Theoretical analysis of the impact of normalizing composite quality indicator components on their extrema

Authors

  • Anatolyi Dolzhanskiy Ukrainian State University of Science and Technology, Dnipro, Ukraine
  • Oksana Bondarenko Ukrainian State University of Science and Technology, Dnipro, Ukraine
  • Oleh Brahynskyi Ukrainian State University of Science and Technology, Dnipro, Ukraine

DOI:

https://doi.org/10.21014/actaimeko.v15i3.2057

Keywords:

individual quality indicators, composite quality indicator, quality management tools, normalization, extremum analysis

Abstract

Quality assessment of complex objects commonly employs composite quality indicators constructed from weighted individual quality indicators and management tools. When these variables differ in units or ranges, normalization to dimensionless values in [0, 1] is required. This transformation yields an alternative quality model whose extremum characteristics may differ from those of the original non-normalized model. This issue has received limited attention in the literature. The aim of this study is to analyse the effect of parameter normalization on the extremum of a composite quality indicator. The analysis considers general quality models based on weighted arithmetic, harmonic, geometric, and quadratic mean aggregation functions, each evaluated with and without normalization of individual quality indicators. The results reveal that normalization affects both the location and type of the extremum, as well as the optimal values of quality management tools, for arithmetic, harmonic, and quadratic mean convolutions. Notably, for the weighted geometric mean, the optimal management tool value is independent of normalization, making this convolution particularly suitable for practical quality management. These findings provide a foundation for developing dedicated back-transformation methodologies to ensure accurate real-world application of results obtained from normalized quality models.

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Published

2026-09-18

Issue

Vol. 15 No. 3 (2026)

Section

Research Papers

License

Copyright (c) 2026 Anatolyi Dolzhanskiy, Oksana Bondarenko, Oleh Brahynskyi

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