National Physical Laboratory

NPL e-Learning Programme

Understanding Uncertainty Budgets

Understanding Uncertainty Budgets


People using measurement in their work need to have an understanding of measurement uncertainty. Measurement uncertainty is often evaluated, controlled and monitored using an uncertainty budget. This course teaches measurement uncertainty through practical examples of uncertainty budgets, because:

  • Uncertainty budgets are a fundamental tool in science and industry, especially in manufacturing, testing and calibration, and they are therefore useful to a wide range of professionals
  • Uncertainty budgets provide a visual way to understand abstract concepts in uncertainty evaluation, and they can thus help to improve the accessibility of those concepts to non-statisticians

The course consists of four modules. Module 1 will allow the learner to read, understand and complete an uncertainty budget. Modules 2–4 are at a more complex level, and allow the learner to understand how an uncertainty budget is formulated.

This course is aimed at

  • Quality managers in industry and manufacturing
  • Testing and calibration professionals
  • Academic and industrial scientists
  • A wider audience interested in the way measurement helps us learn about the world around us

Main objectives

  • Provide an understanding of uncertainty budgets, and the ability to read and use them
  • Provide the ability to complete pre-formulated uncertainty budgets and thus use them to calculate measurement uncertainty in a range of measurement situations
  • Understand how uncertainty budgets are formulated
  • Maximise the accuracy of measurements, by using uncertainty analysis to prioritise areas for improvement in the measurement procedure
  • Develop a wider understanding of measurement uncertainty

Learning objectives (Module 1 – less complex)

  • Understand how the best estimate of a quantity can be found as an average of repeated measured values, with appropriate corrections applied
  • Calculate the variance and standard deviation of a set of repeated measured values
  • Calculate the standard uncertainty of a set of repeated measured values
  • Understand a range of simple probability distributions and when to assign them
  • Understand how the rows of an uncertainty budget evaluate contributions to the combined standard uncertainty from the individual uncertainty contributions
  • Calculate expanded uncertainty from an uncertainty budget, assuming a normal distribution
  • Understand the limitations of the process used, and when to seek advice on using a more complex procedure

Learning objectives (Modules 2–4 – more complex)

  • Understand how the measured quantity depends upon input quantities in a measurement model
  • Understand how to evaluate sensitivity coefficients, given a measurement model
  • Decide when to use absolute and relative uncertainties, and calculate the sensitivity coefficients appropriately
  • Understand when the measured quantity might not be normally distributed
  • Use the t-distribution to characterise a measured quantity
  • Understand how correlated input quantities require a modified approach
  • Understand the principles of evaluating uncertainty in the case of correlated input quantities

Required prior knowledge

We assume very little prior knowledge, other than elementary numeracy, and a basic understanding of the nature of measurement, including calibration. All required statistical concepts are explained as we proceed. In Module 2, there are points at which a basic knowledge of differentiation would help, but it is not essential.

For any introductory concepts of measurement that you would like to explore in more detail, please see our more elementary e-learning courses Introduction to Metrology and Introduction to Measurement Uncertainty


Please note that the information will not be divulged to third parties, or used without your permission