Bayesian Hierarchical Modeling for large-scale sensor calibration

In modern industrial processes, the calibration of sensors plays a crucial role in ensuring the reliability and accuracy of measurements. However, with millions of sensors being produced and calibrated weekly, traditional laboratory calibration methods pose significant challenges in terms of time and cost. Addressing this issue, this thesis explores a Bayesian statistical model designed to enable the efficient calibration of sensor batches by minimizing the need for exhaustive laboratory testing. The proposed approach leverages information from a reference lot of laboratory-calibrated sensors to statistically infer the calibration properties of a new, identical lot of uncalibrated sensors. By calibrating only a small subset of the uncalibrated lot, the model uses Bayesian inference to estimate key parameters and evaluate the overall reliability of the batch. This process significantly reduces the number of sensors requiring direct calibration while maintaining high confidence in their performance. Building on the original model, which combines a binomial prior and a hypergeometric likelihood, this thesis proposes extensions to account for uncertainty in critical parameters. In particular, the introduction of a hierarchical structure, with a hyperprior on the probability of finding out-of-tolerance sensors, enhances the model's flexibility and robustness. These refinements allow for a more detailed and accurate depiction of the variability inherent in industrial calibration processes. The importance of this work lies not only in its practical implications for sensor calibration but also in its broader contribution to demonstrating the potential of Bayesian methods in solving real-world problems. The adoption of statistical approaches like this can lead to significant cost savings, improved efficiency, and broader applicability in various industrial domains.