Application of Mathcad® software in performing uncertainty analysis calculations to facilitate laboratory instruction

Abstract

Uncertainty analysis is a technique for determining an estimate for the interval about a reported result within which the true result is expected to lie with a certain degree of confidence. The uncertainty analysis is an extremely useful tool for all phases of an experimental program from the initial planning (general uncertainty analysis) to detailed design, debugging, testing, and data analysis (detailed uncertainty analysis). The main objective of this article is to describe how Mathcad® software maybe used to facilitate uncertainty analysis calculations in undergraduate laboratory instruction. This objective is accomplished by performing general uncertainty analysis calculations for several example problems using Mathcad®. These examples show how quick uncertainty analysis calculations using Mathcad® during the planning phase of an experiment may assist students to select appropriate measurement equipment. Furthermore, an example of detailed uncertainty analysis is presented to investigate the contributions of the elemental bias and precision error sources, obtain estimates of the bias and precision limits for each measured variable, and illustrate how the measurement errors propagate into the experimental result.