Basic Measurement Uncertainty, Methods and Applications


This course is intended for scientists and engineers interested in evaluating experimental accuracy. It is in complete harmony with national and international standards. After this two-day course, the students will be able to apply uncertainty analysis techniques to many basic experimental test problems in order to help achieve the test objectives more productively and at lower cost. This course assumes students have least BS degrees in engineering or science. Students need to bring calculators or laptops.

Key Topics:

  • The basics of the measurement uncertainty model
  • Statistical considerations
  • The concepts of systematic and random error sources
  • Comparison of US and ISO approaches
  • Use of correlation
  • Uncertainty propagation, calibration errors and more
  • Click below for full outline

Who Should Attend:

This course is intended for scientists and engineers interested in evaluating experimental accuracy.

Course Information:

Type of Course: Instructor-Led Short Course
Course Level: Intermediate
Course Length: 2 days
AIAA CEU's available: Yes


I. Outline
II. Related Documents
III. Fundamentals
IV. Measurement Error
V. Random Error (precision)
B. Student's Table
VI. Uncertainty and Repeatability
VII. Systematic Error (bias)
VIII. Measurement Uncertainty Model
IX. Degrees of Freedom
X. Lexicon, ISO & US/ASME
XI. U95 Calculation Example
A. Degrees of Freedom
XII. Error and Uncertainty
XIII. Calculating Random Uncertainty
XIV. Obtaining Systematic Uncertainties
XV. How to do it summary
XVI. Calibration Uncertainties
XVII. Pre- and Post- Test Analysis
XVIII. Conclusions
XIX. Statistical Considerations
XXI. Pooling SX
XXII. Use of Student's t
XXIII. Uncertainty/Error Propagation
XXIV. Taylor's Series (independent error sources)
XXV. Taylor's Series (non-independent error sources)
XXVI. Compressor Efficiency Example
XXVII. Difficulties, Recommendations, Illustrations
XXVIII. General Expression
XXIX. Weighting by Uncertainty
XXX. Applied Considerations
XXXI. Choice of Units
XXXII. Outliers
A. Thompson's Tau at 5% Significance
XXXIII. Correlation
A. General t-statistic equation
XXXIV. Probability Plots
A. Benard's Formula
B. How to do it summary
XXXV. Instrument Vendor Uncertainty Specifications
XXXVI. Conclusions/Review

Two class experiments: class weight and calibration/propagation
Fourteen in-class homework problems worked and explained



Dr. Ronald H. Dieck served as President of the Instrumentation Systems and Automation Society, ISA, (1998-1999) and also served as the President of the Asian Pacific Federation of Instrumentation and Control Societies, APFICS, (2002). He received his BS in Physics and Chemistry from Houghton College in 1964 and his MS in Physics from Trinity College in 1968. He was employed in aerospace and test measurement instrumentation and metrology for over 35 years. He has been directly responsible for data validity and measurement uncertainty assessment as they relate to metrology, calibration, testing and data analysis. He has been the manager of an instrumentation engineering department for a major aerospace corporation and that corporation's Instrumentation Discipline Chief. Mr. Dieck founded and chaired the Data Analysis and Measurement Uncertainty Committees of the Air Pollution Control Association (APCA) and the ISA. He is a co-author of the American Society of Mechanical Engineers' (ASME) performance test code on Measurement Uncertainty and acts as the uncertainty consultant to the SAE E-31 Committee on Gas Turbine Emission Measurements. Mr. Dieck is the 1977 recipient of the ISA Dr. Charles Stark Draper Award for the best tutorial lecture and the 1988 recipient of the Test Measurements Division Mills Dean III Award for service to ISA. He is the author of the text "Measurement Uncertainty, Methods and Applications, 4th Edition," (2006) and a Fellow of ISA in measurement uncertainty.



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