Evaluation of Homogeneity in Certified Reference Materials (CRM)

The production of Certified Reference Materials (CRM), according to the international standard ISO 17034:2016, has been playing an increasingly role in measurements and accreditation activities of entities/laboratories, with special focus on the field of chemical, biological and clinical tests and physical properties. The IPQ LGR is responsible for the production of various types of CRM, namely gas mixture standards of ethanol in nitrogen (C2H5OH/N2), by gravimetric method according to the international standard ISO 6142-1:2015, and certification by non-dispersive infrared spectroscopy (NDIR) in accordance with ISO 6143:2001. According to ISO 17034:2016, these mixtures have to be evaluated regarding the homogeneity, which is one of the fundamental requirements for the production of CRM. In this communication, the results of the homogeneity study of standards gas mixtures of ethanol in nitrogen are presented, according to a validated measurement procedure, in order to guarantee the traceability to SI units and also to meet the requirements of ISO 17034:2016. The statistical treatment of the data is presented through analysis of variance ANOVA.


Introduction
Certified Reference Materials (CRM) are an important mean of disseminating SI units and are also a support in the credibility and reliability of a measurement or a laboratory. They can be used in the equipment calibration, validation of analytical methods and measurements quality control. They are also applied in interlaboratory comparisons allowing laboratories to evidence their best measurement and calibration capabilities (CMC). The use of CRM is also an important mean of method validation and accuracy and precision evaluation of the measurements, establishing the metrological traceability of the obtained results. The Reference Gas Laboratory (LGR) of the Portuguese Institute for Quality (IPQ) carries out several activities, namely in the field of gas metrology, either by preparing primary gas mixtures, or certifying reference materials. Primary gas mixtures are prepared at the highest level of accuracy by gravimetric methods based on international standards. The composition of gas mixtures is certified by analytical reference methods. The LGR is responsible for the production of gas mixture standards of ethanol in nitrogen (C2H5OH/N2) CRM, by gravimetric method according to the international standard ISO 6142-1:2015 [1], and certification by non-dispersive infrared spectroscopy (NDIR) in accordance with ISO 6143:2001 [2]. These gas mixtures of ethanol in nitrogen were prepared according to a validated measurement procedure, in order to guarantee the traceability to SI units and also to meet the requirements of ISO 17034:2016 [3]. This standard establishes the necessary requirements for the planning and control of production of reference materials (RM) and certified reference materials (CRM) and the homogeneity study is one of the requirements. This study was carried out with twelve mixtures of C2H5OH/N2 that were subjected to three rolling cycles and analysis. Later they were also analyzed over time, on different days, during six days. The statistical treatment of data is presented through analysis of variance ANOVA [4] and by the t-student statistical test [5], when the null hypothesis is rejected.

Preparation of Reference Gas Mixtures
The preparation of gas standards is carried out in accordance to an harmonised procedure, based on the international standard ISO 6142-1:2015 [1]. These primary mixtures are prepared at highest level of accuracy by gravimetric blending methods, as shown in figure 1. Their nominal composition (volume fractions) is estimated by the ideal gas equation, corrected by a compression factor. In an evacuated and passivated cylinder, each component is added through a filling station, where all equipment (pipes, valves etc.) is electro polished and free of oil ( Fig. 2.). The mass of each gaseous component added to the cylinder can be determined through the mass comparator balance, in which masses are calibrated and traceable to the used national standard (Fig. 2.). The traceability of the gas composition to the SI system is ensured by the use of calibrated instrumentation.
where xi is the mole fraction of the component i in the final mixture, i= 1,…., n P is the total number of the parent gases n is the total number of the components in the final mixture mA is the mass of parent gas A determined by weighing, A= 1,……, P Mi is the molar mass of the component i xi,A is the mole fraction of the component i.

Certification of Reference Gas Mixtures
The composition of a gas mixture is determined by separate analysis of the mole fraction of every individual analyte. The procedure for determining the mole fraction of only one individual analyte is described in ISO 6143:2001 [2]. The mixture composition is certified by comparison methods using a set of mixtures with pre-established assigned values. The traceability of these measurements is guaranteed by links to national and international primary gas mixtures standards. In order to establish the relationship between equipment response and the composition of the suite of calibration mixtures, the following aspects must be considered:  [2] and ISO 11095 [6] describe the bracketing and calibration curve methods for determining the composition of gas mixtures. The selection of method is dependent on the available PRMs. Results are expressed together with their measurement uncertainty, according to GUM [7].
The composition of gas mixtures is certified by analytical reference methods such as Gas Chromatography (GC), Non Dispersive Infrared Spectroscopy (NDIR) and Ultra Violet (UV) (Fig. 3.).

Fig. 3. Analytical reference methods.
The CRM of gas mixture standards of ethanol in nitrogen (C2H5OH/N2) are certified by nondispersive infrared spectroscopy (NDIR).

Homogeneity evaluation
In the process of producing a certified reference material, the homogeneity evaluation is an important part of the planning, regarding the ISO 17034:2016 [3]. A material is perfectly homogeneous with respect to a given characteristic or composition if there is no difference between the obtained values of this characteristic from one part to another, according to ISO Guide 35 [8].

Homogenization System
Whenever a gas mixture is prepared it goes throw an homogenization process. The cylinder containing the mixture is placed in a rolling system. See

4
In this study we give special attention to ethanol in nitrogen gas mixtures because the ethanol is a liquid at ambient temperature, which makes the mixing process more complex. In our experiment, we did the evaluation within-bottle homogeneity. This study is necessary to demonstrate that each mixture, prepared individually, is sufficiently homogeneous.
For homogeneity evaluation was chosen a highly repeatable method. This homogeneity study was carried out with twelve mixtures of C2H5OH/N2 with molar fractions of 50 × 10 -6 mol/mol, 212 × 10 -6 mol/mol, 316 × 10 -6 mol/mol and 500 × 10 -6 mol/mol. Three mixtures of each molar fraction were prepared, then they were subjected to three rolling cycles and analysis, corresponding to different homogenization times.

Rolling time
After preparation, each mixture was subjected to an homogenization process on the rolling system and analyzes were carried out to each of the 12 mixtures at 0 minutes, 30 minutes, 60 minutes and 90 minutes of rolling. In Table 1 we can see all the results for the 12 molar fractions (line factor) for all 4 rolling times (column factor).

Rest period
Each of the 12 mixtures were analysed in the Day 1, Day 2,…, until Day 6. In Table 2 we can see all the results for the 12 molar fractions (line factor) for all 6 rest periods (column factor).

Statistical analysis
The statistical analysis were applied not to absolute values but to the difference of each value and the sample mean.

Analysis of variance ANOVA
The Analysis of Variance (ANOVA) [4] which is a method of testing the equality of three or more population means, based on the analysis of the sample variances was applied.
Statistical model: Where yij, represents the j th observation taken at the factor level-i; μ is a parameter common to all factors called the overall mean; i is a random variable that corresponds to the i-level effect of the line factor; j is a random variable that corresponds to the j-level effect of the column factor and ij the random component of the error associated with the j th observation The test is unilateral and the hypotheses are null: 6 and 0 ∶ β1 = β2 = ... = βn = 0 (4) the average of all populations are equal, it means that the factor has no effect.
We use the statistic F: F is the Fisher-Snedcor [4] sampling distribution where: where MS is the mean square between factors (line or column) and MSError is the mean square error. If: then the null hypothesis is rejected at a level of significance , it means that not all population averages are equal, there is factor / treatment effect.
As we can see in Table 3, F0 is higher than the critical value Fcritic for the factor rolling time, indicating that there is at least one situation where the mixture is not homogeneous. In Table 4, we can observe that F0 is higher than the critical value Fcritic for the factor rest period, indicating that there is at least one situation where the mixture is not homogeneous.

Statistical t-student test
With the ANOVA calculations, we have identified the existence of a mixture or mixtures where the value of molar fractions may be considered outliers. When the null hypothesis is rejected, we can use the t-student statistical test [5] for a significance value of 5 %, that is a criteria to deal with outlying measurements. With these criteria, we can use a sample statistic to be compared with a critical value in order to determine the measurements to reject. The statistical test to detect the outliers was the test of the mean of a normal distribution with unknown variance for a significance value of 5 %. The statistical test used is: and the null hypothesis will be rejected if |t0 | > t α/2, n-1 where t α/2, n-1 is a bilateral test with n-1 degrees of freedom. The average of the 48 measurements related with the rolling time factor, will be considered the mean µ0. The 4 rolling time averages will be used to calculate the t 0,025, 3= 4,176. By the observation of Table 5 we can conclude that the measurements from the 0 minutes rolling time should be rejected. 8 Also applying the t-student statistical test, we have the average of the 72 measurements related with the rest period factor that will be considered the mean µ0. The 6 days rest period averages will be used to calculate the t 0,025, 5= 3,163. By the observation of Table 6 we can conclude that the measurements from the day 1 and day 2 should be rejected.

Conclusions
Tests for homogeneity of 12 gas mixture standards of ethanol in nitrogen for candidate reference material were carried out using the ANOVA statistical tool and the t-student statistical test when the null hypothesis is rejected.
With the ANOVA evaluation, we conclude that for the rolling time and for the rest period, F0 > Fc or at least one mean is statistically different, which means that there is at least one situation where the mixture is not homogeneous.
With the t-student test we conclude that: -t0 > tc, for the 0 min rolling time, which means that the cylinder has to roll for at least 30 minutes.
-t0 > tc, for the rest period of 1 and 2 days, which means that the cylinder must be on rest period for at least two days before carrying out the analysis.