In order to improve the efficiency of conformance checking in business process management, a business alignment approach is presented based on transition systems between relation matrices and Petri nets. Firstly, a log-based relation matrix of the events is obtained according to the event log. Then, the events in the relation matrix are observed and the transitions in the model are firing, and the activities in the log and in the model are compared. Next, the states of the log and the model are recorded until no new state can be generated, so a transition system can be obtained which includes optimal alignments between the event log and the process model. Finally, two detailed algorithms are presented to obtain an optimal alignment and all optimal alignments between the trace and the model based on the given cost function, respectively. The availability and effectiveness of the proposed approach are proved theoretically.

Several unexpected behaviors may occur during actual treatment of clinical pathways, which will have negative impact on the implementation and the future work. To increase the performance of current deviation detection algorithms, a method is presented according to business alignment, which can effectively detect the anomaly in the implementation of the clinical pathways, provide judgment basis for the intervention in the process of the clinical pathway implementation, and play a crucial role in improving the clinical pathways. Firstly, the noise in diagnosis and treatment logs of clinical pathways will be removed. Then, the synchronous composition model is constructed to embody the deviations between the actual process and the theoretical model. Finally, algorithm is selected to search for optimal alignment. A clinical pathway for ST-Elevation Myocardial Infarction (STEMI) under COVID-19 is used as a case study, and the superiority and effectiveness of this method in deviation detection are illustrated in the result of experiments.