Online Monitoring of Irregularly Spaced Serially Correlated Univariate Processes

ABSTRACT Statistical process control (SPC) methods are commonly employed in various fields to detect distributional changes in sequential processes. Traditional SPC charts are typically developed under the assumption that in‐control (IC) process observations are independent and normally distributed with identical parameters. However, when these assumptions are violated, recent research has shown that conventional control charts may become unreliable. To address these limitations, various alternative and flexible control charts have been developed to accommodate autocorrelated observations and nonparametric process distributions. Although existing methods can be reliable and effective when their assumptions hold, they still have some limitations. For instance, methods handling autocorrelated data often rely on parametric time series models or assume equally spaced observations, whereas nonparametric control charts that rely on data ranking or categorization typically suffer from information loss. Furthermore, the optimal performance of many control charts in detecting specific shifts often relies on the accurate specification of their parameters in advance. In this paper, we introduce a novel framework for Phase II online monitoring of univariate processes with irregularly spaced observation times and serial correlation, and the IC distribution cannot be adequately modeled by a parametric form. The method first estimates the IC covariance function for irregularly spaced time series using a local linear kernel smoothing procedure, then sequentially decorrelates the process observations. Next, the decorrelated observations are transformed based on their estimated IC distribution such that the transformed data are approximately standard normal. Finally, an adaptive CUSUM chart is employed to monitor the transformed data. Simulation results indicate that the proposed approach is effective across a variety of scenarios.