Bayesian Hierarchical Linear Modeling of Profile Data With Applications to Quality Control of Nanomanufacturing

Abstract

In this paper, we propose to use the multiple ultrasonic attenuation profiles measured at different locations of a specimen to infer the microstructure of metal-matrix nanocomposites. We present a general framework to connect the profile data with both explanatory variables and product quality parameters for quality inference. In particular, a hierarchical linear model with level-2 variance heterogeneity is proposed to model the relationship between ultrasonic attenuation profiles, ultrasonic frequency, and the microstructural parameters of the nanocomposites. An integrated Bayesian framework for model estimation, model selection, and inference of the microstructural parameters is proposed through blocked Gibbs sampling, intrinsic Bayes factor, and importance sampling. The effectiveness of the proposed approach is illustrated through case studies.