Defense Date


Document Type


Degree Name

Master of Science


Mathematical Sciences

First Advisor

David Edwards


The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found.


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Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

May 2010