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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

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Related Experiment Video

Updated: Jun 18, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

A modular approach to linear uncertainty analysis.

J B Weathers¹, R Luck, J W Weathers

¹Shock, Noise, and Vibration Group, Northrop Grumman Shipbuilding, P.O. Box 149, Pascagoula, MS 39568, USA. James.Weathers@ngc.com

ISA Transactions

|November 28, 2009

Summary

This summary is machine-generated.

This study presents a modular uncertainty technique for simplifying large-scale engineering analyses. This method offers comprehensive correlation insights and easier implementation than traditional approaches.

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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Area of Science:

Engineering
Data Analysis
Scientific Computing

Background:

Traditional uncertainty analysis methods can be complex for large-scale problems with multiple inputs/outputs.
Existing techniques often lack comprehensive correlation information between variables.
Integrating uncertainty analysis into experimental or modeling programs can be challenging.

Purpose of the Study:

To introduce a simplified, modular methodology for uncertainty analysis in large-scale engineering problems.
To provide a technique that yields comprehensive correlation information between outputs.
To facilitate easier integration of uncertainty analysis into existing workflows.

Main Methods:

Development of a modular uncertainty technique applicable to problems with constant sensitivities.
Comparison of the modular approach with the traditional propagation of errors methodology.
Methodology for obtaining the covariance matrix for input variables using elemental uncertainties.

Main Results:

The modular technique simplifies uncertainty analysis for large-scale problems.
It provides the same results as traditional methods but with fewer conceptual steps.
The approach enables the acquisition of correlation information between all outputs.
A straightforward method for deriving the input variable covariance matrix is presented.

Conclusions:

The proposed modular uncertainty technique offers a more accessible and comprehensive approach to uncertainty analysis.
Its design allows for straightforward integration into various experimental and modeling systems.
This methodology enhances the understanding of variable correlations, a limitation of traditional methods.