What are the Steps to Calculate Measurement Uncertainty?

Specify the Process and Equation: Before dive in and start calculating uncertainty, it is best to have a plan. The first part of plan should be to classify the measurement procedure or system that wish to evaluate.

If performing indirect measurements that need to calculate your measurement results, you should specify the equation used. This is because each variable in the calculation will have its own uncertainty, which will straight affect the uncertainty associated with the calculated result.

Think of using calibrating torque transducers and standard resistors. Each of these measurement procedures need to use an equation to calculate a result for comparison purposes. To estimate uncertainty, break down the equation and evaluate the uncertainty of each variable.

Identify the Uncertainty Sources: Now that you know your measurement procedure, need to identify the factors that affect uncertainty in measurement results. This procedure is not always easy and can get annoying. So, stay calm, and keep researching. You may be surprised by how many influences can affect measurement results.

Quantify the Magnitude of Uncertainty Components: Before calculating measurement uncertainty, must first determine the magnitude of each contributing factor. To complete this, may essential to perform some data reduction and analysis.

To get started, may want to gather the following items. It will be helpful when analyzing data.

• Calibration Reports.
• Repeatability and Reproducibility Studies.
• Experiment Results.
• Making Manuals and Specifications.
• Technical Documents and Guides.
• Published papers, journal articles, etc.

Using these items, you should be able determine how much uncertainty is contributed from each source. Accreditation bodies and assessors want to see Type A data in uncertainty analysis. This is data collected from Repeatability and Reproducibility studies.

Simulation experiments are just the mathematical estimation of outcomes using equations and variable the input variables to see how it changes the output variable. While it may sound difficult, simulation can be pretty easy to do using an excel spreadsheet.

Convert Uncertainty Components to Standard Deviation Equivalents: The difficult part of the uncertainty analysis is complete, now focus on the easier procedure of calculating measurement uncertainty. To begin, need to decrease each uncertainty contributor to a standard deviation equivalent. This procedure starts with classifying a probability distribution that characterizes the dispersion of data set. choose a probability distribution for each uncertainty contributor. If not, sure which probability distribution best describes data, most people choose the rectangular distribution.

Some of the common probability distributions used are Gaussian, Rectangular, Triangular, Log-Normal, Quadratic, U-shaped. Once select a probability distribution, then identify the equation to decrease each uncertainty contributor to a standard deviation. This will decrease each source to a 1-sigma equivalent, then properly combine them in the next step.

Calculate the Combined Standard Uncertainty: After reduced uncertainty sources to standard deviation equivalents, it is time to combine them. To complete this, use the root sum of squares method. This will mathematically combine uncertainty sources in quadrature.

To start, simply square the value of each uncertainty source. Next, add them all together to calculate the sum. Then, calculate the square-root of the summed value. The result will be Combined Uncertainty.

Calculate the Expanded Uncertainty: In this step, expand combined uncertainty to an acceptable level of confidence. To satisfy ISO/IEC 17025:2005 requirements, must expand uncertainty to approximately 95%. Most people use an expansion factor (k) of 2 to achieve a confidence interval of 95.45%. However, also use an expansion factor of 1.96 for a confidence interval of exactly 95.00%.

Just make sure to select an expansion factor that will constantly use in each of uncertainty analyses. Also, it helps to know why you chose expansion factor so you can justify it to assessors.

Evaluate Uncertainty for Appropriateness: Once calculated the expanded uncertainty, it is best to evaluate uncertainty estimate for appropriateness. Essentially, make sure that measurement uncertainty estimate adequately represents your measurement process and is not overestimated.

A good place to start evaluation is to check and verify that uncertainty estimate is not larger than the Reference Standard Uncertainty, or the uncertainty that was reported in your equipment’s calibration certificates. Next, try looking at other laboratories scopes of accreditation to verify uncertainty calculations are reasonably comparable. Assure that estimates are relatively similar to other laboratories. If not, you may have overestimated or underestimated uncertainty.

Finally, perform a Repeatability and Reproducibility study in laboratory. Verify that your results are not larger than uncertainty estimation. If so, you may have understated your uncertainty estimates. Evaluating uncertainty estimates are critical. It is well to perform the hard work upfront than deal with all the paperwork and headaches that result from being cited a deficiency.

For ISO/IEC 17025 accredited laboratories, it is a mutual practice of Reporting measurement uncertainty in test and calibration certificates. With Measurement Uncertainty Training learn ISO/IEC 17025 fundamentals of measurement uncertainty with Overview of Measurement Uncertainty as well as Practical Measurement Uncertainty Calculation Examples for standard.