This paper considers the problem of achieving improvements through adaptive experimentation. To limit the focus we consider only design spaces with discrete two-level factors. We prove that, in a Bayesian framework, one factor at a time experimentation is an optimally efficient response to step by step accrual of sample information. We derive Bayesian predictive distributions for experimentation outcomes given natural conjugate priors. Using an example based on fatigue life of weld repaired castings, we show how to use our results.

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