Variation Source Identification in Manufacturing Processes Using Bayesian Approach With Sparse Variance Components Prior

Abstract

We present a Bayesian linear random effects’ model for variation source identification in multistage manufacturing processes with a prior for sparse variance components. A modified horseshoe+ (HS+) prior is used to tackle high-dimensional problems with low sample size and sparse variation sources. Furthermore, we introduce the informed HS+ (IHS+) prior that incorporates the likelihood information of possible variation sources. To estimate the variations from the IHS+ prior, a specially designed Gibbs sampler is established. Through a series of numerical experiments and case study, we showed that the proposed IHS+ outperforms the existing prior distributions when variation sources are sparse. Note to Practitioners —Economic globalization brings intense competition among manufacturing enterprises. The key to success in this competitive climate is a prompt response to rapidly changing market demands with high-quality products. Variation reduction is essential for improving process efficiency and product quality. Existing variation source identification approaches generally assume that the amount of measurement data is larger than that of the possible variation sources. We propose a method to identify the process variation sources with limited measurement capability. Moreover, we provide a tool to apply the domain knowledge on the possible variations in the manufacturing processes. The proposed method is flexible and can be adjusted according to the confidence level of the practitioners’ empirical knowledge. The experiments have shown that our method possesses advantageous features in detecting variation sources and estimating the size of variations.