Sequential Change Point Detection in Dynamic Non-Stationary Manufacturing Processes.

Abstract

Sequential monitoring of multivariate time series to detect sudden changes in the data-generating process is a fundamental problem in statistics and signal processing. Most existing detection algorithms assume (a) no cross-correlations between time series components and (b) stationarity with fixed parameters between consecutive change points. These assumptions are often violated in real-world applications, such as manufacturing processes, leading to overfitting or inaccurate change point identification. To address this limitation, we introduce a general modeling framework that incorporates local dynamics and cross-correlations in multivariate time series and propose a novel sequential detection algorithm, dscpd (dynamic sequential change point detection). The method detects abrupt shifts in the mean while accounting for local dynamics through a multivariate random walk model and cross-correlations through a vector autoregressive process. In addition, dscpd estimates shift sizes and constructs confidence intervals, facilitating root cause analysis of sudden changes. We establish theoretical properties under mild conditions, including false-positive rate control, detection power calculations, and localization error bounds. Simulation studies, comparisons with existing methods, and applications to real-world data sets such as paper production and semiconductor manufacturing demonstrate the effectiveness of dscpd for detecting abrupt changes in complex multivariate time series.