Title page for ETD etd-12042005-000931


Type of Document Dissertation
Author Chen, Younan
Author's Email Address yochen@vt.edu
URN etd-12042005-000931
Title Bayesian hierarchical modelling of dual response surfaces
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Ye, Keying Committee Chair
Patterson, Angela N. Committee Member
Prins, Samantha C. Bates Committee Member
Smith, Eric P. Committee Member
Vining, G. Geoffrey Committee Member
Keywords
  • dual response surfaces
  • Bayesian hierarchical model
  • genetic algorithm
Date of Defense 2005-11-29
Availability unrestricted
Abstract
Dual response surface methodology (Vining and Myers (1990)) has been successfully used as a cost-effective approach to improve the quality of products and processes since Taguchi (Tauchi (1985)) introduced the idea of robust parameter design on the quality improvement in the United States in mid-1980s. The original procedure is to use the mean and the standard deviation of the characteristic to form a dual response system in linear model structure, and to estimate the model coefficients using least squares methods.

In this dissertation, a Bayesian hierarchical approach is proposed to model the dual response system so that the inherent hierarchical variance structure of the response can be modeled naturally. The Bayesian model is developed for both univariate and multivariate dual response surfaces, and for both fully replicated and partially replicated dual response surface designs. To evaluate its performance, the Bayesian method has been compared with the original method under a wide range of scenarios, and it shows higher efficiency and more robustness. In applications, the Bayesian approach retains all the advantages provided by the original dual response surface modelling method. Moreover, the Bayesian analysis allows inference on the uncertainty of the model parameters, and thus can give practitioners complete information on the distribution of the characteristic of interest.

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