In many physical processes, there is uncertainty in the parameters which
define the process and this input uncertainty is propagated through the
equations of the process to its output. Experimental design is essential to
quantify the uncertainty of the input parameters. If the process is
simulated by a computer code, propagation of uncertainties is carried out
through the Monte Carlo method by sampling in the input parameter
distribution and running the code for each sample. It is then important to
obtain information about the way in which the parameters are influential on
the output of the process. This is useful in order to decide how to sample
in the input space when propagating uncertainties and on which parameters
experimental effort should be more concentrated. Here, we use dimensional
and similarity analyses to reduce the dimension of the input variable space
with no loss of information and profit from this reduction when propagating
uncertainties by Monte Carlo. Using dimensional analysis, the output is
expressed in terms of the inputs through a series of dimensionless numbers,
a dimension reduction is achieved since there are less dimensionless numbers
than original parameters. In order to minimize the uncertainty of the
estimation of the output, propagation of uncertainties should be carried out
by sampling on the space of the dimensionless numbers and not on the space
of the original parameters. The purpose of this paper is an application of
propagation of uncertainties to a code which simulates the interaction of
metal drilling with a laser beam, where there exists uncertainty in the
absorbed intensity of the beam and the density of the medium. By sampling in
the reduced input space, a substantial variance reduction is achieved for
the estimators of the mean, variance and distribution function of the
output. Moreover, the output is found to depend on the intensity and the
density through their quotient.