OBRABOTKAMETALLOV Vol. 28 No. 1 2026 78 TECHNOLOGY References 1. SuslovA.G., Medvedev D.M., Petreshin D.I., Fedonin O.N. Sistema avtomatizirovannogo tekhnologicheskogo upravleniya iznosostoikost’yu detalei mashin pri obrabotke rezaniem [System for automated wear–resistance technological control of machinery at cutting]. Naukoemkie tekhnologii v mashinostroenii = Science Intensive Technologies in Mechanical Engineering, 2018, no. 5 (83), pp. 40–44. DOI: 10.30987/article_5ad8d291cdd cd8.06334386. Minimum sample size requirements for reliable correlation-regression modeling of surface roughness in milling Mikhail Gimadeev a, *, Vadim Stelmakov b, Maksim Uliskov c Pacifi c National University, 136 Tihookeanskaya St., Khabarovsk, 680035, Russian Federation a https://orcid.org/0000-0001-6685-519X, 009063@togudv.ru; b https://orcid.org/0000-0003-2763-1956, 009062@togudv.ru; c https://orcid.org/0009-0001-9858-423X, 2016104779@togudv.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2026 vol. 28 no. 1 pp. 64–80 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2026-28.1-64-80 ART I CLE I NFO Article history: Received: 25 December 2025 Revised: 12 January 2026 Accepted: 19 January 2026 Available online: 15 March 2026 Keywords: Sample size Surface roughness Correlation Regression model Milling Root mean square error Funding This work has funded by the Ministry of science and higher education of Russian Federation (project № FEME– 2024–0010). ABSTRACT Introduction. Investigating the statistical relationships between milling parameters and surface roughness requires a correct selection of the sample size, as amplitude parameters and form parameters respond diff erently to data limitations. The reliability of correlation-regression analysis depends on meeting the assumptions of normality and the stability of the estimates, making the determination of the minimum number of observations essential for constructing reliable surface roughness models. The purpose of this work is to develop a methodology for estimating the minimum sample size required to build statistically signifi cant correlation-regression models that describe the relationship between the technological parameters of the milling process and surface roughness characteristics, ensuring statistical reliability of the results and enabling accurate prediction of machined surface quality. Methodology. The normality of the surface roughness parameter distributions after milling was assessed using the Shapiro–Wilk, Anderson–Darling, and Pearson’s chi-squared tests. Multicollinearity among the technological factors was analyzed using the variance infl ation factor (VIF), while the adequacy of the regression models was verifi ed using the mean absolute error (MAE) and root mean square error (RMSE) metrics. The minimum required sample size was determined by considering statistical test power and Fisher’s z-transformation. Results and discussions. The analysis of pairwise correlation coeffi cients revealed that amplitude roughness parameters exhibit stable relationships even at n = 16, while profi le shape parameters (Rsk, Rku) are characterized by weak or negative correlations and require a substantially larger sample size. The constructed matrix of the minimum number of observations confi rms that for a number of relationships, especially those involving Rsk, hundreds of measurements are necessary, which justifi es the selection of the most informative parameter combinations. Increasing the sample size to n = 128 reduces estimation bias, stabilizes the correlations for amplitude parameters, and reveals a weakening of the relationships for Rsk and Rku. Rank correlation analysis confi rmed a monotonic dependence between Rz and Rt and the independence of Rsk from amplitude characteristics. The verifi cation of the normality of the distributions and the absence of multicollinearity among the factors ensured the validity of the constructed regression models, which demonstrated high accuracy and consistent error behavior. For citation: Gimadeev M.R., Stelmakov V.A., Uliskov M.V. Minimum sample size requirements for reliable correlation-regression modeling of surface roughness in milling. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2026, vol. 28, no. 1, pp. 64–80. DOI: 10.17212/1994-6309-2026-28.1-64-80. (In Russian). ______ * Corresponding author Gimadeev Mikhail R., Ph.D. (Engineering), Associate Professor Pacifi c National University, 136 Tihookeanskaya st., 680035, Khabarovsk, Russian Federation Tel.: +7 924 216-31-39, e-mail: 009063@togudv.ru
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