In many physical processes, there is uncertainty in the parameters whichdefine the process and this input uncertainty is propagated through theequations of the process to its output. Experimental design is essential toquantify the uncertainty of the input parameters. If the process issimulated by a computer code, propagation of uncertainties is carried outthrough the Monte Carlo method by sampling in the input parameterdistribution and running the code for each sample. It is then important toobtain information about the way in which the parameters are influential onthe output of the process. This is useful in order to decide how to samplein the input space when propagating uncertainties and on which parametersexperimental effort should be more concentrated. Here, we use dimensionaland similarity analyses to reduce the dimension of the input variable spacewith no loss of information and profit from this reduction when propagatinguncertainties by Monte Carlo. Using dimensional analysis, the output isexpressed in terms of the inputs through a series of dimensionless numbers,a dimension reduction is achieved since there are less dimensionless numbersthan original parameters. In order to minimize the uncertainty of theestimation of the output, propagation of uncertainties should be carried outby sampling on the space of the dimensionless numbers and not on the spaceof the original parameters. The purpose of this paper is an application ofpropagation of uncertainties to a code which simulates the interaction ofmetal drilling with a laser beam, where there exists uncertainty in theabsorbed intensity of the beam and the density of the medium. By sampling inthe reduced input space, a substantial variance reduction is achieved forthe estimators of the mean, variance and distribution function of theoutput. Moreover, the output is found to depend on the intensity and thedensity through their quotient.