We address the optimization of a computer model, where each simulation either fails or returns a valid output performance. We suggest a joint Gaussian process model for classification of the inputs (computation failure or success) and for regression of the performance function. We discuss the maximum likelihood estimation of the covariance parameters, with a stochastic approximation of the gradient. We then extend the celebrated expected improvement criterion to our setting of joint classification and regression, thus obtaining a global optimization algorithm. We prove the convergence of this algorithm. We also study its practical performances, on simulated data, and on a real computer model in the context of automotive fan design.