Automating mixture model fitting of task durations for process conformance checking

Process task duration data often exhibit multiple peaks, indicating differences in, for example, customer ages and preferences, resource capabilities or the day/hour of a week. This heterogeneous data, which captures diverse customer patterns, should be represented using different models, resulting in an overall mixture model. This paper introduces gamma mixture models to represent various customer patterns in task duration data, with a focus on automating the fitting process. The approach involves a two-stage procedure: first, divide-and-conquer using peak-, equidistance- and cluster-based techniques to partition data, and automatically fit gamma distributions to each subset. The second stage then improves the fitted mixture model by directly searching the log-likelihood surface. The method is compared with the expectation–maximization (EM) algorithm and an open tool (HyperStar), using both artificially generated datasets and a publicly available hospital billing dataset, demonstrating its effectiveness and time efficiency in modelling heterogeneous process duration data. Furthermore, a case study on process conformance checking is conducted using the hospital billing dataset, highlighting a potential application area for the method in process mining.