Monitoring time between events has become increasingly important in statistical process control, especially in applications where event timing provides more informative insights than direct measurement of quality characteristics. Traditional approaches for monitoring univariate and multivariate time-between-events data often depend on parametric assumptions and conventional statistical control charts, which can be inadequate when the underlying distributions are unknown, complex, or subject to change. In this study, we address these limitations by developing a monitoring framework based on the Gumbel’s bivariate exponential distribution, tailored for real-world applications involving two dependent variables. Recognizing the challenges posed by parameter estimation and distributional assumptions, we extend our model to include both parametric and nonparametric structures. Moreover, conventional statistical control charts are found to exhibit reduced performance in nonparametric settings, particularly in detecting complex and unknown process changes. To address this limitation, a machine learning–based control chart is proposed, which incorporates an artificial neural network enhanced by an attention mechanism. In this framework, statistical features derived from the Gumbel’s bivariate exponential process are imported as memory-based input features. The attention mechanism is employed to guide the model in focusing on the most relevant temporal dependencies, thereby enhancing its sensitivity to subtle shifts. This hybrid approach is designed to improve the early detection of out-of-control conditions and reduce the risk of nonconforming products or harmful events in dynamic environments. Through extensive Monte Carlo simulations, encompassing shifts in scale, dependency parameters, and various nonparametric distributional changes (with the underlying process type known), the detection capability of the proposed method has been evaluated. The results show that the proposed method generally provides faster time-to-signal for OOC conditions across most scenarios, although its superiority is not universal. As a practical application, an employee communication network within a company, analogous to social network monitoring, is considered, representing a novel context for time between events-based surveillance. It is demonstrated that the proposed method can effectively detect unnatural or anomalous communication patterns between employees, highlighting its potential for identifying irregularities in networked environments.

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