Using Phase-type Models to Monitor and Predict Process Target Compliance

Processes are ubiquitous, spanning diverse areas such as business, production, telecommunications and healthcare. They have been studied and modelled for many years in an attempt to increase understanding, improve efficiency and predict future pathways, events and outcomes. More recently, process mining has emerged with the intention of discovering, monitoring, and improving processes, typically using data extracted from event logs. This may include discovering the tasks within the overall processes, predicting future trajectories, or identifying anomalous tasks. We focus on using phase-type process modelling to measure compliance with known targets and, inversely, determine suitable targets given a threshold percentage required for satisfactory performance. We illustrate the ideas with an application to a stroke patient care process, where there are multiple outcomes for patients, namely discharge to normal residence, nursing home, or death. Various scenarios are explored, with a focus on determining compliance with given targets; such KPIs are commonly used in Healthcare as well as for Business and Industrial processes. We believe that this approach has considerable potential to be extended to include more detailed and explicit models that allow us to assess complex scenarios. Phase-type models have an important role in this work.