Minimum sample size requirements for reliable correlation-regression modeling of surface roughness in milling
Year: 2026
Type: article
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 differently 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 significant 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 inflation factor (VIF), while the adequacy of the regression models was verified 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 coefficients revealed that amplitude roughness parameters exhibit stable relationships even at n = 16, while profile 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 confirms that for a number of relationships, especially those involving Rsk, hundreds of measurements are necessary, which justifies 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 confirmed a monotonic dependence between Rz and Rt and the independence of Rsk from amplitude characteristics. The verification 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.
Institution: Pacific National University
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7138300058