A Review of Bayesian Reliability Approaches to Multiple Response Surface Optimization

ABSTRACT This chapter is a review of recently proposed Bayesian predictive approaches to response surface optimization, in particular multiple response surface optimization. The posterior predictive distribution of a regression model is used to compute the posterior probability that a vector of response variables, Y, is contained in a specified region, A, conditional on a vector of predictive factors, x. Response surface optimization can then be achieved by maximizing this posterior probability with respect to x. For a chosen regression model, all of the uncertainty, as well as the correlation among the response types, is accounted for through the posterior predictive distribution. Some previously published frequentist approaches had not accounted for the correlation among the response types and many have ignored some aspects of model parameter uncertainty.