TCVN-11018-2015-Animal-feeding-stuffs-cereals-milled-cereal-products

• Số hiệu: TCVN11018:2015
• Loại văn bản: Tiêu chuẩn Việt Nam
• Nơi ban hành: ***
• Người ký: ***
• Ngày ban hành: Năm 2015

1	45° line (ideal line with bias, = 0 and slope b = 1)	a	intercept
2	45° line displaced by bias,		bias
3	linear regression line with yref-intercept, a	yNIRS	near infrared spectroscopy predicted values
4	outliers	yref	reference value

NOTE The outliers have a strong influence on the calculation of the slope and should be removed if the results are to be used for adjustments.

Figure 1 — Scatter plot for a validation set, y_ref = f(a + by_NIRS)

6.3  The bias

Most of the time, a bias or systematic error is what is observed with NIR models. Bias can occur due to: new samples of a type not previously seen by the model, drift of the instrument, drift in wet chemistry, changes in the process, and changes in the sample preparation.

With the number of independent samples, n, the bias (or offset) is the mean difference, , and can be defined as:

                    (2)

where e_i is the residual as defined in Equation (1) or:

                                  (3)

Where:

...

...

...

  is the i^th predicted value obtained when applying the multivariate NIR model;

and

 is the mean of the predicted values;

 is the mean of the reference values.

The significance of the bias is checked by a t-test. The calculation of the bias confidence limits (BCLs), T_b, determines the limits for accepting or rejecting equation performance on the small set of samples chosen from the new population.

                     (4)

Where:

α  is the probability of making a type I error;

t  is the appropriate t-value for a test with degrees of freedom associated with SEP and the selected probability of a type I error (see Table 1);

...

...

...

s_SEP  is the standard error of prediction (see 6.5).

EXAMPLE With n = 20, and s_SEP = 1, the BCL_s are:

               (5)

This means that the bias tested with 20 samples must be higher than 48 % of the standard error of prediction to be considered as different from zero.

Table 1 – Values of the t-distribution with a probability, α = 0,05 = 5 %

n

t

n

t

...

...

...

t

n

t

5

2,57

11

2,20

17

2,11

...

...

...

2,01

6

2,45

12

2,18

18

2,10

75

1,99

...

...

...

2,36

13

2,16

19

2,09

100

1,98

8

2,31

...

...

...

2,14

20

2,09

200

1,97

9

2,26

15

2,13

...

...

...

2,04

500

1,96

10

2,23

16

2,12

40

2,02

...

...

...

1,96

NOTE The Excel1 function TINV can be used

6.4  Root mean square error of prediction (RMSEP)

The RMSEP, s_RMSEP, (C.3.6) is expressed mathematically as:

                      (6)

Where:

e_i  is the residual of the i^th sample;

n  is the number of independent samples.

This value can be compared with SEC (C.3.3) and SECV (C.3.4).

...

...

...

­­                   (7)

Where:

n  is the number of independent samples;

s_SEP  is the standard error of prediction (see 6.5);

 is the bias or systematic error.

There is no direct test for RMSEP. This is the reason for separating the systematic error, bias or and the random error,SEP or s_SEP.

6.5  Standard error of prediction (SEP)

The SEP, s_SEP, or the standard deviation of the residuals, which expresses the accuracy of routine NIR results corrected for the mean difference (bias) between routine NIR and reference method, can be calculated by using the following Equation:

                  (8)

...

...

...

n  is the number of independent samples;

e_i  is the residual of the i^th sample;

  is the bias or systematic error.

The SEP should be related to the SEC (C.3.3) or SECV (C.3.4) to check the validity of the calibration model for the selected validation set.

The unexplained error confidence limits (UECLs), T_UE, are calculated from an F-test (ratio of 2 variances) (see Reference [19] and Table 2).

Where:

s_SEC the standard error of calibration (C.3.3);

α  is the probability of making a type I error;

...

...

...

M = n_c - p - 1 is the denominator degrees of freedom associated with SEC (standard error of calibration);

In which:

n_c  is the number of calibration samples;

p  is the number of terms or PLS factors of the model.

NOTE 1  SEC can be replaced by SECV which is a better statistic than SEC; very often SEC is too optimistic, s_SECV > s_SEC.

EXAMPLE With n = 20, α = 0,05, M = 100 and s_SEC = 1.

T_UE = 1,30                     (10)

This means that, with 20 samples, a SEP can be accepted that is up to 30 % larger than the SEC.

NOTE 2  The Excel2) function FINV can be used.

...

...

...

Table 2 - F-values and square root of the F-values as a function of the degrees of freedom of the numerator associated with SEP and of the denominator associated with SEC

[see definitions under Equation (9)]

F_(α:v,M)

d

Degrees of freedom
(SEP)

Degrees of freedom
(SEC)

Degrees of freedom
(SEP)

Degrees of freedom
(SEC)

...

...

...

100

200

500

1 000

50

100

200

500

100

...

...

...

2,40

2,31

2,26

2,23

2,22

5

1,55

1,52

1,50

...

...

...

1,49

6

2,29

2,19

2,14

2,12

2,11

6

1,51

...

...

...

1,46

1,45

1,45

7

2,20

2,10

2,06

2,03

2,02

...

...

...

1,48

1,45

1,43

1,42

1,42

8

2,13

2,03

1,98

...

...

...

1,95

8

1,46

1,43

1,41

1,40

1,40

9

2,07

...

...

...

1,93

1,90

1,89

9

1,44

1,41

1,39

1,38

1,37

...

...

...

2,03

1,93

1,88

1,85

1,84

10

1,42

1,39

1,37

...

...

...

1,36

11

1,99

1,89

1,84

1,81

1,80

11

1,41

...

...

...

1,36

1,34

1,34

12

1,95

1,85

1,80

1,77

1,76

...

...

...

1,40

1,36

1,34

1,33

1,33

13

1,92

1,82

1,77

...

...

...

1,73

13

1,39

1,35

1,33

1,32

1,32

14

1,89

...

...

...

1,74

1,71

1,70

14

1,38

1,34

1,32

1,31

1,30

...

...

...

1,87

1,77

1,72

1,69

1,68

15

1,37

1,33

1,31

...

...

...

1,29

16

1,85

1,75

1,69

1,66

1,65

16

1,36

...

...

...

1,30

1,29

1,29

17

1,83

1,73

1,67

1,64

1,63

...

...

...

1,35

1,31

1,29

1,28

1,28

18

1,81

1,71

1,66

...

...

...

1,61

18

1,30

1,31

1,29

1,27

1,27

19

1,80

...

...

...

1,64

1,61

1,60

19

1,34

1,30

1,28

1,27

1,26

...

...

...

1,69

1,58

1,52

1,49

1,48

29

1,30

1,26

1,23

...

...

...

1,22

49

1,60

1,48

1,42

1,38

1,37

49

1,27

...

...

...

1,19

1,17

1,17

99

1,53

1,39

1,32

1,28

1,26

...

...

...

1,24

1,18

1,15

1,13

1,12

199

1,48

1,34

1,26

...

...

...

1,19

199

1,22

1,16

1,12

1,10

1,09

499

1,46

...

...

...

1,22

1,16

1,13

499

1,21

1,14

1,11

1,08

1,07

...

...

...

1,45

1,30

1,21

1,14

1,11

999

1,20

1,14

1,10

...

...

...

1,05

6.6  Slope

The slope, b, of the simple regression y = a +  is often reported in NIR publications.

Notice that the slope must be calculated with the reference values as the dependent variable and the predicted NIR values as the independent variable, if the calculated slope is intended to be used for adjustment of NIR results (like in the case of the inverse multivariate regression used to build the prediction model).

From the least squares fitting, the slope is calculated as:

                        (11)

Where:

 is the covariance between reference and predicted values;

  is the variance of the n predicted values.

...

...

...

a =  -                    (12)

Where:

 is the mean of the reference values;

b  is the slope.

As for the bias, a t-test can be calculated to check the hypothesis that b = 1

                (13)

Where:

n  is the number of independent samples;

  is the variance of the n predicted values;

...

...

...

                        (14)

In which:

n  is the number of independent samples,

a  is the intercept Equation (12),

b  is the slope Equation (11),

y_i  is the i^th reference value,

 is the i^th predicted value obtained when applying the multivariate NIR model.

(RSD is like the SEP when the predicted values are corrected for slope and intercept. Do not confuse bias and intercept — see also Figure 1.) The bias equals the intercept only when the slope is exactly one.

The slope, b, is considered as different from 1 when

...

...

...

t_obs  is the observed t-value, calculated according to Equation (13);

t_{(1 - α/2)}  is the t-value obtained from Table 1 for a probability of α = 0,05 (5 %).

Too narrow a range or an uneven distribution leads to inappropriate correction of the slope even when the SEP is correct. The slope can only be adjusted when the validation set covers a large part of the calibration range.

EXAMPLE For n = 20 samples with a residual standard deviation [Equation (14)] of 1, a standard deviation of the predicted values of  = 2 and a calculated slope of b = 1,2, the observed t_obs value is 1,7 and then the slope is not significantly different from 1 as the t-value (see Table 1) for n = 20 samples is 2,09. If the slope is 1,3, the t_obs value is 2,6 and then the slope is significantly different from 1.

7  Sampling

Sampling is not part of the method specified in this Standard. Recommended sampling procedures are given in TCVN 4325 (ISO 6497)^[5] and TCVN 9027 (ISO 24333)^[6].

It is important that the laboratory receive a truly representative sample which has not been damaged or changed during transport or storage.

8  Procedure

8.1  Preparation of test sample

...

...

...

Samples for routine measurements should be prepared in the same way as validation samples. It is necessary to apply standard conditions.

Before the analysis, the sample should be taken in such a way as to obtain a sample representative of the material to be analysed.

For specific procedures, see specific NIR standards.

8.2  Measurement

Follow the instructions of the instrument manufacturer or supplier.

The prepared sample should reach a temperature within the range included in the validation.

8.3  Evaluation of result

To be valid, routine results shall be within the range of the calibration model used.

Results obtained on samples detected as spectral outliers cannot be regarded as reliable.

...

...

...

9.1  Control sample

At least one control sample should be measured at least once per day to check instrument hardware stability and to detect any malfunction. Knowledge of the true concentration of the analyte in the control sample is not necessary. The sample material should be stable and, as far as possible, resemble the samples to be analysed. The parameter(s) measured should be stable and, as far as possible, identical to or at least biochemically close to the sample analyte. A sample is prepared as in 8.1 and stored in such a way as to maximize the storage life. These samples are normally stable for lengthy periods, but the stability should be tested in the actual cases. Control samples should be overlapped to secure uninterrupted control.

The recorded day-to-day variation should be plotted in control charts and investigated for significant patterns or trends.

9.2  Instrument diagnostics

For scanning spectrophotometers, the wavelength or wavenumber (see 4.1) accuracy and precision should be checked at least once a week or more frequently if recommended by the instrument manufacturer, and the results should be compared to specifications and requirements (4.1).

A similar check of the instrument noise shall be carried out weekly or at intervals recommended by the manufacturer.

9.3  Instruments in a network

If several instruments are used in a network, special attention has to be given to standardization of the instruments according to the manufacturer's recommendations.

10  Running performance check of calibration

...

...

...

The suitability of the calibration for the measurement of individual samples should be checked. The outlier measures used in the calibration development and validation can be applied, e.g. Mahalanobis distance and spectral residuals. In most instruments, this is done automatically.

If the sample does not pass the test, i.e. the sample does not fit into the population of the samples used for calibration and/or validation, it cannot be determined by the prediction model, unless the model is changed. Thus the outlier measures can be used to decide which samples should be selected for reference analysis and included in a calibration model update.

If the calibration model is found to be suitable for the measured sample, the spectrum is evaluated according to the validated calibration model.

NIR methods should be validated continuously against reference methods to secure steady optimal performance of calibrations and observance of accuracy. The frequency of checking the NIR method should be sufficient to ensure that the method is operating under steady control with respect to systematic and random deviations from the reference method. The frequency depends inter alia on the number of samples analysed per day and the rate of changes in sample population.

The running validation should be performed on samples selected randomly from the pool of analysed samples. It may be necessary to resort to some sampling strategy to ensure a balanced sample distribution over the entire calibration range, e.g. segmentation of concentration range and random selection of test samples within each segment or to ensure that samples with a commercially important range are covered.

The number of samples for the running validation should be sufficient for the statistics used to check the performance. For a solid validation, at least 20 samples are needed (to expect a normal distribution of variance). One can fill in the results of the independent validation set for starting the running validation. To continue about 5 to 10 samples every week is quite sufficient to monitor the performance properly. Using fewer samples, it is hard to take the right decision in case one of the results is outside the control limits.

10.2  Control charts using the difference between reference and NIR results

Results should be assessed by control charts, plotting running sample numbers on the abscissa and the difference between results obtained by reference and NIR methods on the ordinate; ± 2s_SEP (95 % probability) and ± 3 s_SEP (99,8 % probability) may be used as warning and action limits where the SEP has been obtained on a test set collected independently of calibration samples.

If the calibration and the reference laboratories are performing as they should, then only one point in 20 points should plot outside the warning limits and two points in 1 000 points outside the action limits.

...

...

...

The following rules used in combination have proved to be useful in detection of problems:

a) one point outside either action limit;

b) two out of three points in a row outside a warning limit;

c) nine points in a row on the same side of the zero line.

Additional control charts plotting other features of the running control (e.g. mean difference between NIR and reference results, see ISO 9622 [8]) and additional rules may be applied to strengthen decisions.

In the assessment of results, it should be remembered that SEP and measured differences between NIR and reference results also include the imprecision of reference results. This contribution can be neglected if the imprecision of reference results is reduced to less than one-third of the SEP (see Reference [19]).

To reduce the risk of false alarms, the control samples should be analysed independently (in different series) by both NIR spectrometry and reference methods to avoid the influence of day-to-day systematic differences in reference analyses, for example.

If the warning limits are often exceeded and the control chart only shows random fluctuations (as opposed to trends or systematic bias), the control limits may have been based on a SEP value that is too optimistic. An attempt to force the results within the limits by frequent adjustments of the calibration does not improve the situation in practice. The SEP should instead be re-evaluated using the latest results.

If the calibration equations after a period of stability begin to move out of control, the calibration should be updated. Before this is done, an evaluation should be made of whether the changes could be due to changes in reference analyses, unintended changes in measuring conditions (e.g. caused by a new operator), instrument drift or malfunction etc. In some cases, a simple adjustment of the constant term in the calibration equation may be sufficient (an example is shown in Figure B.6). In other cases it may be necessary to run a complete re-calibration procedure, where the complete or a part of the basic calibration set is expanded to include samples from the running validation, and perhaps additional samples selected for this purpose (an example is shown in Figure B.7).

...

...

...

Other control charts, e.g. using z-scores, may be used.

11  Precision and accuracy

11.1  Repeatability

The repeatability, i.e. the difference between two individual single test results, obtained with the same method on identical test material in the same laboratory by the same operator using the same equipment within a short interval of time, which should not be exceeded in more than 5 % of cases, depends on the sample material, the analyte, sample and analyte variation ranges, method of sample presentation, instrument type, and the calibration strategy used. The repeatability should be determined in each case.

11.2  Reproducibility

The reproducibility, i.e. the difference between two individual single test results, obtained on identical test material by different laboratories and by different operators at different times, which should not be exceeded in more than 5 % of cases, depends on the sample material, the analyte, sample and analyte variation ranges, method of sample presentation, instrument type, and the calibration strategy used. The reproducibility should be determined in each case.

11.3   Accuracy

The accuracy, which includes uncertainty from systematic deviation from the true value on the individual sample (trueness) and uncertainty from random variation (precision), depends inter alia on the sample material, the analyte, sample and analyte variation ranges, method of sample presentation, instrument type, and the calibration strategy used. The accuracy should be determined in each case. The reported SEP and RMSEP values also include uncertainty of reference results which may vary from case to case.

12  Test report

...

...

...

a) all information necessary for complete identification of the sample;

b) the test method used, with reference to the relevant Standard;

c) all operating details not specified in this Standard or regarded as optional, together with details of any incidents which may have influenced the test results;

d) the test result(s) obtained;

e) the current SEP and bias, estimated from running a performance test on at least 20 test samples (see Article 10).

Annex A

(informative)

Guidelines for specific NIR standards

...

...

...

These standards should follow the ISO format and give specific information regarding:

a) type of samples and constituents or parameters determined followed by “near infrared spectrometry” and the calibration model(s) used in the title and the scope;

b) calibration model, preferably in the form of a table, including number of samples, range s_SEP validation set and RSQ for each parameter (examples are given in Tables A.1 and A.2);

c) the reference methods used for the validation under “normative references”;

d) the spectroscopic principle (e.g. NIR, NIT) and calibration principle (e.g. PLS, ANN);

e) the procedure(s) including preparation of the test sample(s), measurement and quality control;

f) precision data as determined by an interlaboratory test according to TCVN 6910-2 (ISO 5725-2)^[22].

Table A.1 - Calibration set

Component

...

...

...

Number of samples, N

Minimum content, % mass fraction

Maximum content, % mass fraction

Fat

As is

7 401

0,3

18,5

Moisture

...

...

...

17 799

0,8

18,0

Protein

As is

17 165

6,0

74,1

Fibre

...

...

...

2 892

0,2

26,8

Starch

As is

1 140

3,0

62,1

Table A.2 – Validation set

...

...

...

Model

Number of samples, N

Accuracy,
s_SEP

Minimum content, % mass fraction

Maximum content, % mass fraction

RSQ (C.3.9)

Fat

ANN

183

...

...

...

2,8

12,9

0,94

Moisture

ANN

183

0,47

9,2

12,3

...

...

...

Protein

ANN

179

0,72

11,0

29,1

0,96

Fibre

ANN

...

...

...

1,11

0,5

18,0

0,90

Starch

PLS

113

1,80

7,8

...

...

...

0,92

Annex B

(informative)

Examples of figures

KEY

1

± 3s limits, where s is standard deviation

...

...

...

reference values

2

45° line (ideal line with slope, b = 1 and bias,  = 0)

y_NIRS

near infrared predicted values

3

regression line

...

...

...

Figure B.1 - Example: No outliers

KEY

1

series 1, indicating a spectral outlier

5

series 5

2

series 2

...

...

...

series 6

3

series 3

y

absorbance

4

series 4

λ

wavelength

...

...

...

KEY

1          outlier

Figure B.3 — Principal component analysis score plot with an x-outlier

KEY

1  outlier

y_ref  reference values

y_NIRS  near infrared predicted values

...

...

...

Figure B.4 - Scatter plot with a y-outlier

KEY

1

± 3s limits

4

outlier

2

45° line

...

...

...

reference values

3

regression line                   

y_NIRS

near infrared predicted values

Figure B.5 - Example determination of ADF in forages with a y-outlier

KEY

1  upper action limit (UAL, +3 s_SEP)

...

...

...

3  lower warning limit (LWL, -2 s_SEP)

4  lower action limit (LAL, -3 s_SEP)

n  run number

y_ref  reference values

y_NIRS  near infrared predicted values

No points are outside the UAL or the LAL. However, nine points in a row (e.g. 14 to 22) are on the same side of the zero line. That indicates a bias problem. Two points (27 and 28) out of three points are outside the LWL but none are outside the UWL. This also indicates a bias problem. No increase in random variation is observed. The spread is still less than 3 s_SEP.

In conclusion, the calibration should be bias adjusted.

Figure B.6 - Example: Control chart for determination of fat content,
as a percentage mass fraction, in cereals

...

...

...

1  upper action limit (UAL, +3 s_SEP)

2  upper warning limit (UWL, +2 s_SEP)

3  lower warning limit (LWL, -2 s_SEP)

4  lower action limit (LAL, -3 s_SEP)

n  run number

y_ref  reference values

y_NIRS  near infrared predicted values

Viewing the first 34 points, one point is outside the UAL. This indicates a serious problem. Two points (22 and 23) out of three points are outside the UWL. Two separate points are also outside the LWL. The spread is uniform around the zero line (the nine points rule is obeyed) but five out of 34 points are outside the 95 % confidence limits (UWL, LWL) and one out of 34 points is outside the 99,9 % confidence limits (UAL, LAL). This is much more than expected.

One reason for this picture could be that the SEP value behind the calculation of the limits is too optimistic. This means the limits should be widened. Another reason could be that the actual samples are somewhat different from the calibration samples. To test this possibility, the calibration set was extended to include the control samples and a new calibration was developed. The performance of this calibration was clearly better, as shown by the control samples numbers 35 to 62.

...

...

...

Annex C

(informative)

Supplementary terms and definitions

C.1   General

C.1.1

Reference method

Validated method of analysis internationally recognized by experts or by agreement between parties.

NOTE 1    A reference method gives the “true value” or “assigned value” of the quantity of the measurand.

...

...

...

C.1.2

Indirect method

Method that measures properties that are functionally related to the parameter(s) to be determined and whose obtained signal is related to the “true” value(s) as determined by the reference method(s).

C.1.3

Near infrared spectroscopy

NIRS

Measurement of the intensity of the absorption of near-infrared light by a sample within the range 770 nm to 2 500 nm (12 900 cm^-1 to 4 000 cm^-1).

NOTE   NIRS instruments use either part of, the whole, or ranges that include this region (e.g. 400 nm to 2 500 nm). Multivariate calibration techniques are then used to relate a combination of absorbance values either to composition or to some property of the samples.

C.1.4

...

...

...

NIR

Type of near infrared spectroscopy where the basic measurement is the absorption of near-infrared light diffusely reflected back from the surface of a sample collected by a detector in front of the sample.

C.1.5

Near infrared transmittance

NIT

Type of near infrared spectroscopy where the basic measurement is the absorption of near-infrared light that has travelled through a sample and is then collected by a detector behind the sample.

C.1.6

NIRS network

Number of near infrared instruments, operated using the same calibration models, which are usually standardized so that the differences in predicted values for a set of standard samples are minimized.

...

...

...

Standardization of an instrument

Process whereby a group of near infrared instruments are adjusted so that they predict similar values when operating the same calibration model on the same sample(s).

NOTE A number of techniques can be used but these can be broadly defined as either pre-prediction methods where the spectra of samples are adjusted to minimize the differences between the response of a “master” instrument and each instrument in the group and “post-prediction” methods where linear regression is used to adjust the predicted values produced by each instrument to make them as similar as possible to those from a “master” instrument.

C.1.8

z-score

Performance criterion calculated by dividing the difference between the near infrared predicted result and the true or assigned value by a target value for the standard deviation, usually the standard deviation for proficiency assessment.

NOTE   This is a standardized measure of laboratory bias, calculated using the assigned value and the standard deviation for proficiency assessment. 

C.2  Calibration techniques

C.2.1

...

...

...

PCA

Form of data compression, which for a set of samples works solely with the x (spectral) data and finds principal components (factors) according to a rule that says that each PC expresses the maximum variation in the data at any time and is uncorrelated with any other PC.

NOTE The first PC expresses as much as possible of the variability in the original data.  Its effect is then subtracted from the x data and a new PC derived again expressing as much as possible of the variability in the remaining data. It is possible to derive as many PCs as there are either data points in the spectrum or samples in the data set, but the major effects in spectra can be shown to be concentrated in the first few PCs and therefore the number of data that need to be considered is dramatically reduced.

PCA produces two new sets of variables at each stage: PC scores represent the response of each sample on each PC; PC loadings represent the relative importance of each data point in the original spectra to the PC.

PCA has many uses, e.g. in spectral interpretation, but is most widely used in the identification of spectral outliers.

C.2.2

Principal component regression

PCR

Technique which uses the scores on each principal component as regressors in a multiple linear regression against values representing the composition of samples.

...

...

...

When used in NIRS, the regression coefficients in PC space are usually converted back to a prediction model using all the data points in wavelength space.

C.2.3

Partial least squares regression

PLS

Form of data compression which uses a rule to derive the factors consisting of allowing each factor in turn to maximize the covariance between the y data and all possible linear combinations of the x data.

NOTE: PLS is a balance between variance and correlation with each factor being influenced by both effects. PLS factors are therefore more directly related to variability in y values than are principal components. PLS produces three new variables, loading weights (which are not orthogonal to each other), loadings, and scores which are both orthogonal.

PLS models are produced by regressing PLS scores against y values. As with PCR, when used in NIRS, the regression coefficients in PLS space are usually converted back to a prediction model using all the data points in wavelength space.

C.2.4

Multiple linear regression

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Technique using a combination of several X variables to predict a single y variable.

NOTE: In NIRS, the X values are either absorbance values at selected wavelengths in the NIR or derived variables such as PCA or PLS scores.

C.2.5

Artificial neural network

ANN

Non-linear modeling technique loosely based on the architecture of biological neural systems.

NOTE: The network is initially “trained” by supplying a data set with several x (spectral or derived variables such as PCA scores) values and reference y values. During the training process, the architecture of the network may be modified and the neurons assigned weighting coefficients for both inputs and outputs to produce the best possible predictions of the parameter values.

Neural networks require a lot of data in training.

C.2.6

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Any model where a number of x values are used to predict one or more y variables.

C.2.7

Outlier

Member of a set of values which is inconsistent with the other members of that set. [ISO 5725-1: 1994^[21]. 3. 21]

NOTE: For NIRS data, outliers are points in any data set that can be shown statistically to have values that lie well outside an expected distribution. Outliers are normally classified as either x- (spectral) outliers or y- (reference data) outliers.

C.2.8

x-outlier

Outlier related to the NIR spectrum

NOTE: An x-outlier can arise from a spectrum with instrumental faults or from a sample type that is radically different from the other samples or in prediction, a sample type not included in the original calibration set.

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y-outlier

Outlier related to error in the reference data, e.g. an error in transcription or in the value obtained by the reference laboratory.

C.2.10

Leverage

Measure of how far a sample lies from the centre of the population space defined by a model.

NOTE: Samples with high leverage have high influence on the model. Leverage is calculated by measuring the distance between a projected point and the centre of the model.

C.2.11

Mahalanobis distance

Global h-value

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NOTE 1: Mahalanobis distance is a non linear measurement. In PC space, a set of samples usually form a curve shaped distribution. The ellipsoid that best represents the probability distribution of the set can be estimated by building the covariance matrix of the samples. The Mahalanobis distance is simply the distance of the test point from the centre of mass divided by the width of the ellipsoid in the direction of the test point.

NOTE 2 In some software, the Mahalanobis distance is referred to as the “global n-value” and outlier detection depends upon how many standard deviations of h a sample is from the centre.

C.2.12

Neighbourhood h

Distance in principal component space between a data point and its n nearest neighbours, which indicates whether a sample is isolated or in a well-populated part of the distribution.

C.2.13

Residual

Difference between an observed value of the response variable and the corresponding predicted value of the response variable. [ISO 3534-3:1999^[1^2^], 1.21]

NOTE: For NIRS data, a residual is the difference between a reference value and the value predicted by a regression model. Residuals are used in the calculation of regression statistics.

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Spectral residual

Residual after chemometric treatment (e.g. PCA, PLS) of a spectrum arising from spectral variation not described by the model.

C.2.15

Test set

When testing a regression model, any set of samples that excludes those used to develop the calibration.

C.2.16

Independent test set

Test set that consists of samples that are from a different geographical region, a new industrial plant or have been collected at a later time (e.g. from a different harvest) than those used to create and validate a regression model.

NOTE: These samples form a “true” test of a prediction model.

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Validation set

Samples used to validate or “prove” a calibration.

NOTE: The validation set usually contains samples having the same characteristics as those selected for calibration. Often alternate or n^th samples (ranked in order of the constituent of interest) are allocated to the calibration and validation data sets from the same pool of samples.

C.2.18

Monitoring set

Set of samples that is used for the routine control of calibration models.

C.2.19

Cross-validation

Method of generating prediction statistics where, repeatedly, a subset of samples are removed from a calibration population, a model being calculated on the remaining samples and residuals calculated on the validation subset; when this process has been run a number of times, calculation of prediction statistics on all the residuals.

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CAUTION:  There are disadvantages to the use of cross-validation. First, cross-validation statistics tend to be optimistic when compared with those for an independent test set. Second, if there is any duplication in the calibration data (e.g. the same sample scanned on several instruments or at different times) it is necessary to always assign all copies of the same sample to the same crossvalidation segment, otherwise very optimistic statistics are produced.

C.2.20

Overfitting

Addition of too many regression terms in a multiple linear regression.

NOTE: A result of overfitting, when samples not in the calibration set are predicted, is that statistics such as RMSEP or SEP are much poorer than expected.

C.2.21

Score plot

Plot where the score on one principal component (PC) or partial least squares (PLS) factor is plotted against that of another PC or PLS factor.

NOTE: Scores are most useful if sample ID or concentration values are used to identify each point in the plot. Patterns in the data can then be seen which are not obvious from the raw data.

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See also Article 6.

C.3.1

Bias

Difference between the mean reference value y and the mean value predicted by the NIR model y.

C.3.2

Bias confidence limit

BCL

h

Value greater than which a bias is significantly different from zero at the confidence level specified.

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C.3.3

Standard error of calibration

SEC

^sSEC

For a calibration model, an expression of the average difference between predicted and reference values for samples used to derive the model.

NOTE: As for definitions C.3.4 to C.3.7, in this statistic, this expression of the average difference refers to the square root of the sum of squared residual values divided by the number of values corrected for degrees of freedom, where 68 % of the errors are below this value.

C.3.4

Standard error of cross-validation

SECV

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For a calibration model, an expression of the bias-corrected average difference between predicted and reference values for the subset of samples selected as prediction samples during the cross-validation (C.2.19) process.

C.3.5

Standard error of prediction

Standard error of prediction corrected for the bias

SEP

SEP(C)

^sSEP

Expression of the bias-corrected average difference between predicted and reference values predicted by a regression model when applied to a set of samples not included in the derivation of the model.

NOTE: The SEP covers a confidence interval of 68 % (multiplied with 1,96 an interval of 95 %).

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Root mean square error of prediction

RMSEP

^sRMSEP

Expression of the average difference between reference values and those predicted by a regression model when applied to a set of samples not included in the derivation of the model.

NOTE: RMSEP includes any bias in the predictions.

C.3.7

Root mean square error of cross-validation

RMSECV

^sRMSECV

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NOTE: RMSECV includes any bias in the predictions.

C.3.8

Unexplained error confidence limit

UECL

T_UE

Limit which a validation SEP must exceed in order to be significantly different from the standard error of calibration at the confidence limit specified.

C.3.9

RSQ

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NOTE: When expressed as a percentage it represents the proportion of the variance explained by the regression model.

C.3.10

Slope

b

(regression line), representation of the amount y increases per increase in x.

C.3.11

Intercept

(regression line) value of y when x is zero

C.3.12

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Expression of the average size of the difference between reference and fitted values after a slope and intercept correction has been performed.

C.3.13

Covariance

Measure of how much two random variables vary together.

NOTE: If, for a population of samples, an increase in x is matched by an increase in y then the covariance between the two variables will be positive. If an increase in x is matched by a decrease in y then the covariance will be negative. When values are uncorrelated then the covariance is zero.

Bibliography

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[2] TCVN 4328-2 (ISO 5983-2) Animal feeding stuffs — Determination of nitrogen content and calculation of crude protein content — Part 2: Block digestion and steam distillation method

[3] TCVN 4331 (ISO 6492) Animal feeding stuffs — Determination of fat content

[4] TCVN 4326 (ISO 6496) Animal feeding stuffs — Determination of moisture and other volatile matter content

[5] TCVN 4325 (ISO 6497) Animal feeding stuffs — Sampling

[6] TCVN 4329 (ISO 6865) Animal feeding stuffs — Determination of crude fibre content — Method with intermediate filtration

[7] TCVN 7076 (ISO 8258) Shewhart control charts

[8] TCVN 6835 (ISO 9622) Whole milk — Determination of milkfat, protein and lactose content — Guidance on the operation of mid-infrared instruments

[9] TCVN 6555 (ISO 11085) Cereals, cereals-based products and animal feeding stuffs — Determination of crude fat and total fat content by the Randall extraction method

[10] TCVN 9589 (ISO 13906) Animal feeding stuffs — Determination of acid detergent fibre (ADF) and acid detergent lignin (ADL) contents

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[12] TCVN 8133-1 (ISO 16634-1) Food products — Determination of the total nitrogen content by combustion according to the Dumas principle and calculation of the crude protein content — Part 1: Oilseeds and animal feeding stuffs

[13] TCVN 8133-2 (ISO/TS 16634-2) Food products — Determination of the total nitrogen content by combustion according to the Dumas principle and calculation of the crude protein content — Part 2: Cereals, pulses and milled cereal products

[14] TCVN 8125 (ISO 20483) Cereals and pulses — Determination of the nitrogen content and calculation of the crude protein content — Kjeldahl method

[15] TCVN 9663 (ISO 21543) Milk products — Guidelines for the application of near infrared spectrometry

[16] TCVN 9027 (ISO 24333) Cereals and cereal products — Sampling

 [17] NÆS, T., ISAKSSON, T., FEARN, T., DAVIES, T. A user-friendly guide to multivariate calibration and classification. Chichester: NIR Publications, 2002. 344 p.

[18] SHENK, J.S., WESTERHAUS, M.O., ABRAMS, S.M. Protocol for NIRS calibration: Monitoring analysis results and recalibration. In: Marten, G.C., Shenk, J.S., Barton, F.E., editors. Near infrared reflectance spectroscopy (NIRS): Analysis of forage quality, pp. 104-110. Washington, DC: US Government Printing Office, 1989. (USDA ARS Handbook 643.)

[19] SØRENSEN, L.K. Use of routine analytical methods for controlling compliance of milk and milk products with compositional requirements. IDF Bull. 2004, (390), pp. 42-49

[20] ISO 3534-3:1999 Statistics - Vocabulary and symbols - Part 3: Design of experiments

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[22] TCVN 6910-2 (ISO 5725-2) Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method

[23] ISO 8196-1 Milk - Definition and evaluation of the overall accuracy of alternative methods of milk analysis - Part 1: Analytical attributes of alternative methods