A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering

In recent years, Bayesian analyses have become increasingly popular for solving industrial related problems. This paper illustrates the use of Bayesian methods in response surface methodology (RSM) in the context of “off-line quality” improvement. RSM and Bayesian Linear Regression - an approach which uses the prior information to make a more efficient inference - are considered together. Results from different estimators are compared for the first time ever. Bayesian linear regression uses the prior information in the high uncertainty state of the response function to make more efficient and more realistic inferences than can be obtained with classical regression. Several different values of the prior distribution of the parameter and uncertainty analysis will be presented for comparative purposes. The effect of the change in the prior information and variances will be illustrated by using an example from the literature.

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