Bayesian hierarchical modeling for monitoring optical profiles in low-E glass manufacturing processes

Low-emittance (low-E) glass manufacturing has become an important sector of the glass industry for energy efficiency of such glasses. However, the quality control scheme in the current processes is rather primitive and advanced statistical quality control methods need to be developed. As the first attempt for this purpose, this article considers monitoring of optical profiles, which are typical quality measurements in low-E glass manufacturing. A Bayesian hierarchical approach is proposed for modeling the optical profiles, which conducts model selection and estimation in an integrated framework. The effectiveness of the proposed approach is validated in a numerical study, and its use in Phase I analysis of optical profiles is demonstrated in a case study. The proposed approach will lay a foundation for quality control and variation reduction in low-E glass manufacturing.

[1]  Ming-Hui Chen,et al.  Computing marginal likelihoods from a single MCMC output , 2005 .

[2]  Mahmoud A. Mahmoud,et al.  On the Monitoring of Linear Profiles , 2003 .

[3]  S. Chib,et al.  Marginal Likelihood From the Metropolis–Hastings Output , 2001 .

[4]  J. H. Wilkinson,et al.  IMPROVING THE ACCURACY OF COMPUTED EIGENVALUES AND EIGENVECTORS , 1983 .

[5]  Xiao-Li Meng,et al.  Warp Bridge Sampling , 2002 .

[6]  William H. Woodall,et al.  Statistical monitoring of nonlinear product and process quality profiles , 2007, Qual. Reliab. Eng. Int..

[7]  Willis A. Jensen,et al.  Monitoring Correlation Within Linear Profiles Using Mixed Models , 2008 .

[8]  Joseph Hilbe,et al.  Data Analysis Using Regression and Multilevel/Hierarchical Models , 2009 .

[9]  G. Casella,et al.  The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models , 1996 .

[10]  R. Kass,et al.  Bayes Factors and Approximations for Variance Component Models , 1999 .

[11]  D. Arasteh,et al.  Savings from energy efficient windows: Current and future savings from new fenestration technologies in the residential market , 1993 .

[12]  Lisa Heschong,et al.  Residential Windows: A Guide to New Technologies and Energy Performance , 1996 .

[13]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[14]  Rassoul Noorossana,et al.  Statistical Analysis of Profile Monitoring , 2011 .

[15]  A. Gelman Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[16]  Donald E. Myers,et al.  Linear and Generalized Linear Mixed Models and Their Applications , 2008, Technometrics.

[17]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[18]  Douglas C. Montgomery,et al.  Using Control Charts to Monitor Process and Product Quality Profiles , 2004 .

[19]  R. Wolfinger,et al.  Nonconjugate Bayesian Analysis of Variance Component Models , 2000, Biometrics.

[20]  P. Green Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[21]  M. Clyde,et al.  Model Uncertainty , 2003 .

[22]  P. Gustafson,et al.  Conservative prior distributions for variance parameters in hierarchical models , 2006 .

[23]  Amirhossein Amiri,et al.  A case study on monitoring polynomial profiles in the automotive industry , 2009, Qual. Reliab. Eng. Int..

[24]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo Methods for Computing Bayes Factors , 2001 .

[25]  R. Noorossana,et al.  Phase II Monitoring of Autocorrelated Polynomial Pro les in AR(1) Processes , 2010 .

[26]  E Memarzadeh Lotfabad,et al.  STRUCTURAL AND MAGNETIC STUDY OF ACTIVE SCREEN PLASMA NITRIDED FE73:5SI13:5B9NB3CU1 AND FE77SI11B9NB2:4CU0:6RIBBONS , 2010 .

[27]  Rassoul Noorossana,et al.  Phase I Monitoring of Polynomial Profiles , 2008 .

[28]  John Carmody,et al.  Window Systems for High-Performance Buildings , 2004 .

[29]  S. Chib Marginal Likelihood from the Gibbs Output , 1995 .

[30]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[31]  William H. Woodall,et al.  Introduction to Statistical Quality Control, Fifth Edition , 2005 .

[32]  Rassoul Noorossana,et al.  Multivariate Linear Profiles Monitoring , 2011 .

[33]  B. Carlin,et al.  Bayesian Model Choice Via Markov Chain Monte Carlo Methods , 1995 .

[34]  William H. Woodall,et al.  Current research on profile monitoring , 2007 .

[35]  Rassoul Noorossana,et al.  Monitoring polynomial profiles in quality control applications , 2009 .