Shown here are additional references for Homogeneity:

Abstract:

International standard guidelines recognise that data from a precision experiment should be checked for outliers as a matter of routine before finalising the precision estimates. The reason is that results affected by uncontrolled variation in the analytical procedure occur at the rate of a few percent. In a precision experiment containing 20 or so results, even a single outlier can have deleterious effects on the precision estimates. Dedicated tests are recommended to identify which experimental unit has method replicates with unusually large deviation – the current preferred approach is Cochran's test described in ISO 5725-2:1994. Cochran's test can only detect a single experimental unit with unusually large replicates (that one with the maximum deviation between replicates), and so this test must be iterated after excluding the identified experimental unit to determine the presence of additional unusually large replicate deviations. An alternative approach is to use the model of the precision experiment directly to detect and identify outliers. This approach is traditionally called ‘model diagnostics’ or ‘residual analysis’. Model diagnostics is commonly prescribed as “a step” in data analysis in texts on linear regression and analysis of variance (ANOVA). This approach can simultaneously detect and identify multiple experimental units which exhibit unusually large deviation between method replicates. We illustrate this approach using data obtained from

a homogeneity study under a two-stage fully nested random effects ANOVA design conducted at the International Atomic Energy Agency (IAEA) in 2014 on a uranium bearing material. The measurands are elemental impurity concentrations relative to uranium determined by ICP-MS.

 

Highlights:

• The IAEA's standard procedure for purity analysis can only produce 8 determinations in a single analyst working day. To achieve the minimum required m = 10 samples, the samples in the study were analysed over the course of multiple days. Results within each day are subject to a unique instrument calibration and possible significant calibration uncertainty. This violates the required method repeatability conditions.
• The study adopted a two-stage fully nested random effects ANOVA in order to control for variability attributable to calibration.
• The model diagnostic approach addresses several shortcomings of Cochran's test:

1. The diagnostics approach appeals directly to the assumption that method replicates are Gaussian distributed (an assumption which is required by Cochran's test) and uses this assumption to identify anomalies.
2. Cochran's test can only test for ‘one anomaly at a time’, specifically that bottle with the largest difference, and must be iterated. In contrast the diagnostics approach can show simultaneously all bottles with unusually large within-bottle differences. Therefore, in a single application, the analyst can immediately learn how many experimental units and which ones are affected by unusually large differences between method replicates.
3. As Cochran's test necessarily assumes that the design is balanced (i.e. each bottle has the same number of replicates) both replicates from a bottle must be excluded to iterate Cochran's test. The diagnostic approach does not require this assumption and can be applied to unbalanced ANOVA models.

• Model diagnostics was applied to a homogeneity study for scandium and praseodymium in a high purity uranium material following four steps in the data analysis:

1. Initial data analysis by graphical inspection and initial ANOVA
2. Diagnostic analysis identifying anomalies and outliers.  Inspect for assignable cause and decide on removal.
3. Update ANOVA calculation and graphic after outlier removal.
4. Diagnostic analysis after outlier removal to justify final model fit.

Abstract:

During the stability monitoring of a certified reference material (CRM) solution in acetonitrile, a decreased concentration of one of the certified analytes in reference samples was detected in opposition to the value in normally stored samples. The reference temperature was chosen well below the storage temperature due to the common concept that any degradation or chemical reaction takes place at a slower rate at lower temperatures.

To investigate the cause of the lower concentration in the reference samples, chromatograms of the samples were compared, and the paper presents a possible explanation for the effect.

 

Highlights:

• It became obvious that a chemical reaction takes place at -70°C as indicated by additional peaks in the chromatograms of the reference samples.
• The certified analytes are DNPH-formaldehyde (DNPH: Dinitrophenylhydrazine) derivative, where one of those components showed the effect.
• The mixture of neat materials in acetonitrile presumably showed cryo-concentration in the reference samples stored at -70°C (matrix frozen) versus the real samples stored at -20°C (matrix liquid). The freezing point of acetonitrile is approximately -45°C.
• As a result, from those observations, it is recommended that care has to be taken when extrapolating stability results to conditions (e.g. lower temperature) that have never been tested.
• Especially with a phase transition involved, those unusual effects could happen, that are often not on someone`s radar.

Abstract:

The Joint Research Centre (JRC) was working on a feasibility study to develop biodiesel certified reference materials (CRMs) for parameters from EN 14214, a European standard for requirements and test methods for biodiesel. The candidate material (Rapeseed oil fatty methyl esters) was obtained from a commercial source. During the CRM preparation, care was taken to create a stable and homogeneous material, and extensive homogeneity testing is described in the publication. The ANOVA approach was applied for within and between ampoule standard deviations, and then the maximum heterogeneity u*bb calculated. To ensure the stability of the material, some stabilisation precautions were taken, and short term as well as long term stability studies conducted. To ensure the CRM is fit for purpose, the shelf life of each component was calculated for a target uncertainty similar to the method RSD.      

Highlights:

• The candidate material was bought from a commercial source with a certificate of analysis (CoA) indicating the suitability of the material.
• Part of the material was mixed with an anti-oxidant.
• Careful planning was conducted including the number of units needed, the type of material and the quantity per unit.
• The ampouling was done using suitable equipment.
• Upon quantifying the between ampoule heterogeneity, all parameters of interest were tested to detect unexpected problems, e.g. contamination during processing.
• Ampoules were selected by random stratified sampling over the whole batch, for homogeneity measurements under repeatability conditions. The order of measurement did not correspond to the filling sequence.
• The homogeneity testing dataset was screened for outliers using the Grubbs procedure and regression analysis was conducted to check for possible trends in the filling sequence. Also, the distribution of results was checked using normal probability plots and histograms.
• Depending on the behaviour of the different analytes, various approaches were taken to compute s_bb/u_bb.
• After calculation, u_bb was compared with RSD_{standard method} and RSDR_{standard method}.        
• For stability testing, an isochronous study with a reference temperature of -8°C was applied. Outliers were detected with a Grubbs test and the slope of the data points tested for significance with a t-test.
• The short-term study included a 60°C storage, where samples stored 1, 2, and 4 weeks were afterwards compared to samples from storage at 4°C and 18°C.
• The long-term study used ampoules drawn by stratified random sampling; storage intervals were 4, 8 and 12 months.
• The uncertainty of stability was calculated as uncertainty of the slope multiplied by shelf life (if no trend present).
• It was defined that "Dispatch conditions must be chosen so that uncertainty of stability during transportation is negligible".

Abstract:

The use of a replicated Latin square design for reference material homogeneity assessment is illustrated by application to a homogeneity study of eight high-purity organic materials certified for melting point. The design controlled for both a three-level location effect and a run effect. Variance components were extracted using mixed effects modelling using a restricted maximum likelihood method. An alternative classical ANOVA calculation is also given. Once a need for blocking and randomisation is admitted, the use of the replicated Latin square design adds little in

terms of operating complexity, and with current software, the analysis of the resulting data is straightforward. The effect of appreciable numerical rounding by the instrument software was investigated and shown to be acceptable for the particular example. Estimation of the scale of location and run effects showed that in this example the location effect was both statistically and practically significant, while the run effect was not statistically significant at the 95% level of confidence. The design allowed unbiased estimates of between-unit variances in the presence of both interfering effects.

 

Highlights:

• This approach for assessment of homogeneity was chosen, because the measurement facility used for certification was not appropriate.  Firstly, the run time for individual observations would be too long and secondly, the required mass for an aliquot was in the order of 2 g, which was too large for a useful homogeneity study.  End users of melting point CRMs typically use the materials to check capillary equipment that uses samples sizes in the 2 to 10 mg range.
• The bench top instrument used could accept up to three samples per temperature run in three distinct locations, which added both a possible run effect and a location effect as nuisance effects to the study.
• The paper demonstrates the use of replicated 3 X 3 Latin square design for the elimination of two nuisance effects during a homogeneity study.
• Increasing the number of units of material to 12 and replicating the design four times gives effective degrees of freedom comparable to the recommendation of ISO Guide 35.
• Three ways for the extraction of the main effects and relevant variance components from the replicated Latin square design are presented, i.e. using software to apply a classical ANOVA, the manual construction of an ANOVA table and using mixed effects modelling software.
• The effect of the rounding of the instrument used on the calculated variances is also evaluated.
• A very useful appendix is provided for the manual calculation for a replicated Latin square design with one fixed effect.