Functional regression-based monitoring of quality of service in hospital emergency departments

This article focuses on building a statistical monitoring scheme for service systems that experience time-varying arrivals of customers and have time-varying service rates. There is lack of research in the systematic statistical monitoring of large-scale service systems, which is critical for maintaining a high quality of service. Motivated by the emergency department at a major academic medical center, this article intends to fill this research gap and provide a practical statistical monitoring scheme capable of detecting changes in service using readily available time stamp data. The proposed method is focused on building a functional regression model based on customer arrival and departure time instances from an in-control system. The model finds the expected departure intensity function for an observed arrival intensity on any given day of operation. The mean squared difference between the expected departure intensity function and the observed departure intensity functions is used to generate an alarm indicating a significant change in service. This methodology is validated using simulation and real data case studies. The proposed method can identify patterns of inefficiency or delay in service that are hard to detect using traditional statistical monitoring algorithms. The method offers a practical approach for monitoring service systems and determining when staffing levels need to be re-optimized.