Modern Process Monitoring

In Statistical Process Control, control charts are often used to detect undesirable behavior of sequentially observed quality characteristics. Designing a control chart with desirably low False Alarm Rate (FAR) and detection delay (ARL1) is an important challenge especially when the sampling rate is high and the control chart has an In-Control Average Run Length, called ARL0, of 200 or more, as commonly found in practice. Unfortunately, arbitrary reduction of the FAR typically increases the ARL1. Motivated by eigenvector perturbation theory, we propose the Eigenvector Perturbation Control Chart for computationally fast nonparametric profile monitoring. Our simulation studies show that it outperforms the competition and achieves both ARL1 ≈ 1 and ARL0 > 10^6.  

In this talk, we will present a new methodology for conducting online profile monitoring of functional data response using Markov random field approximations to detect when the process shifts from an in-control state to an out-of-control state. Functional profile monitoring problems typically assume a fixed functional form for an in-control process. Novel to our approach is a relaxation of this assumption, which allows for random functional processes that incorporate both randomness in the underlying function and error in the observation of the function. Such constructs will result in non-zero and potentially strong correlations between response values at different points in the functional domain, violating common assumptions of independent errors found in much of the literature. Markov random fields provide a means of modeling dependence among observations of the functional response as well as a framework for detecting when the observed functional behavior of a process deviates from the typical behavior of the in-control process. We outline a learning and monitoring methodology that shows promise toward a wide range of functional profile monitoring problems under weak assumptions. We discuss the theoretical properties of our methodology and showcase its empirical performance in both simulation studies and through an application.  

Spatio-temporal process monitoring (STPM) has garnered significant attention recently due to its wide range of applications, including environmental monitoring, disease surveillance, and streaming image processing. Monitoring spatial data streams presents unique challenges, as these data often exhibit complex structures, such as latent spatio-temporal correlations, intricate spatio-temporal mean patterns, and nonparametric distributions. As a result, STPM is a challenging research problem. In practice, when a spatial process experiences a distributional shift (e.g., a mean shift) at a specific time, it is critical to detect this shift promptly, as it often signals a structural change in the process (e.g., a disease outbreak). Statistical process control charts are a key analytic tool for addressing sequential decision-making problems like these. However, traditional control charts are not well-suited to STPM due to the inherent complexity of spatial data streams. In this talk, we will explore recent advancements in control charts developed specifically for STPM and discuss their applications in infectious disease surveillance. 

This study extends recently developed univariate statistical process monitoring (SPM) methods for location and scale to the multivariate setting. Our approach enables the joint monitoring of multiple sequences of critical quality characteristics that exhibit both cross-correlation and autocorrelation. By leveraging copula models, this distribution-free framework addresses the complexities of modern process monitoring, particularly when traditional assumptions such as normality and independence are not met. 

Statistical process control (SPC) charts are widely utilized in various fields to identify distributional shifts of sequential processes. Conventional SPC charts are designed for cases when in-control (IC) process observations are independent and identically distributed at different observation times and the IC process distribution belongs to a parametric family. In practice, however, these assumptions are rarely valid. To address this issue, there have been some existing discussions in the SPC literature for handling cases where these assumptions are not valid. Although many existing charts are effective for detecting shifts across a wide spectrum when their model assumptions are valid, their optimal performance for detecting shifts depends on the pre-specified parameters. Additionally, further analysis is often required to estimate the time of shift after a signal is given. In this paper, we propose a new multivariate online monitoring scheme, where process observations are first preprocessed, including data decorrelation and transformation. Subsequently, this preprocessed data is projected onto a one-dimensional space, and finally, a univariate adaptive control chart is applied to the projected data for online monitoring. The design and implementation of the new method is relatively simple, since it eliminates the need for pre-specifying control chart parameters and provides a formula for determining control limit. Moreover, it can provide an estimate of the shift's location immediately after a shift is detected. Numerical studies demonstrate that the proposed online monitoring scheme is robust to the IC process distribution and short-range serial correlation, and effective in detecting shifts of various magnitudes.