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.

Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.