Extended Gamma Mixture Model for Process Duration Analysis

Sally McClean, Ulster University

Co-authors: Lingkai Yang, Chinese Institute of Coal Science; Malcolm Faddy, Formerly Queensland University of Technology; Mark Donnelly, University of Ulster; Kashaf Khan, BT Group; Kevin Burke, University of Limerick

Abstract: Modelling process durations is crucial in business process mining, where data often exhibits multimodal patterns due to factors such as customer demographics, resource variations, and time influences. Gamma mixture models are well-suited for such data as they handle non-negative values and generalise exponential and Erlang distributions. In this work, we take a statistical-modelling approach to use gamma distributions for peak durations, uniform distributions for flatter segments, and exponential distributions for the tail. Additionally, the model incorporates statistical survival analysis to address left-truncated and right-censored data, effectively capturing incomplete customer journeys. Concept drift detection is applied to track temporal changes in process durations, enhancing adaptability and predictive accuracy in process mining and machine learning.