Keywords: qualimetry object, quality indicator, mathematical dependencies, rectangle method, trapezoid method


The subject of research in the article is a method for determining a complex quality indicator of qualimetry objects that have quality indicators with different units of measurement. The purpose of the work is proposing a method for determining a complex quality indicator of multicriteria objects of qualimetry, using integration methods. The article solves the following task: to investigate the possibility of assessing the quality of qualimetry objects by graph analytical method, ie to apply the principle of determining the area and volume under curved surfaces both on the plane and in space, created by combining estimates of unit quality indicators on dimensionless scale. The following methods are used: mathematical statistics; qualimetry. The following results were obtained: the analysis of scientific literature on quality assessment of qualimetry objects in terms of existing mathematical relationships between the measured quality indicators and their assessment on a dimensionless scale was carried out. It was shown that, as a rule, mathematical dependences are nonlinear and their research is reduced to the development of universal methods that could be applied to objects of qualimetry, regardless of their nature, complexity, importance, etc. Research that involves nonlinear relationships between measured quality scores and their estimates on a dimensionless scale should be based on quality ideology and have a physical explanation. Having single quality indicators in a single (dimensionless) rating scale, it is proposed to determine a single comprehensive quality indicator of the object of qualimetry using integration methods. It is proposed to find the area under the broken curve, which is built as a result of combining estimates of quality indicators on a dimensionless scale over a period of observations. Since the calculation of definite integrals by the Newton-Leibniz formula is not always possible, to solve practical problems, it is enough to know the approximate value of a certain integral with a given degree of accuracy, so it is proposed to use methods of numerical integration, methods: rectangles and trapezoids. A method for determining a generalized indicator of the quality of the object of qualimetry, which can be considered universal, as it can be used for multi-criteria assessment of the quality of objects of qualimetry of different nature. Conclusions: To determine the complex quality indicator of multicriteria qualimetry objects, it is proposed to apply integration by the method of average rectangles. The method of definition of a complex indicator of quality of object of qualimetry with application of integration which considers receipt of estimations of unit indicators of quality is proposed.


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Author Biographies

Olena Cherniak, Ukrainian Engineering Pedagogics Academy
PhD (Engineering Sciences), Senior Lecturer of the Department of Labour Safety, Standardization and Certification
Nataliia Sorocolat, Ukrainian Engineering Pedagogics Academy
Graduate Student of the Department of Labour Safety, Standardization and Certification
Iryna Kanytska, Ukrainian Engineering Pedagogics Academy
Graduate Student of the Department of Labour Safety, Standardization and Certification


Aleksandrov, P. S. (1968), Analytical Geometry Lectures [Lektsii po analiticheskoy geometrii], Nauka, Moscow, 912 p.

Harrington, E. C. Jr. (1965), "The desirability Function", Industr. Quality Control, April, P. 2–9.

Azgal'dov, G. G., Rajhman, Je. P. (1972), About kvalimetriia [O kvalimetrii], Izdatel'stvo standartov, Moscow, 172 p.

Trishch, R. M., Slityuk, E. A. (2006), "Generalized point and interval evaluation items ICE workmanship" ["Obobshchonnaya tochechnaya i interval'naya otsenki kachestva izgotovleniya detali DVS"], Eastern-European Journal of Enterprise Technologies, No. 1/2 (19), P. 63–67.

Trishch, R. M., Slityuk, E. A. (2006), "Spot and interval evaluation of product quality" ["Tochechnaja i interval'naja ocenki kachestva izdelij"], Bulletin of the NTU "KhPI". Collection of scientific works, No. 27, P. 96–102.

Ginevičius, R., Trishch, H. Petraškevičius, V. (2015), "Quantitative assessment of quality management systems’ processes", Economic Research-Ekonomska Istraživanja, No. 28:1, P. 1096–1110. DOI:

Trishch, R., Maletska, O., Cherniak, O., Semionova, Ju., Jancis, V. (2020), "Analysis of the requirements of international and national standards for measure-ment methods and metrological equipment", Innovative Technologies and Scientific Solutions for Industries, No. 1 (11), P. 156–162. DOI:

Cherniak, O., Trishch, R., Kim, N., Ratajczak, S. (2020), "Quantitative assessment of working conditions in the workplace", Engineering Management in Production and Services, No. 12 (2), P. 99–106. DOI:

Trisch, R., Gorbenko, E., Dotsenko, N., Kim, N., Kiporenko, A. (2016), "Development of qualimetric approaches to the processes of quality management system at enterprises ac-cording to international standards of the ISO 9000 series", Eastern-European Journal of Enterprise Technologies, No. 4/3 (82), P. 18–24. DOI:

Ginevičius, R., Podvezko, V. (2007), "Complex assessment of sustainable development of state regions with emphasis on ecological and dwelling conditions", Ekologija, No. 53, P. 41–48.

Ginevičius, R., Podvezko, V. (2008), "A feasibility study of multicriteria methods application to quantitative evaluation of social phenomena", Business: Theory and Practice, No. 9, P. 81–87. DOI:

Ginevičius, R., Podviezko, A. (2013), "The evaluation of financial stability and soundness of Lithuanian Banks", Ekonomska istraživanja: znanstveno stručni časopis, No. 26, P. 191–208.

Ginevičius, R., Suhajda, K., Šimkūnaitė, J. (2014), "Lithuanian experience of quantitative evaluation of socioeconomic system position by multicriteria methods", Procedia – Social and Behavioral Sciences, No. 110, P. 952–960. DOI:

Šimelytė, A., Antanavičienė, J. (2013), "The effect of investment promotion on FDI flows: A case of the Baltic States", Business: Theory and Practice, No. 14, P. 200–208. DOI:

Beinoraitė, Š., Drejeris, R. (2014), "Population entrepreneurship measurement model", Business: Theory and Practice, No. 15, P. 199–209. DOI:

Krivka, A. (2014), "Complex evaluation of the economic crisis impact on Lithuanian industries", Journal of Business Economics and Management, No. 15, P. 299–315. DOI:

Brauers, W., Ginevičius, R., Podviezko, A. (2014), "Development of a methodology of evaluation of financial stability of commercial banks", Panoeconomicus, No. 61, P. 349–367. DOI:

Hashemkhani Zolfanir, S., Maknoon, E., Zavadskas, K. (2015), "Multiple Nash equilibriums and evaluation of strategies. New application of MCDM methods", Journal of Business Economics and Management, No. 16, P. 290–305. DOI:

"Method of rectangles" ["Metod prjamougol'nikov"], available at: (last accessed 28.11.2020).

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