On Measurement Uncertainties Derived from "Metrological Statistics"

Abstract

As measurement uncertainties are closely tied up with error models, it might be of interest to review a model, which the author assigns to "Metrological Statistics". Given that the random errors are normally distributed, the experimentalist could either refer to B.L. Welch's concept of "effective degrees of freedom" or to the multidimensional Fisher-Wishart distribution density. In the first case, different numbers of repeated measurements are admissible, in the latter it is strictly required to have equal numbers of repeated measurements. In error propagation, however, only the latter mode of action opens up the possibility of designing confidence intervals according to Student and confidence ellipsoids according to Hotelling. Another point of view, closely linked to the choice of the numbers of repeated measurements, refers to the customary practice of attributing equal rights to statistical expectations and empirical estimators. However, the Fisher-Wishart distribution density suggests using only the information which is realistically accessible to experimentalists, namely empirical estimators. For the handling of unknown systematic errors, either the existence of a (rectangular) distribution density may be assumed or, and this is proposed here, they may be classified as time-constant quantities, biasing expectations and suspending a lot of tools and procedures of error calculus well-established otherwise.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2001
Accession Number
ADP013726

Entities

People

  • Michael Grabe

Tags

DTIC Thesaurus Topics

  • Arithmetic
  • Computer Simulations
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Intervals
  • Linear Systems
  • Measurement
  • Metrology
  • Observation
  • Probability
  • Random Variables
  • Simulations
  • Statistics
  • Technical Information Centers
  • Uncertainty

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.
  • Systems Analysis and Design