Spark spectrometry, also called spark OES or spark optical emission spectrometry, like most analytical instrumentation, is comparative. This means that it requires a sample of a known composition for accurate calibration. These known samples are called reference materials, and measurements of unknown samples can be compared to them to determine the amount of uncertainty in those measurements.
After the spark spectrometer is calibrated and the unknown sample is measured, the measurement uncertainty for that unknown sample must be calculated. The question thus follows: what method should one use for calculating the measurement of uncertainty?
There are two main methods for calculating the uncertainty in measurement. They are known as “top-down” and “bottom-up.”
Top-down method requires multiple measurements
The top-down method is relatively easy to use and can be implemented using a straightforward Excel file. The top-down method allows for the global recording of all influence factors by measuring one or two reference samples. It also allows for the recording of hidden systematic influences. Some disadvantages of the top-down method for calculating measurement uncertainty include the fact that reference and test objects may not always be comparable. The method also might not be suitable for certain high-quality requirements.
To calculate uncertainties using the top-down method, the unknown sample must be analyzed with at least four or more measurements. One or two reference samples with similar composition are then selected, using the same matrices as the unknown sample with assurance that they are certified, traceable reference samples with similar analytical content to the unknown sample. The control sample is measured under identical conditions to the unknown, again with at least four or more measurements.
Next, four uncertainty contributions need to be calculated: error from the unknown sample’s standard deviation; error from the certificate of the reference sample; error from the analysis of the reference sample’s standard deviation; and the difference between the measured and certified value of the reference sample. Then, taking the control sample’s measured concentration and the absolute standard deviation, the average concentration and the extended combined measurement uncertainty can be calculated for each element.
An Excel file can be used to automate this process. With the proper algorithms and formulas programmed into the spreadsheet, the program can automatically calculate each element’s average concentration and the extended combined measurement uncertainty.
Bottom-up method to calculate measurement uncertainty
While the top-down method is straightforward, it can be time-consuming and require some statistical skills to implement. To counter this, a software-based “bottom-up” method of calculating measurement uncertainty has been developed. The bottom-up method estimates most contributors to measurement uncertainty directly from the measurement results. This method requires a minimum of two measurements (significantly fewer than the top-down method) to display the uncertainty, using the standard deviation as a parameter.
In the bottom-up method, the calibration model’s uncertainty is considered. For instance, a calibration curve for carbon in low alloy steel can be made, with each point on the curve representing a certified reference material (CRM) used to calculate the intensity recorded during the instrument’s calibration, plotted against the known certified mass percentage of the material.
The uncertainty from the CRM’s certificate and the precision of the intensities recorded during the measurement of the samples are used to create a “cloud” of uncertainty for each sample, which is displayed as a rectangle and used to calculate the confidence interval of the correlation curve. The correlation curve is linear and independent of the calibration model.
Using this approach, the uncertainty can be calculated from the multi-regression model, and the combined uncertainty can be calculated by combining the uncertainty from the calibration model with the precision of the unknown sample, using the standard deviation recorded during the measurement of the unknown sample.
This method does not require statistical skills, and available optical emission spectrometry (OES) software can provide the calculation. The measurement uncertainty can be easily plotted with the analysis and average. The software-provided results also include information about sample homogeneity.
This “partial” uncertainty of measurements directly calculated by a spark spectrometer’s software may be completed with a factor coming from other sources of uncertainty, which can be determined via experiments with different operators or sample preparation methods.
In addition to meeting the requirements of ISO 17025, this bottom-up approach can be used in product conformance testing. For example, it could determine if a product’s chemical composition falls within a given set of specification limits for a given element, because uncertainty of measurement plays a role in this determination.
Overall, the bottom-up method employed by analytical software is a fast and easy way to determine measurement uncertainty. The method is an effective way to meet compliance standards for spark spectrometry and the reporting of uncertainty in measurements.
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