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.peer-reviewe

Using Markov Models to Characterize and Predict Process Target Compliance

Processes are everywhere, covering disparate fields such as business, industry, telecommunications, and healthcare. They have previously been analyzed and modelled with the aim of improving understanding and efficiency as well as predicting future events and outcomes. In recent years, process mining has appeared with the aim of uncovering, observing, and improving processes, often based on data obtained from logs. This typically requires task identification, predicting future pathways, or identifying anomalies. We here concentrate on using Markov processes to assess compliance with completion targets or, inversely, we can determine appropriate targets for satisfactory performance. Previous work is extended to processes where there are a number of possible exit options, with potentially different target completion times. In particular, we look at distributions of the number of patients failing to meet targets, through time. The formulae are illustrated using data from a stroke patient unit, where there are multiple discharge destinations for patients, namely death, private nursing home, or the patient’s own home, where different discharge destinations may require disparate targets. Key performance indicators (KPIs) of this sort are commonplace in healthcare, business, and industrial processes. Markov models, or their extensions, have an important role to play in this work where the approach can be extended to include more expressive assumptions, with the aim of assessing compliance in complex scenarios

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners