# Measurement uncertainty - conformity assessment

### Introduction

Laboratories accredited according to ISO/IEC 17025 have to report uncertainties, "when the uncertainty affects compliance to a specification limit.

Therefore those who are responsible to supervise complaince to e.g. legal limits are more and more confronted with reported uncertainties. Thsi results in questions like:

**"Is 51 really significantly higher than 50?"**

Analysts are asked this or similar. The answer of course depends on the magnitude of the measurement uncertainty. How would the nswer look like, if we assume that the uncertainty range includes the limit?

Let us assume (for simplicity reasons) that the results are normally distributed. Then the estimated uncerztainty enables us to estimate the probability that the limit is exceeded. Then we could have the following situation:

from [1]

If we want to give a scientifically sound answer, we come to the following conclusion (see also [2]):

*"The probability that the 'true' value of the measurand in the sample is below the limit is estimated to be 68%,
the probability that it is higher to 32%"*

This statement generally will not satisfactory.

We need to have a clear procedure how to handle the measurement uncertainty in conformity assessment.

It is obvious that this should be demanded from those who are responsible for determining the specification limit. Unfortunately often those people are not familiar with uncertainty issues. Therefore they are advised to seek for assiatance by analytical experts [1].

### Possible procedures for the assessment

**Possibility 1:**

A(n upper) limit is exceeded, if the measurement result with its complete reported uncertainty range is above the limit.

(from [1])

This procedure involves the risk to take a wrong decision, i.e. a value is accepted that in fact is above the limit. In this case the superviser has to take this risk. It is obvious that this procedure normally should be used if with a high probability it has to be proven that somebody exceeded a limit (e.g. with its product or with waste water ingredients etc.) with a high probability. The burden of proof is on the superviser's side.

**Possibility 2:**

The limit is not exceeded, if the measurement is below the limit by more than the reported uncertainty.

(from [1])

Again we have a risk to take a wrong decision. A measurement result that in fact is below the limit might be judged as non-compliant. Now the risk is completely on the side of supervised. In many case the supervised has the burden to prove that the product is within the specification. In these cases this procedure is appropriate.

**Possibility 3:**

But there is also a middle course. In this case the masurement results indicates non-compliance, if the value itself is above the limit, no matter what the uncertainty is.

(from [1])

The risk to take a worng decision is shared.

### Magnitude of the measurement uncertainty

The risk to take a wrong decision is unavoidable. The question is, who has to take the risk and of course how big is the risk. We quantify the risk with the uncertainty. Therefore it is especially important to correctly estimate uncertainties. It is then in the interest of the one who has to take the risk to limit the risk and therefore to limit the allowed uncertainty. But of course the uncertainties have to be realistic. Nobody benefits from the report of unrealistic low uncertainties that cannot be realised.

It is also essential to clearly define the conditions for the estimation of uncertainties, especially the following aspects:

- the confidence level has to be defined and to be reported with the uncertainty. A 95% confidence level, i.e. an expanded uncertainty with a coverage factor 2, is generally used. The "true" value is then expected within the uncertainty range with a probability of 95%.
- when estimating the uncertainty the precision
*as well as*a possible bias have to be taken into account.

### Customers and measurement uncertainty

It is a problem to develop a reasonable understanding of measurement uncertainties in the laboratory. But it is ecen more difficult to explain thsi to customers. So customer education is needed

In Sweden a leaflet was developped to explain that. This leaflet is freely available from the EURACHEM website for all interested people [3].

It is very important that the measurement uncertainty is *not* intrepreted as a quality criterion for laboratories. Ith as rather to be
checked that the uncertainty reported by the laboratory is sufficient for the intended use of the measurement result.

**A rivalry of laboratories based on measurement uncertainties would tempt many laboratories to report unrealistic low uncertainties.
Therewith the intended use would be extremely endangered.**

### References:

[1] Koch, M.: Messunsicherheit und Grenzwerte. Vom Wasser **103**, 7-10 (2005)