This work is motivated by a problem of optimizing printed circuit board manufacturing using design of experiments. The data are binary, which poses challenges in model fitting and optimization. We use the idea of failure amplification method to increase the information supplied by the data and then use a Bayesian approach for model fitting. The Bayesian approach is implemented using Gaussian process models on a latent variable representation. It is demonstrated that the failure amplification method coupled with a Bayesian approach is highly suitable for optimizing a process with binary data. Copyright © 2010 John Wiley & Sons, Ltd.