Introduction and Overview
Under ISO 17025 (clause 5.4.6) laboratories are required to estimate the uncertainty of measurement in all tests. At present, however, testing laboratories are not required to report uncertainty except under the following circumstances.
The purist might well argue that a knowledge of the uncertainty is essential for the interpretation of any measurement but in practice accreditation bodies do not take this view. Hence reporting of uncertainty is only required at the client’s request. However it must be emphasised that the laboratory still has to carry out the estimation and assessors will need to see the result of this exercise.
The general approach to uncertainty of measurement requires the following steps.

Consider the method and identify any areas of uncertainty not covered by the intermediate precision study and quantify them. Typical examples of this type of uncertainty will be instrument calibrations, issues of purity of standards, uncertainty in concentration of calibration solutions and other references.
Textile and leather testing involve chemical measurements, physical measurements and measurement of relevant properties such as colour fastness. The uncertainty in chemical measurements is dealt with in detail in the part of this website dedicated to chemical testing [HL here]. Some examples of uncertainty estimates for other areas of textile and leather testing are shown below.
Weight Per Unit Area
Procedure Outline
Selfevidently this measurement will be subject to uncertainties resulting from the measurement of area and from weighing. The method, in outline, involves the following.
Intermediate Precision (Type A Uncertainty)
An intermediate precision exercise was carried out as part of method validation where a cloth of high homogeneity was subjected to the test 11 times using three different operators and spread over three weeks. In each case the same balance and ruler were used throughout. The result of this exercise returned a mean value of 372.346 g for the 25 cm square with a standard deviation of ±4.321 g. Expressed as a percentage this is 372.346± 1.605%.
This represents the uncertainty arising from the laboratory’s actual operations and is effectively the inhouse reproducibility for the method. It will largely derive from differences between operators and over time in measurement of the sample. There is not likely to be any significant similar operator effect derived from the weighings as the operation is simple and digital.
The same balance and ruler were used throughout the contributions. Hence the uncertainty in weighing with that balance and in the calibration of the ruler need, additionally, to be taken into account.
Weighing Uncertainty(Type B )
The uncertainty in a weighing is a combination of three contributions.
The uncertainty in weighing with this balance is calculated below.
Source of Uncertainty

Value (g)

Nature of Value

Distribution Type

Calculation to Provide Standard Uncertainty

Value of Standard Uncertainty (g)

Uncertainty in annual balance calibration.

±0.0003

95% confidence interval based on coverage factor of 2.

Normal

0.0003/2

0.00015

Uncertainty due to tolerance on daily check.

±0.001

Tolerance for drift

Rectangular

0.001/Ö 3

0.0005774

Uncertainty due to digital display resolution.

±0.0005

Tolerance created by limitations on display resolution.

Rectangular

0.0005/Ö 3

0.0002887

Combined Uncertainty (square root of 0.00015^{2} + 0.000577^{2} + 0.0002887^{2})

0.000662

This is the absolute uncertainty, in grams, of weighing with this balance. For the sample concerned, weight 372.346 g the percentage uncertainty is 0.000178%.
Area Uncertainty Due to Uncertainty in Ruler Calibration (Type B)
The measurement is done with a 30 cm ruler marked in millimetres. The quoted uncertainty of calibration, as a 95% confidence interval, is ±0.2 mm. The standard uncertainty will be ±0.1 mm assuming a normal distribution.
Expressed as a percentage of the 25 cm (250 mm) measurement this is ±0.04%.
In order to obtain an area two measurements are made so the 0.04% must be incorporated twice by taking the square root of the sum of the squares, i.e. square root of (0.04^{2} + 0.04^{2}) = ± 0.0566%. The uncertainties are combined in this way and not simply added as there is no reason to suppose they would both operate with the same sign.
We now have values for all of the contributions to uncertainty as percentages. Note that expression of the uncertainties in this relative fashion as opposed to as raw values is essential as we are now going to combine them to get an overall uncertainty. We cannot do this directly as we would then be combining cm and grams which is clearly absurd !
Combined Uncertainty
Source of Uncertainty

Value %

Type A uncertainty from intermediate precision

1.605

Uncertainty in weighing

0.000178

Uncertainty due to measurement of sample area

0.0566

Combined Uncertainty (square root of 1.605^{2} + 0.000178^{2} + 0.0566^{2})

1.606

Converted back into grams for the weighing of 372.346 g this means an absolute standard uncertainty of ±5.980 g for the 25 cm square. In terms of square meters the result is 5957.536 g per square meter with a standard uncertainty of 95.678 g per square meter. Applying a coverage factor of 2 we have a 95% confidence interval of ±191.356 g per square meter.
Note the following points.
