Using Markov Models to Characterize and Predict Process Target Compliance

Abstract

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.