Learning to optimize termination decisions under hybrid uncertainty of system lifetime and task duration

The lifetime distribution of engineering systems typically demonstrates significant heterogeneity, influenced by various factors such as material quality, manufacturing variations, usage intensity, and environmental conditions. Meanwhile, the distribution of random task durations can vary considerably, depending on resource availability, task complexity, and external disruptions. Accurately characterizing these heterogeneities is vital for improving the overall operational efficiency of engineering systems. This study explores optimal task termination decisions that effectively address the hybrid uncertainty stemming from the diverse distributions of system lifetimes and task durations. Utilizing a Bayesian statistical learning framework, the study models the uncertainties associated with random task durations and system lifetimes through unobserved distribution parameters. Bayesian parameter updating techniques are employed to derive posterior distributions for these parameters, informed by observed data collected during task executions regarding task durations and system lifetimes. By iteratively refining these parameters, the study dynamically determines the optimal task termination time. Furthermore, the properties of the optimal task termination decisions are investigated within a Markov Decision Process framework. A series of numerical examples are presented to validate the theoretical findings and highlight the practical implications of the proposed approach. The experimental results reveal a potential cost reduction of up to 45.11% compared to existing policies, emphasizing the efficacy and of the proposed methodology.