Bayesian Prior Elicitation and Sensitivity Analysis in Hierarchical Reliability Models : An Application of IMS Run-to-failure Bearings Dataset
Gunasekara, Niluka Lakmali (2026)
2026
Master's Programme in Computing Sciences and Electrical Engineering
Informaatioteknologian ja viestinnän tiedekunta - Faculty of Information Technology and Communication Sciences
Hyväksymispäivämäärä
2026-06-08
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tuni-202606057019
https://urn.fi/URN:NBN:fi:tuni-202606057019
Tiivistelmä
This thesis investigates the role of prior knowledge elicitation in Bayesian reliability modelling for rolling element bearings, and assesses how posterior inference and sensitivity are affected by different elicitation methods.
Three hierarchical Bayesian Weibull models are developed and compared, each differing only in the prior distributions. Model M1 derives its prior through a fitting approach using catalogue load ratings and bearing life equations. Model M2 adopts a supra-Bayesian approach, synthesizing the catalog prior with life-scaled Pronostia experimental data. Model M3 uses a weakly informative prior as a baseline.
The IMS bearing dataset is used as the experimental testbed. Kurtosis is selected as the vibration feature and failure onset times are determined by expert visual inspection of the kurtosis trajectories. The posterior is estimated using the No-U-Turn Sampler (NUTS) via PyMC. Models are compared using prior predictive conflict checks and direct RUL prediction accuracy against ground truth.
Results show that the supra-Bayesian model M2 achieves the best prior calibration confirmed by prior-data conflict checks, and produces the narrowest posterior credible intervals, demonstrating that principled synthesis of multiple prior sources reduces uncertainty more effectively. All three models converge toward similar posterior regions for the shape parameter (ˆμβ ≈ 1.5 - 2.7), confirming moderate wear-out behaviour. M2 consistently produces the median RUL estimates closest to the true values for all three failed bearings. For the Test 1 bearings, their sensitivity to prior specifications is limited to approximately 200–220 h. However, all three models tend to overestimate the RUL of S2 B1. The thesis concludes with a discussion of the methodological positioning of population-level Bayesian reliability models relative to degradation-trajectory approaches, and identifies directions for future work.
Three hierarchical Bayesian Weibull models are developed and compared, each differing only in the prior distributions. Model M1 derives its prior through a fitting approach using catalogue load ratings and bearing life equations. Model M2 adopts a supra-Bayesian approach, synthesizing the catalog prior with life-scaled Pronostia experimental data. Model M3 uses a weakly informative prior as a baseline.
The IMS bearing dataset is used as the experimental testbed. Kurtosis is selected as the vibration feature and failure onset times are determined by expert visual inspection of the kurtosis trajectories. The posterior is estimated using the No-U-Turn Sampler (NUTS) via PyMC. Models are compared using prior predictive conflict checks and direct RUL prediction accuracy against ground truth.
Results show that the supra-Bayesian model M2 achieves the best prior calibration confirmed by prior-data conflict checks, and produces the narrowest posterior credible intervals, demonstrating that principled synthesis of multiple prior sources reduces uncertainty more effectively. All three models converge toward similar posterior regions for the shape parameter (ˆμβ ≈ 1.5 - 2.7), confirming moderate wear-out behaviour. M2 consistently produces the median RUL estimates closest to the true values for all three failed bearings. For the Test 1 bearings, their sensitivity to prior specifications is limited to approximately 200–220 h. However, all three models tend to overestimate the RUL of S2 B1. The thesis concludes with a discussion of the methodological positioning of population-level Bayesian reliability models relative to degradation-trajectory approaches, and identifies directions for future work.