Process Duration Modeling and Concept Drift Detection using Phase-Type Distributions

Efficient processes are of significant importance for the operation of organizations and companies, and the duration of cases is one of the key factors in measuring process efficiency. Modeling the duration of processes not only helps in evaluating efficiency but also provides other KPIs, such as predictions for completion time. Also, processes may change over time, a phenomenon known as concept drift, which can lead to the model no longer being able to accurately characterize the process. In this paper, the process duration is modeled using the phase-type distribution, where the number of phases is determined by hypothesis testing. Then, the divergence between the models of different time periods is used to assess the extent of change in the process duration. The proposed method is first validated on synthetic data to evaluate its fitting capability, where the log-likelihood of the fitted model is nearly identical to that of the ground truth, with a difference less than 0.02%. It is then applied to real-world data for fitting and drift detection, and the results are consistent with the actual observations.