A Dynamic Screening System for Early Detection of Multiple Interconnected Events

Sequential monitoring of temporal processes is essential in various fields for the early detection of critical events, such as airplane failures or disease occurrences. This task typically involves sequential decision-making across many related processes. Conventional statistical process control charts are generally designed for detecting an event of interest in a single process and thus inadequate for this task. Recently, several versions of the dynamic screening system (DySS) have been developed to monitor a population of processes. However, these DySS methods focus solely on the early detection of a single event (e.g., the occurrence of a particular disease) and cannot handle scenarios where multiple distinct events are involved. In practice, detecting multiple events is important and common. For example, we may be concerned with several medical conditions in patients or different types of failures in airplanes. This problem is significantly more challenging than single-event detection, as different events are often interconnected and can occur at different times. To address this complexity, we propose the concept of conditional risks for multiple events, using single-index multinomial logistic regression modeling. Based on this, we develop a new DySS method for the early detection of multiple events by sequential monitoring of the related conditional risks. Numerical studies demonstrate that this method provides an effective analytical tool for the early detection of multiple interconnected events.