Monte Carlo Uncertainty Propagation with the NIST Uncertainty Machine

Abstract

Monte Carlo simulations for uncertainty propagation take as inputs the uncertainty distribution for each variable and an equation for the calculation of a desired quantity. The desired quantity is then calculated by randomly drawing from the specified uncertainty distributions of the input variables. This calculation is then repeated many times (often 106 or greater) with new random drawings each time. The resulting uncertainty distribution of the calculated value is directly obtained from the many random trials. Monte Carlo uncertainty propagation has the advantage of both being easy to interpret and allowing for a wide variety of uncertainty distributions. Monte Carlo uncertainty propagation methods have not been widely used in the undergraduate curriculum due to the lack of availability of easy to implement solutions for carrying out these simulations. Fortunately, the National Institute of Standards and Technology (NIST) developed a Monte Carlo uncertainty propagation calculator, "NIST Uncertainty Machine", that is freely available and accessible via a web interface. The NIST Uncertainty Machine makes the propagation of uncertainty with Monte Carlo simulations easy to implement in the undergraduate curriculum.