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A HANDY TOOL FOR CONVENIENT ERROR PROPAGATION ANALYSIS: A USER FORM FOR ERROR INFLUENCE COEFFICIENTS

Sheldon M. Jeter

Georgia Institute of Technology

INTRODUCTION

Complete uncertainty analysis in experimental engineering requires two distinct and complementary calculations. Statistical analysis of repeated measurements is needed to compute the Uncertainty A, which is the uncertainty due to random variation. Complementary physical analysis of the measurement system is also needed to evaluate the Uncertainty B or the range in possible bias or built in error. The more interesting and important applications of Uncertainty B analysis are encountered when considering an indirect measurement. An indirect measurement is merely a value calculated from a set of direct measurements. Error Propagation Analysis (EPA) is usually necessary to estimate the Uncertainty B for indirect measurements.

This paper first reviews the basic principles of experimental uncertainty. It then reviews the principles and pertinent details of EPA. It next presents an example that illustrates the calculations of Uncertainty A and Uncertainty B. The latter calculation requires EPA, so the paper presents and explains an Excel User Form to facilitate this task. The example demonstrates that this form makes even relatively complex EPA simple and quick.

TYPES OF UNCERTAINTY

Common experience and a little scrutiny reveal that two types of experimental uncertainty exist, random and systematic. Conventional practice and consensus standards (ISO, 1995) also recognize these two types. Formally, the random uncertainty is called Uncertainty A. It is operationally defined as the uncertainty that can be evaluated by statistical analysis of the experimental data. The measure of Uncertainty A is an error limit based on observed random variation in the data. Conventionally, Uncertainty A has been called imprecision. In contrast, the systematic uncertainty known as Uncertainty B must be evaluated by physical analysis of the entire measurement system. Uncertainty B is explicitly not a measure of random variation. Instead, it is the estimated possible range

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright 2005, American Society for Engineering Education

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Jeter, S. (2005, June), A Handy Tool For Convenient Error Propagation Analysis: A User Form For Error Influence Coefficients Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14693