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# Measurement Uncertainties

## Introduction

All measurement data is subject to uncertainty and a measured value is only complete if it is accompanied by an appropriate statement of the associated uncertainty. Understanding and evaluating uncertainty is important to anyone wishing to make good quality measurement and, in particular, where the measurement data is used to:

• maintain quality control during production processes
• show compliance with regulations
• undertake research and development
• calibrate instruments
• demonstrate traceability to national measurement standards
• develop, maintain and compare national and international measurement standards

In many cases quantifying measurement uncertainty and expressing it in a valid form are not straightforward tasks. Extensive knowledge (metrological, mathematical and statistical) may be needed to obtain high quality results on which you, your customers and regulatory organisations can rely.

## Science

In order to make a statement concerning the measurement of a quantity of interest it is required to provide an estimate of the quantity, through measurement, and an associated uncertainty. The uncertainty is a numerical measure of the quality of the estimate. It can take the form of a standard uncertainty, which is the uncertainty associated with the estimate expressed as a standard deviation. It can also take the form of a coverage interval, which is the uncertainty expressed as an interval within which values of the quantity are expected to lie with a stated (coverage) probability.

There are established rules for the evaluation of uncertainty. The 'Guide to the expression of uncertainty in measurement' (GUM), published by the International organisation for Standardisation (ISO), is the primary document regarding uncertainty in measurement. The United Kingdom Accreditation Service (UKAS) publishes the document 'M3003: The expression of uncertainty and confidence in measurement', based on the GUM, for accredited laboratories in the UK.

Other approaches to uncertainty evaluation, underpinned by Bayesian considerations, are under development, including the use of Monte Carlo methods. These are intended to be used for more general measurement problems than directly covered by the GUM. The approaches are to be described in Supplements to the GUM and other supporting documents.

## Application

NPL has a highly experienced team of technical experts in the area of uncertainty evaluation. We are part of a world-class physical metrology organisation, with experience and expertise in this field that is unique in the UK. Our team is playing a leading international role in promoting the GUM and extending the application of the GUM through the preparation of the supporting documents.

We offer a range of services including advice, consultancy and training in the areas of uncertainty evaluation, statistical analysis and modelling. We provide a free technical advice service and would be pleased to discuss any uncertainty evaluation problems or applications with you.

## Measurement Uncertainties research

### Propagation of Distributions

The propagation of distributions offers a more general capability than the law of propagation of uncertainty. It is relevant when the conditions for that law to apply do not hold or when there is doubt over whether they hold.

## Measurement Uncertainties sectors and applications

### Football, Doping and Uncertainties

Doping tests in sport are commonplace today. Some recent 'nandrolone' cases in football involved high-profile international players who were tested 'positive' after UEFA Cup and Serie A matches. The outcomes of investigations into doping depend on the presence and (if a threshold is given) on the maximum concentration of a substance. Such thresholds are given if the substance may be present in the body for reasons other than the abuse of drugs.

## Measurement Uncertainties collaboration

• ### Committees

We contribute to standards activities undertaken by six organisations.
• ### Interlaboratory Comparisons

Having confidence in measurement results requires a quantitative statement of the quality of the results, with such a statement taking the form of measurement uncertainties associated with the results.

## A Monte Carlo Method for Evaluating Measurement Uncertainty

NPL is looking at the need for a new one-day training course on using a Monte Carlo method for evaluating measurement uncertainty.