Use of design of experiments and Monte Carlo method for instruments optimal design

A common issue in the design of measurement instruments is the comparison between different solutions in terms of components of the measurement chain, data processing or even measurement principles; the predicted instrumental uncertainty is the driving parameter for such a comparison. While in many situations the linearization of the measuring model allows using the standard ISO GUM procedure, in complex cases it might be necessary to proceed with Monte Carlo simulations as per ISO GUM supplement 1. This paper describes a method that combines the factorial design of experiments (DOE) and the ISO GUM supplement 1 uncertainty evaluation method to guide the instrument designer in the instrument configuration optimization. The proposed approach allows estimating, in the design phase, the overall instrumental uncertainty for different configurations, the instrument sensitivity to the accuracy in the measurements of its inputs and the effects on systematic and random measurement errors deriving from the choice of all instrumental variables. The use of data populations selected with the DOE criteria allows recovering valuable parameters equivalent to the sensitivity factors of the GUM linearized approach. The data analysis allows separating the critical factors that must be accurately controlled from those only weakly affecting the measurement uncertainty. The method has been applied to a case study where the metrological performances of a system devoted to the measurement of the acoustic radiation emitted by a vibrating panel in a reverberant enclosure had to be assessed.