Traceability and Uncertainty in Chemical and Physical Measurement

by Alex William,
Eurachem Working Group on Measurement Uncertainty


Establishment of the traceability and the evaluation of the uncertainty of the result of a measurement are essential in order to establish its comparability and fitness for purpose. There are both similarities and differences in the way that the concepts of traceability and uncertainty have been utilised in physical and chemical measurement. CIPM have only in the last decade set up programs in chemical metrology similar to those that have been in existence for physical metrology for over a century. However, analytical chemists over that same period have also developed techniques, based on the concepts of traceability and uncertainty, to ensure that their results are comparable and fit for purpose.

This paper contrasts these developments in physical and chemical metrology and identifies areas where these two disciplines can learn from each other.


Traceability and uncertainty are fundamental properties of all measurements. Although it is only recently that they have been given a high profile as part of quality assurance and accreditation, their importance has always been recognised by the measurement community. Indeed they were recognised by Galileo, the founder of experimental science. In his famous experiments to study the motion of a ball down an inclined plane, he developed a scale for his measurements of time utilising a water clock. The clock was based on weighing the amount of water flowing out of a large vessel. This enabled him to establish a stable reference for his time measurements and to show that the distance travelled by the ball was proportional to the square of the time. Without this stable reference he would not have been able to establish this relationship.

All measurements are made relative to some scale or standard and are therefore traceable to this scale or standard. The uncertainty on the result will be the uncertainty on the realisation of the scale or standard and the uncertainty on making measurements relative to that scale. The concepts of uncertainty and traceability have developed in different ways in physics and chemistry, leading until recently to quite different approaches to measurements in these two disciplines, but now a convergence of approach is emerging.

First I would like to discuss the developments in the concepts of traceability and then in uncertainty in these two areas and show how lessons can be learnt from both that are leading to a common approach.


The object of traceability is to enable comparability of measurement results. This is not just in order to be able to compare results of the measurements on the same sample but also to compare results on different samples to see whether the value of the quantity being measured is larger in one sample than the other. To achieve this, common reference scales must be used in both measurements.

The importance of using common reference scales has been recognised for centuries. For example, in England, King John introduced 'consistent measures throughout the land' in 1215. Other countries also had their own measurements scales standards. Many city museums show the standard measures used for trade within the city or local state. As trade widened so did the need for comparability of measurement results and the use of common units widened. The many different measurement scales were harmonised with the introduction of the metric system and the SI units under the Convention of the Metre, signed in 1875. An excellent summary of the historical development of units of measurement is given in the NBS Special Publication 420 (1). Under the Convention of the Metre an hierarchical chain of national and international measurement standards has been developed for the a measurement of most of physical quantities.

Chemical analytical measurements were to a large extent left out of these developments. The vast number of chemical compounds and sample matrices made it very difficult to establish an hierarchical system of standards similar to those used in physical metrology. As in physical metrology, comparability of results was only achieved locally. For example in the UK the local control laboratories achieved agreement with each other and with the referee laboratory, the LGC, by the development and use of common methods of analysis.

International comparability was also achieved in certain trade sectors again by use of common methods, for example use of AOAC official methods in the food sector. The suitability of the method was checked by means of a collaborative study, which provided parameters that described the spread in results that might be expected from laboratories using this method and gave direct evidence of the comparability of the results. This meant that, in general, comparability was only possible between results obtained using the same method. This comparability could be extended if suitable reference materials were available and in the (rare) case where the value of reference material was itself traceable to SI, then a system of traceability similar to that for physical measurements could be established.


It is both fortunate and unfortunate that both the repeatability and reproducibility of measurement results follow fairly closely the Normal or Gaussian distribution. Fortunate in that a vast number of statistical methods for analysing data have been developed based on the properties of the Normal distribution. But unfortunate, in that has led to the concentration both on the use of the term error and on the errors arising from random effects.

This has led to confusion between error and uncertainty and some neglect of the uncertainty arising from systematic effects. This has meant that, for many years, there has been confusion in the use of the terminology and an over emphasis on the uncertainty arising from random effects. For example, at the National Physical Laboratory in the UK in the early 1970s, there was an inconsistency on how the accuracy of results was reported on the measurement certificates. In the Radioactivity Section where I worked the measurement certificates stated 'the accuracy of the result is not claimed to be better than +/- 3 percent'. A quite misleading statement since in fact nothing is claimed about the actual accuracy.

Faced with the situation, I was tasked with some colleagues to produce a guide on the statement of accuracy. This guide (2) was published in 1973 and recommended the use of the terms 'random uncertainty' and 'systematic uncertainty' to describe the uncertainty arising from random and systematic effects respectively. The guide recommended stating the 'random uncertainty' and the 'systematic uncertainty' separately, since at that time there was no agreed way of combining them. The discussion during the preparation of this guide highlighted the problems that had arisen due to the confusion between the terms error and uncertainty. It was mistakenly claimed by some that random uncertainty on result of one measurement became a systematic uncertainty when that result was used in subsequent measurements. This was clear confusion between the terms 'random error' and 'random uncertainty' and a misinterpretation of the term 'systematic uncertainty'.

In 1980 the BIPM published its own recommendations (3), based on some proposals made by Dr Muller. These recommendations formed the basis for the ISO Guide to the expression of uncertainty in measurement (3) with which we are now all familiar. These discussions on uncertainty took place mainly between the national measurement institutes and associated calibration laboratories. To a large extent most testing and analytical laboratories were unaware of these developments. In addition although the general principles for evaluating uncertainty set out in the ISO guide can be applied to chemical measurements, the examples and to a certain extent the detailed methodology are based on the hierarchical system of standards. This has meant that extra guidance on the evaluation of uncertainty in analytical measurements has had to be developed, which takes into account the way in which comparability is achieved in analytical chemistry and utilises the data obtained from method validation and collaborative studies. This guidance is given in the revised EURACHEM guide Quantifying Uncertainty in Analytical Measurement (4).

What Lessons Can Be Learnt?

At first sight, the physical system would appear to have significant advantages. The traceability is achieved by comparison with an hierarchical chain of standards each having its own stated uncertainty. This complies with the requirements for traceability set out in ISO 17025 where the emphasis is on providing traceable calibrations for the measuring equipment. However this approach overlooks one important point, it does not take into account any difference in response of the measurement system to the standard and the sample being measured. These differences can often be a major, if not the largest, source of uncertainty and weakest link in the traceability chain.

For example, in the case of DC resistance measurements, leakage currents can introduce errors that are large compared to the uncertainty on the calibration of the measuring equipment. Similarly, inter-lead capacitance can affect the results of AC impedance measurements. There are several effects in other areas of metrology, for example the effect of the force on the measuring probe when making the mechanical measurements of length or of phase shifts when making optical measurements. Although these effects may be small they nevertheless can be significant compared with the claimed uncertainty.

In chemical analysis the difference in response of the measurement system to a reference material standard of the sample can be very large. Indeed, in many cases it can be impossible to evaluate. To overcome this, standard methods are developed and validated, often by means of collaborative studies and in many cases the performance of the laboratory is checked by participation in proficiency testing schemes. In addition, although the traceability of results is only to the defined method used, the uncertainty on the result can be based on experimental data obtained from validation and collaboration studies. However comparability is often limited to results obtained using the same method.

In contrast, methods used in physical metrology are very rarely subject to collaborative study. Neither are the results of the more routine measurements intercompared (the exception being intercomparisons carried out at the highest level by BIPM). The present program of key intercomparisons will provide data on the agreement between national standards. However this will not be sufficient to ensure comparability of results of routine measurements without some further work to demonstrate that traceability to these standards has been established taking into account any differences between the properties of the standards and the sample being measured. In addition, in physical measurements, the uncertainty is not usually evaluated from an experimental study of the method but relies on identifying and evaluating the individual uncertainty components. This means that there is a danger of overlooking a component, particularly one arising from the properties of the sample being measured.

Thus physical measurements would benefit from obtaining direct evidence of comparability by carrying out at least some collaborative studies to check that any differences between the response of their measurement system to the sample of the standard have been correctly accounted for. Proficiency testing schemes could also be more widely utilised. At the present moment, undue reliance is placed on the effectiveness of the use of calibrated instruments.

For chemical analysis, the need is to develop a hierarchical system. A start on this has been made by CIPM, utilising primary methods of analysis. It is envisaged that these primary methods will be used to provide suitable reference materials for using more routine analysis. This will provide a means of achieving traceability to SI. However, only a limited range of reference materials will be available and it will still be necessary to determine the difference in response of the measurement system to these reference materials and the samples being analysed. Work on this is already being carried out in a number of institutes and we are seeing the convergence of approach between physical and chemical measurements.


  1. NHS Special Publication 420,
    The International Bureau of Weights and Measures
    1875 To 1975 Burns.
  2. P. J. Campion, J. E. A. Williams.
    A code of practice for the detailed statement of accuracy. National Physical Laboratory, HMSO. 1973.
  3. Guide to the Expression of Uncertainty in Measurement, ISO 1993.
  4. EURACHEM/CITAC guide,
    Quantifying Uncertainty in Analytical Measurement. Second edition.