1. Uncertainty of Measurement
Developing Uncertainty Budgets in Civil Engineering Test Methods By
Sandiswa Jekwa
The reason why I chose to discuss civil engineering test methods is because 1. I don’t know any other test methods and 2. I think civil engineering materials and their test methods are unique because of issues such as the difficulty of obtaining a particular material property and things like material variability. Its only in civil materials that a I think a test result has been described as not giving the answer but rather an “indication”

2. What is Uncertainty? Are you sure? Well I mean… It depends hey…
Okay look…I’m only 80% sure
“Uncertainty is the value assigned to a measurement result that describes, within a defined level of confidence, the range expected to contain the true measurement result.” – Measurement Systems Analysis 4th Ed.
Uncertainty is the answer you get to the question “Are you sure?”
So this means a result that expresses uncertainty basically says this piece of string is 10mm +/- 0.5mm at a confidence interval of 95%. The true length of the piece of string is between 9.5mm and 10.5mm.

3. Why is Uncertainty Important?
Improves the quality of our test results.
Improves the decision making process in design, construction and maintenance.
Assists in identifying areas, apparatus and environments that create large amounts of uncertainty.

4. What is an Uncertainty Budget?
A tool to quantify uncertainty.
An itemized list of all the sources of uncertainty and their magnitude. All of which are added to provide an overall uncertainty on a specific test method, in a specific laboratory, with specific apparatus and specific testers.

5. Statistical Analysis Principles
The Central Limit Theorem
Mean and Standard Deviation
Identifying Probability Distributions
Central Limit Theorem: states that the sum of a number of probability distributions will tend towards the normal distribution. So we can assume our answer will be normally distributed.

6. Data Required Repeatability Test Results Reproducibility Test Results
Calibration Certificates and Verification Forms
Reference Standards

7. Sources of Uncertainty
Repeatability
Reproducibility
Environment
Cosine Errors
Parallax Errors
Calibration
Reference Standards etc…

8. Methodology Identify Sources of Uncertainty
Categorise as Type A or Type B
Calculate Standard Deviation or Value of Uncertainty
Identify Probability Distribution
Calculate Standard Uncertainty using Divisors and Standard Uncertainty
Calculate Sensitivity Coefficient
Calculate Combined Standard Uncertainty and Expanded Uncertainty

9. Categories of Uncertainty
Type A
Uncertainty obtained from statistical calculations
Type B
Any other method used to obtain an uncertainty value.
Type A will have normal distributions and Type B may be a variety of distributions.

10. Probability Distributions
Normal Distribution
Rectangular
Triangular
U-shaped (Not used in civil test methods)
U-shaped (Not used in civil test methods) but used in radio frequency.

11. Sensitivity Coefficients
Calculating the rate of change between the input variable and the measurand under review.
∆L = L0 x α x ∆T will require ci = cm/°C

12. Combined and Expanded Uncertainty
Standard Uncertainty
Combined Standard Uncertainty
Expanded Uncertainty

13. Example

14. Example

15. Important Notes Minimum sample size is 10 per Type A (COLTO, 6?)
Comparison with PR1/Chapter 7:

16. Constraints
Time
Skills
Data Format