Appendix - Example A6: The Determination of Crude Fibre in Animal Feeding Stuffs


The determination of crude fibre by a regulatory standard method.

Measurement Procedure
The measurement procedure is a standardised procedure involving the general steps outlined in figure a6.1. These are repeated for a blank sample to obtain a blank correction

The fibre content as a percentage of the sample by weight, Cfibre, is given by:


a is the mass (g) of the sample. (Approximately 1 g)
b is the loss of mass (g) after ashing during the determination;
c is the loss of mass (g) after ashing during the blank test.

Identification of Uncertainty Sources
A full cause and effect diagram is provided as figure A6.9.

Quantification of Uncertainty Components
Laboratory experiments showed that the method was performing in house in a manner that fully justified adoption of collaborative study reproducibility data. No other contributions were significant in general. At low levels it was necessary to add an allowance for the specific drying procedure used. Typical resulting uncertainty estimates are tabulated below (as standard uncertainties) (table A6.1).

Table A6.1: Combined Standard Uncertainties

Fibre content (%w/w) Standard uncertainty u(Cfibre) (%w/w) Relative standard uncertainty u(Cfibre) / Cfibre
2.5 0.12
5 0.4 0.08
10 0.6 0.06

Example A6: The Determination of Crude Fibre in Animal Feeding Stuffs: Detailed Discussion

A6.1 Introduction

Crude fibre is defined in the method scope as the amount of fat-free organic substances which are insoluble in acid and alkaline media. The procedure is standardised and its results used directly. Changes in the procedure change the measurand; this is accordingly an example of an empirical method.

Collaborative trial data (repeatability and reproducibility) were available for this statutory method. The precision experiments described were planned as part of the in-house evaluation of the method performance. There is no suitable reference material (i.e. certified by the same method) available for this method.

A6.2 Step 1: Specification

The specification of the measurand for more extensive analytical methods is best done by a comprehensive description of the different stages of the analytical method and by providing the equation of the measurand.

A6.2.1 Procedure

The procedure, a complex digestion, filtration, drying, ashing and weighing procedure, which is also repeated for a blank crucible, is summarised in figure A6.2. The aim is to digest most components, leaving behind all the undigested material. The organic material is ashed, leaving an inorganic residue. The difference between the dry organic/inorganic residue weight and the ashed residue weight is the "fibre content". The main stages are:

  1. Grind the sample to pass through a 1mm sieve
  2. Weigh 1g of the sample into a weighed crucible
  3. Add a set of acid digestion reagents at stated concentrations and volumes. Boil for a stated, standardised time, filter and wash the residue.
  4. Add standard alkali digestion reagents and boil for the required time, filter, wash and rinse with acetone.
  5. Dry to constant weight at a standardised temperature ("constant weight" is not defined within the published method; nor are other drying conditions such as air circulation or dispersion of the residue).
  6. Record the dry residue weight.
  7. Ash at a stated temperature to "constant weight" (in practice realised by ashing for a set time decided after in house studies).
  8. Weigh the ashed residue and calculate the fibre content by difference, after subtracting the residue weight found for the blank crucible.

Figure A6.2: Flow diagram illustrating the stages in the regulatory method for the determination of fibre in animal feeding stuffs


The fibre content as a percentage of the sample by weight, Cfibre, is given by:

Cfibre =


is the mass (g) of the sample. Approximately 1 g of sample is taken for analysis.
b is the loss of mass (g) after ashing during the determination.
c is the loss of mass (g) after ashing during the blank test.

A6.3 Step 2: Identifying and Analysing Uncertainty Sources

A range of sources of uncertainty was identified. These are shown in the cause and effect diagram for the method (figure A6.9 more...). This diagram was simplified to remove duplication following the procedures in appendix d; this, together with removal of insignificant components, leads to the simplified cause and effect diagram in figure A6.10 more...

Since prior collaborative and in-house study data were available for the method, the use of these data is closely related to the evaluation of different contributions to uncertainty and is accordingly discussed further below.

A6.4 Step 3: Quantifying Uncertainty Components

Collaborative Trial Results

The method has been the subject of a collaborative trial. Five different feeding stuffs representing typical fibre and fat concentrations were analysed in the trial. Participants in the trial carried out all stages of the method, including grinding of the samples. The repeatability and reproducibility estimates obtained from the trial are presented in table A6.2.

Table A6.2: Summary of results from collaborative trial of the method and in-house repeatability check

  Fibre content (% w/w)
Sample Collaborative trial results In-house repeatability standard deviation
Mean Reproducibility standard deviation (sR) Repeatability standard deviation (sr)
A 2.3 0.293 0.198 0.193
B 12.1 0.563 0.358 0.312
C 5.4 0.390 0.264 0.259
D 3.4 0.347 0.232 0.213
E 10.1 0.575 0.391 0.327

As part of the in-house evaluation of the method, experiments were planned to evaluate the repeatability (within batch precision) for feeding stuffs with fibre concentrations similar to those of the samples analysed in the collaborative trial. The results are summarised in table a6.2. Each estimate of in-house repeatability is based on 5 replicates.

The estimates of repeatability obtained in-house were comparable to those obtained from the collaborative trial. This indicates that the method precision in this particular laboratory is similar to that of the laboratories which took part in the collaborative trial. It is therefore acceptable to use the reproducibility standard deviation from the collaborative trial in the uncertainty budget for the method. To complete the uncertainty budget we need to consider whether there are any other effects not covered by the collaborative trial which need to be addressed. The collaborative trial covered different sample matrices and the pre-treatment of samples, as the participants were supplied with samples which required grinding prior to analysis. The uncertainties associated with matrix effects and sample pre-treatment do not therefore require any additional consideration. Other parameters which affect the result relate to the extraction and drying conditions used in the method. These were investigated separately to ensure the laboratory bias was under control (i.e., small compared to the reproducibility standard deviation). The parameters considered are discussed below.

Loss of Mass on Ashing

As there is no appropriate reference material for this method, in-house bias has to be assessed by considering the uncertainties associated with individual stages of the method. Several factors will contribute to the uncertainty associated with the loss of mass after ashing:

  • Acid concentration;
  • Alkali concentration;
  • Acid digestion time;
  • Alkali digestion time;
  • Drying temperature and time;
  • Ashing temperature and time.

Reagent Concentrations and Digestion Times

The effects of acid concentration, alkali concentration, acid digestion time and alkali digestion time have been studied in previously published papers. In these studies, the effect of changes in the parameter on the result of the analysis was evaluated. For each parameter the sensitivity coefficient (i.e., the rate of change in the final result with changes in the parameter) and the uncertainty in the parameter were calculated.

The uncertainties given in table A6.3 are small compared to the reproducibility figures presented in table a6.2. For example, the reproducibility standard deviation for a sample containing 2.3 % w/w fibre is 0.293 % w/w. The uncertainty associated with variations in the acid digestion time is estimated as 0.021 % w/w (i.e., 2.3 x 0.009). We can therefore safely neglect the uncertainties associated with variations in these method parameters.

Table A6.3: Uncertainties associated with method parameters

Parameter Sensitivity coefficient Note 1 Uncertainty in parameter Uncertainty in final result as RSD Note 4
Acid concentration 0.23 (mol l-1)-1 0.0013 mol l-1 Note 2 0.00030
Alkali concentration 0.21 (mol l-1)-1 0.0013 mol l-1 Note 2 0.00048
Acid digestion time 0.0031 min-1 2.89 mins Note 3 0.0090
Alkali digestion time 0.0025 min-1 2.89 mins Note 3 0.0072


  1. The sensitivity coefficients were estimated by plotting the normalised change in fibre content against reagent strength or digestion time. Linear regression was then used to calculate the rate of change of the result of the analysis with changes in the parameter.
  2. The standard uncertainties in the concentrations of the acid and alkali solutions were calculated from estimates of the precision and trueness of the volumetric glassware used in their preparation, temperature effects etc. See examples A1-A3 for further examples of calculating uncertainties for the concentrations of solutions.
  3. The method specifies a digestion time of 30 minutes. The digestion time is controlled to within ±5 minutes. This is a rectangular distribution which is converted to a standard uncertainty by dividing by .
  4. The uncertainty in the final result, as a relative standard deviation, is calculated by multiplying the sensitivity coefficient by the uncertainty in the parameter.

Drying Temperature and Time

No prior data were available. The method states that the sample should be dried at 130°C to "constant weight". In this case the sample is dried for 3 hours at 130°C and then weighed. It is then dried for a further hour and re-weighed. Constant weight is defined in this laboratory as a change of less than 2 mg between successive weighings. In an in-house study, replicate samples of four feeding stuffs were dried at 110, 130 and 150°C and weighed after 3 and 4 hours drying time. In the majority of cases, the weight change between 3 and 4 hours was less than 2 mg. This was therefore taken as the worst case estimate of the uncertainty in the weight change on drying. The range ±2 mg describes a rectangular distribution, which is converted to a standard uncertainty by dividing by . The uncertainty in the weight recorded after drying to constant weight is therefore 0.00115 g. The method specifies a sample weight of 1 g. For a 1 g sample, the uncertainty in drying to constant weight corresponds to a standard uncertainty of 0.115 % w/w in the fibre content. This source of uncertainty is independent of the fibre content of the sample. There will therefore be a fixed contribution of 0.115 % w/w to the uncertainty budget for each sample, regardless of the concentration of fibre in the sample. At all fibre concentrations, this uncertainty is smaller than the reproducibility standard deviation, and for all but the lowest fibre concentrations is less than 1/3 of the sR value. Again, this source of uncertainty can usually be neglected. However for low fibre concentrations, this uncertainty is more than 1/3 of the sR value so an additional term should be included in the uncertainty budget (see table a6.4).

Table A6.4: Combined Standard Uncertainties

Fibre content
Standard uncertainty u(Cfibre) (%w/w) Relative standard uncertainty
u(Cfibre) / Cfibre
2.5 0.12
5 0.4 0.08
10 0.6 0.06

Ashing Temperature and Time

The method requires the sample to be ashed at 475 to 500°C for at least 30 mins. A published study on the effect of ashing conditions involved determining fibre content at a number of different ashing temperature/time combinations, ranging from 450°C for 30 minutes to 650°C for 3 hours. No significant difference was observed between the fibre contents obtained under the different conditions. The effect on the final result of small variations in ashing temperature and time can therefore be assumed to be negligible.

Loss of Mass after Blank Ashing

No experimental data were available for this parameter. However, as discussed above, the effects of variations in this parameter are likely to be small.

A6.5 Step 4: Calculating the Combined Standard Uncertainty

This is an example of an empirical method for which collaborative trial data were available. The in-house repeatability was evaluated and found to be comparable to that predicted by the collaborative trial. It is therefore appropriate to use the sR values from the collaborative trial. The discussion presented in Step 3 leads to the conclusion that, with the exception of the effect of drying conditions at low fibre concentrations, the other sources of uncertainty identified are all small in comparison to sR. In cases such as this, the uncertainty estimate can be based on the reproducibility standard deviation, sR, obtained from the collaborative trial. For samples with a fibre content of 2.5 % w/w, an additional term has been included to take account of the uncertainty associated with the drying conditions.

Standard Uncertainty

Typical standard uncertainties for a range of fibre concentrations are given in the table a6.4.

Expanded Uncertainty

Typical expanded uncertainties are given in table A6.5 below. These were calculated using a coverage factor k of 2, which gives a level of confidence of approximately 95%.

Table A6.5: Expanded Uncertainties

Fibre content (%w/w) Expanded uncertainty U(Cfibre) (%w/w) Expanded uncertainty as CV(%)
2.5 0.62 25
5 0.8 16
10 0.12 12