Allameh Tabataba’i University Press Journal of Data Science and Modeling 3060-8082 3 1 2024 12 01 Health Monitoring of Industrial Equipment Based on a Single Output Parameter Using a Bayesian Two-Sample Test in Hilbert Space 281 300 20833 10.22054/jdsm.2026.86633.1072 EN Mohammad Mehdi Abdollahi Statistics Dept., Faculty of Statistics, Mathematics and Computer, Allameh Tabataba&#039;i University M. Bameni Moghadam Statistics Dept., Faculty of Statistics, Mathematics and Computer, Allameh Tabataba&#039;i University Journal Article 2025 06 29 This study investigates the application of Bayesian two-sample testing in Hilbert space to monitor the health status of industrial equipment. The proposed method evaluates distributional differences between operational data samples to detect faults or anomalies. Unlike traditional multivariate techniques, our approach pro-vides higher sensitivity to subtle distributional shifts and supports visual insights into posterior distributions. Real-world experiments on industrial sensor outputs demonstrate the method’s effectiveness in early fault detection, reducing mainte-nance costs and downtime. This makes Bayesian two-sample testing in Hilbert space a powerful tool for predictive maintenance strategies.<br />This study investigates the application of Bayesian two-sample testing in Hilbert space to monitor the health status of industrial equipment. The proposed method evaluates distributional differences between operational data samples to detect faults or anomalies. Unlike traditional multivariate techniques, our approach pro-vides higher sensitivity to subtle distributional shifts and supports visual insights into posterior distributions. Real-world experiments on industrial sensor outputs demonstrate the method’s effectiveness in early fault detection, reducing mainte-nance costs and downtime. This makes Bayesian two-sample testing in Hilbert space a powerful tool for predictive maintenance strategies. https://jdscm.atu.ac.ir/article_20833_134d065b7bbe747834cd27f5a39d67cd.pdf