Computer simulation modeling is an important part of engineering design. The process of creating quality products under variable conditions is called robust engineering design. Frequently these simulation models are expensive to run and it can take many runs to find the appropriate parameter settings of the engineering design. To reduce the cost of robust engineering design, it has been proposed that statistical models be used to predict the results of the simulator at unobserved values of the inputs. This involves running experiments on the computer simulation models, or computer experiments. Computer experiments have no random error and frequently involve a large number of experimental factors; because of this, there are many reasons why standard prediction and design methods may not work well. Methods from spatial statistics, frequently refered to as kriging, are used to predict new observations of the simulation model. A generalized linear model with unknown covariance parameters is used on several examples of high dimensions. The model requires estimation of the covariance function parameters and methods are described for parameter estimation and model building. Latin hypercube sampling is used for the experimental design. Latin hypercube sampling is as easy to use as Monte Carlo sampling and has been shown to have better estimation properties. The space filling properties of Latin hypercube sampling are investigated here and shown to fill the design space more uniformly than Monte Carlo sampling. These statistical methods are applied to two circuit simulation models. The results show that these methods work well on computer experiments and can form the basis for a methodology in robust engineering design. Although these methods have been applied to circuit design problems, the methods are applicable to a wide variety of computer simulation models. Robust engineering design received a great deal of attention when Taguchi's ideas were introduced. An investigation into the methods that Taguchi introduced revealed some shortcomings from a statistical view. General conclusions are drawn about the efficacy of traditional Taguchi methods compared with the prefered model-based approach of the thesis.