A Study of the Response Surface Methodology Model with Regression Analysis in Three Fields of Engineering

• Published in: Applied system innovation Vol. 8; no. 4; p. 99
• Main Authors: Chen, Hsuan-Yu, Chen, Chiachung
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 21.07.2025
• Subjects: Accuracy; Data points; Datasets; Design of experiments; Engineering; Mathematical functions; Mathematical models; Nanomaterials; Normality; Optimization; Regression analysis; Research methodology; Response surface methodology; Semiconductors; Statistical analysis; Textbooks; Variables; Variance
• ISSN: 2571-5577; 2571-5577
• DOI: 10.3390/asi8040099

Researchers conduct experiments to discover factors influencing the experimental subjects, so the experimental design is essential. The response surface methodology (RSM) is a special experimental design used to evaluate factors significantly affecting a process and determine the optimal conditions for different factors. The relationship between response values and influencing factors is mainly established using regression analysis techniques. These equations are then used to generate contour and surface response plots to provide researchers with further insights. The impact of regression techniques on response surface methodology (RSM) model building has not been studied in detail. This study uses complete regression techniques to analyze sixteen datasets from the literature on semiconductor manufacturing, steel materials, and nanomaterials. Whether each variable significantly affected the response value was assessed using backward elimination and a t-test. The complete regression techniques used in this study included considering the significant influencing variables of the model, testing for normality and constant variance, using predictive performance criteria, and examining influential data points. The results of this study revealed some problems with model building in RSM studies in the literature from three engineering fields, including the direct use of complete equations without statistical testing, deletion of variables with p-values above a preset value without further examination, existence of non-normality and non-constant variance conditions of the dataset without testing, and presence of some influential data points without examination. Researchers should strengthen training in regression techniques to enhance the RSM model-building process.