Evaluation of uncertainties in measurements by Monte Carlo simulations with an application for laserscanning

The trapezoidal and triangular distribution recommended by the "Guide to the Expression of Uncertainty in Measurement (GUM)" are derived to obtain methods for drawing random samples from them. It is demonstrated that variances, covariances and confidence intervals of these distributions can be estimated by the random variates. This method is also applicable for the convolution of different types of distributions like the triangular and the normal distribution. Monte Carlo simulations give in addition estimates of the expected values, variances, covariances and confidence regions of unknown parameters derived from the measurements. Furthermore, hypotheses for the parameters can be tested. This method is applied for the determination of the surface of a motorway by laserscanning. The variances of a laserscanner are specified which are sufficiently small to decide whether detected deformations of the surface are permissible or not.