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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.

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

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.

Instrument Calibration

Instrument Calibration

Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
Analytical Balance Calibration
An analytical balance measures mass and requires regular calibration to...

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...

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...

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

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Uncertainty quantification for radiation measurements: Bottom-up error variance estimation using calibration

T Burr¹, S Croft², T Krieger¹

¹Nuclear Fuel Cycle Analysis, International Atomic Energy Agency, Box 100, 1400 Vienna, Austria.

Applied Radiation and Isotopes : Including Data, Instrumentation and Methods for Use in Agriculture, Industry and Medicine

|December 25, 2015

Summary

This summary is machine-generated.

This study refines bottom-up uncertainty quantification (UQ) using calibration data to improve agreement with top-down UQ. The goal is to identify unknown error sources in measurement processes, particularly in nuclear material assay.

Keywords:

Classical calibration Enrichment meter principle Errors in predictors Inverse regression Uncertainty

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Area of Science:

Metrology and Measurement Science
Statistical Analysis
Nuclear Engineering

Background:

Top-down uncertainty quantification (UQ) often yields larger error variances than bottom-up UQ due to un recognized error sources in fielded methods.
Discrepancies between top-down and bottom-up UQ hinder a complete understanding of measurement processes.
Existing bottom-up UQ methods may not fully account for calibration uncertainties.

Purpose of the Study:

To refine bottom-up uncertainty estimation by incorporating calibration information.
To achieve better agreement between refined bottom-up and top-down UQ estimates when no unknown error sources exist.
To develop a method for detecting omitted error sources when top-down UQ exceeds refined bottom-up UQ.

Main Methods:

Development of a refined bottom-up uncertainty approach for four simple linear calibration cases.
Consideration of inverse regression and classical regression, with and without non-negligible error in predictors.
Utilizing simulation for uncertainty estimation due to the inadequacy of analytical approximations with small calibration datasets.

Main Results:

The refined bottom-up UQ approach aims for agreement with top-down UQ within a specified tolerance in the absence of unknown errors.
The study supports the tendency for inverse regression to exhibit lower error variance than classical regression, even with predictor errors.
Calibration parameter estimates perform differently depending on the regression method and whether predictor errors are considered.

Conclusions:

The refined bottom-up UQ method, incorporating calibration, provides a more robust assessment of measurement uncertainty.
Discrepancies between refined bottom-up and top-down UQ serve as indicators of unaddressed error sources.
The findings are particularly relevant for nuclear material assay, such as gamma spectroscopy, and highlight the importance of simulation for UQ with limited calibration data.