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”

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.

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.

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.

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.

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

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

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

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.

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.

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

Combined and Expanded Uncertainty Standard Uncertainty Combined Standard Uncertainty Expanded Uncertainty

Example

Example

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

Constraints Time Skills Data Format