.