Abstract
Previous research on event log data analysis has primarily focused on identifying critical and frequent events, as well as qualitatively assessing correlations between event occurrences. However, the probabilistic behavior of frequently occurring events over time remains poorly understood. Through an in-depth exploratory analysis, we reveal that the (log) inter arrival times of events follow some mixture distributions with two modes, suggesting the presence of transitions between latent states. To better understand the data-generating mechanism underlying these frequent events, we employ Markov Modulated Renewal Processes (MMRPs), a type of hidden Markov model, to capture the patterns exhibited in the inter-arrival times between successive events. Due to limitations in record precision, some inter-arrival times are recorded as zero. To address this issue, we propose a simple data imputation algorithm to generate non zero inter-arrival times, facilitating inference on the inter-arrival time distributions and the underlying MMRPs. The effectiveness of the algorithm is validated using synthetic data. Finally, we evaluate the proposed model on real manufacturing system data, uncovering key insights into system states.