Automation of evaluation of the interlaboratory comparisons results by means of software

The number of interlaboratory comparisons of measurement results increase, and the number of their participants requires providers to automate data processing procedures. The article is devoted to developing software for the calculation automation and display of interlaboratory comparisons results. The article analyzes the existing software and identifies its main shortcomings. Peculiarities of the application of E n , z and ξ criteria are considered. Features of using the Python programming language for calculations and data display are described. Using the example of conducted interlaboratory comparisons, the possibilities of the developed software for automating calculations and data analysis, and displaying results, are demonstrated.


Introduction
Interlaboratory comparison of measurement results (ILC) is an important part of the metrological activity, which provides an opportunity to ensure the accuracy and reliability of measurements, to compare the results of different laboratories work, and to identify possible errors or deviations. The results of the laboratory's participation in the MPR should be evaluated using the statistical performance criteria of E n -criteria, z-criteria, ξ-criteria, which are given in DSTU EN ISO/IEC 17043 [1] , and are considered in more detail in DSTU ISO 13528 [2] , as well as recommendations on their application and visual display are given [3] .
The condition for obtaining accreditation by a calibration or testing laboratory is participation in the ILC [4] . Also, the laboratories that have already received accreditation should take part in the ILC with other accredited laboratories during the accreditation cycle. Thus, there is a need for conducted MPRs for a large number of participants in various fields of calibration and testing.
Providers and the pilot laboratory are tasked with developing the methodology, organization, and implementation of the ILC. Since processing ILC results requires a lot of time, the implementation of calculations automation and analysis of ILC results, their visualization is an urgent task, the solution of which will significantly simplify and speed up the work of MPR providers.

Analysis of the latest research and publications in which the solution to the issue started
The use of computing capabilities of computers provides an opportunity to simplify data processing procedures, introduce automation of calculations and graphical display of results, make predictions, etc. [5] .
General and specialized software that makes it possible to calculate the results of ILC, as well as to present them in tabular and graphical form exists.
The most common general software is Microsoft Excel [6] . The advantages of Microsoft Excel are the flexibility of settings and the ability to process data that Software such as XLSTAT [7] provides wide opportunities for data analysis and display, including data processing in accordance with recommendations [2] , namely the calculation of robust values. A special feature of XLSTAT is that it is an add-in to Microsoft Excel. The disadvantage of the software is the lack of statistical functioning calculations criteria and its high cost.
Among the specialized software, PROLab [8] should be noted as specially designed for planning, organizing, conducting, and analyzing ILC in accordance with requirements [1] and recommendations [2] , qualification testing, and validation of methods. PRO-Lab provides an opportunity to calculate and visualize the evaluation of ILC results according to the Z , Zu , Zeta , Z ' or E n criteria. However, the disadvantages are the settings' complexity, the lack of an intuitive interface, and the price.

Selection of unresolved problem aspects and tasks formulation
The analysis of available solutions for automating the ILC results calculations, their evaluation, and graphical display allows us to conclude that there is an urgent need to create software that can provide an opportunity to automatically calculate the values of ILC results assessment criteria such as: E n -criterion, z-criterion, ξ -criterion, and present them in tabular and graphical form.

Basic material
The Python language has powerful libraries for data processing, such as NumPy [9] , Pandas [10] , and SciPy [11] . These libraries can be used to analyze data obtained from measurement tools. Python also has libraries for data visualization, for example, Matplotlib and Seaborn [12] , etc. These libraries can be used to display data in a convenient format that makes it easy to understand and analyze measurement results and evaluate results. Therefore, Python was chosen to develop the software's source code, using libraries for mathematical calculations, visualization of results, and providing a convenient user interface.

Calculation of error values and indicators E n , z and ξ ξ
Mathematical expressions for the criteria that must be calculated, as well as conditional expressions for evaluating the obtained results according to [1] , according to which the algorithms were devel-    Fig. 2   For the z criterion, if the value is greater than 3, the value 'r' corresponding to red is written in the array of colors, and the code of the laboratory is entered in the array of negative results, if the value is greater than 2 and less than or equal 3, the value 'm' corresponding to purple is written, and the code of the laboratory is entered into the array of doubtful results, otherwise, the value 'b' corresponding to the blue color is written, and the code of the laboratory is entered into the array of positive results.
A fragment of the algorithm's structure for evaluating the results according to the z criterion is presented in Fig. 2 Negative results indicate that the laboratory still does not meet its own deviation requirements and/or the resulting uncertainty is underestimated and requires revision. Since the ξ criterion is similar to the E n criterion, it is advisable to use E n for analysis, as required by [3] . The math library is used to calculate E n , and z.

Display of calculation and analysis results
For approbation of the program, the data of ILC conducted by SE «Ukrmetrteststandart» in 2018 on frequency measurement were used [13] . The

Conclusions
The software has been developed, which provides an opportunity to automate calculations and analysis of criteria for evaluating the results of the ILC. The advantages of the software are the ability to read data and save the results in *.xls/*.xlsx format files, the ability to evaluate the results of the ILC according to the E n -criterion, as required NAAU for providers and the z-criterion, the creation of a text file report based on the evaluation of the results of the ILC for all participants.
The obtained results of deviation and uncertainty estimates are displayed using graphs, and the calculat-