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Related Concept Videos

Propagation of Uncertainty from Random Error00:59

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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...
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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.
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Uncertainty in Measurement: Accuracy and Precision03:37

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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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Uncertainty in Measurement: Reading Instruments02:46

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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...
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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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Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers:
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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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Calculation of Measurement Uncertainty Using Prior Information.

S D Phillips1, W T Estler1, M S Levenson1

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899-0001.

Journal of Research of the National Institute of Standards and Technology
|December 24, 2016
PubMed
Summary
This summary is machine-generated.

Bayesian inference enhances measurement uncertainty calculations by incorporating prior data, potentially reducing expanded uncertainty by up to 85%. This method aids in verifying workpiece conformance to specifications like ISO 14253-1.

Keywords:
Bayesianbiaserrormeasurement uncertaintyuncertainty

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Area of Science:

  • Metrology and Measurement Science
  • Statistical Inference
  • Quality Control

Background:

  • Traditional measurement uncertainty calculations often do not leverage available prior information.
  • Incorporating prior knowledge can lead to more accurate and efficient uncertainty assessments.
  • International standards like ISO 14253-1 provide frameworks for assessing conformance to specifications.

Purpose of the Study:

  • To present a Bayesian inference approach for integrating prior information into measurement uncertainty calculations.
  • To demonstrate the potential reduction in expanded uncertainty using this Bayesian method.
  • To apply the Bayesian approach to workpiece conformance testing under ISO 14253-1 and explore modifications to uncertainty guard bands.

Main Methods:

  • Utilizing Bayesian inference to combine prior knowledge with measurement data.
  • Calculating measurement uncertainty with the Bayesian approach.
  • Applying the method to assess workpiece conformance to specifications.
  • Investigating adjustments to expanded uncertainty guard bands for enhanced conformance zones.

Main Results:

  • The Bayesian approach can effectively reduce expanded uncertainty by up to 85% in typical examples.
  • The method provides a viable framework for proving workpiece conformance according to ISO 14253-1.
  • A procedure for modifying guard bands was discussed to increase the conformance zone.

Conclusions:

  • Bayesian inference offers a powerful tool for refining measurement uncertainty and improving conformance assessment.
  • The integration of prior information leads to more precise and potentially larger conformance zones.
  • This approach has significant implications for quality control and metrology practices.