Modelling Task Durations Towards Automated, Big Data, Process Mining

Business processes are generally time-sensitive, impacting factors such as customer expectations, cost efficiencies, compliance requirements, supply chain constraints, and timely decision-making. Time analysis is therefore crucial for customer understanding and process congestion minimisation. Existing process mining methods mainly employ basic statistics, process discovery and data mining techniques. These approaches often lack a structured model or profile to characterise the data related to the duration of individual process tasks. Consequently, it can be difficult to comprehensively understand critical observations such as trends, peaks, and valleys of task durations. This paper proposes a parsimonious generic representation of task duration data that addresses these limitations. A mixture model comprising gamma, uniform and exponential distributions is proposed that allows for peaked components corresponding to durations terminating near a particular value (the peak) with, in addition, flatter components for durations terminating more randomly between the peaks. The modelling is validated using examples from patient billing and the telecom industry. In each scenario, the corresponding fitted models offer a good representation of the underlying process tasks. The model can therefore be used to improve knowledge of these tasks in terms of the mixture components and what they might represent, such as the root causes of task termination. The paper also considers information criteria more appropriate for large data sets where very small effects can appear “significant” using techniques developed for smaller data sets.