## 1 Introduction  
In the modern manufacturing industry, the quality of mechanical products is of paramount importance. The manufacturing of these products involves complex processes that demand stringent control measures to ensure accuracy and consistency throughout production. Critical quality characteristics are particularly significant, as they directly influence the final product's performance, reliability, and lifespan [1]. Consequently, accurately predicting the processing quality of these critical characteristics is vital for maintaining a competitive edge and adhering to industry standards. In recent years, scholars have extensively explored the identification of key quality features and the prediction of processing quality in machining. The machining process of mechanical parts typically involves multiple steps, each targeting different quality characteristics. It is essential to identify the most significant quality characteristics based on specific evaluation criteria to enable in-depth analysis in subsequent studies. The Analytic Hierarchy Process (AHP), developed by [PERSON] in 1971, is a multi-criteria decision-making method that assists decision makers in ranking the pros and cons of different options by hierarchically decomposing complex problems [2]. For example, [PERSON] et al. [3] applied AHP to identify key influencing factors in the complex deformation of flexible materials during processing. They developed a model with importance as the target layer, processing attributes as the criterion layer, and deformation influencing factors as the index layer, systematically analyzing the relative importance of each factor. [PERSON] et al. [4] introduced the fuzzy consistent matrix and fuzzy analytic hierarchy process (FAHP), which,by incorporating a fuzzy function, enhances the consistency of the judgment matrix in the traditional AHP, thereby reducing the impact of subjective factors and uncertainty. Additionally, the causal matrix method identifies key influencing factors based on the degree of influence that input variables have on output variables [5]. [PERSON] utilized the causal matrix method to evaluate the manufacturing process of conical picks, treating each process as an input and the critical quality characteristics as outputs [6]. However, current analysis methods, such as AHP, FAHP, and the causal matrix method, are significantly affected by subjective factors, highlighting the urgent need for a quantitative approach to enhance the objectivity and consistency of the analysis. [PERSON] introduced information entropy in information theory, originally applying it to communication to measure the average uncertainty of discrete random variables. When calculated using a base-2 logarithm, the unit of information entropy is expressed in bits [7]. [PERSON] et al. [8] applied information theory to establish a reliability analysis model for the machining process, where the uncertainty of machining quality is assessed using vertex entropy, and the error transfer effect is quantified by the mutual information transfer coefficient. [PERSON] et al. [9] developed a \"stability entropy\" method based on information entropy, which enables real-time calculation of cutting stability through spindle load data. Additionally, [PERSON] et al. [10] proposed a method based on information transfer entropy that achieved early fault warning and root cause tracking of CNC lathes using net entropy calculation and a sliding window method. While information entropy theory has been widely employed to analyze error transmission, evaluate CNC machining stability, and diagnose faults, there is a noticeable gap in research regarding the identification of crucial quality features in machining. To address this gap, the present study introduces information entropy as a tool for quantitatively screening crucial quality features. Machining quality prediction aims to evaluate potential quality issues during machining, identify process defects in advance, and implement early warning measures to enhance product quality and reliability.