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Online Mathematical Toolbox for Analytical Standard Uncertainty Evaluation

Uncertainty evaluation plays an important role in ensuring that a designed system can indeed achieve its desired performance. There are three standard methods to evaluate the propagation of uncertainty: analytic linear approximation; Monte Carlo (MC) Simulation; and analytical methods using mathematical representation of the Probability Density Function (PDF).

The analytic linear approximation method is inaccurate for highly non-linear systems which is limiting its application. The MC simulation approach is the most widely used technique as it is accurate, versatile and applicable to highly non-linear systems. However it does not define the uncertainty of the output in terms of those of its inputs. Therefore designers who use this method need to re-simulate their systems repeatedly for different combinations of input parameters. The most accurate solution can be attained using the analytical method based on PDF. However, it is unfortunately too complex to employ.

Here, we introduce the use of an Analytical Standard Uncertainty Evaluation (ASUE) toolbox that automatically performs the analytical method for multivariate polynomial systems. The ASUE toolbox was specifically designed for engineers and designers and is therefore simple to use. It provides the exact solution obtainable using the MC simulation, but with an additional output uncertainty expression as a function of its input parameters.

Use the toolbox

The best citations for using ASUE toolbox are:

  1. Y. C. Kuang, A. Rajan, M. P.-L. Ooi, and T. C. Ong, "Standard uncertainty evaluation of multivariate polynomial," Measurement, vol. 58, pp. 483-494, Dec. 2014.
  2. A. Rajan, M. P.-L. Ooi, Y. C. Kuang, and S. N. Demidenko, "Analytical Standard Uncertainty Evaluation Using Mellin Transform," Access, IEEE, vol. 3, pp. 209-222, 2015.