# Reliability Analysis of Multi-Process Machining Based on Information Entropy
## 1 Introduction  
The reliability of the machining process refers to the ability to continuously produce products that meet technical requirements under specified process conditions. The reliability of the machining process determines the quality of machined products. Improving the reliability of the machining process can reduce the defective rate of products and improve economic benefits. Therefore, related design theories and technologies with process reliability have become one of the key factors to enhancing the core competitiveness of enterprises [1]. So far, many scholars have carried out related research on improving the reliability of the machining process and have made significant progress. The reliability of critical processes has a significant impact on the overall reliability of the machining process. Therefore, when analyzing the reliability of the machining process, we should identify the critical processes first [2]. Currently, methods combining qualitative and quantitative analysis are used to determine critical processes, such as the Analytic Hierarchy Process (AHP) [3, 4], fuzzy comprehensive evaluation analysis [5], Fuzzy AHP [6], Failure Mode Effects and Criticality Analysis (FMECA) [7], the cause and effect matrix [8], etc. These methods have a wide range of applications in practical production. The Analytic Hierarchy Process is a simple and systematic analysis method that is concise and practical, and fewer quantitative data are required in the analysis process. There are fewer quantitative data and more qualitative components in AHP, so it is not convincing [9]. Compared with AHP, fuzzy AHP and fuzzy comprehensive evaluation analysis overcome the influence of subjective factors and uncertain factors on evaluation results to a certain extent. The FMECA method takes each process as the analysis subject and comprehensively evaluates the possible failure effects and failure causes of each failuremode. It also evaluates the risk level of each item, and then finds out the weak links of the machining process [7]. However, the FMECA method still relies on the subjective consciousness of the evaluators when evaluating the grades. Overall, the above methods strongly depend on subjective factors and cannot quantitatively analyze each process well. Therefore, these methods have certain limitations. At the same time, the transmission of machining error between processes (error transmission) will also affect the reliability of the machining process [10]. Therefore, analyzing the error transmission is worthy of attention. Currently, the related research on error transmission is mainly based on error flow theory [11], partial correlation coefficients [12; 13] and weighted networks [14; 15], and has established some error transfer models. In terms of mathematics, the state space model based on the error flow theory describes the influence of the previous process on the quality eigenvalue of the following process. This model has been widely used in auto body manufacturing [16; 17]. The error transfer model based on the partial correlation coefficient calculates the correlation between two variables, after controlling the influence of other variables on the two variables analyzed [12]. The state space model based on the error flow theory requires that the machining state of the current process is entirely determined by the machining state of the previous process [18]. In the actual machining process, the machining quality of the current process is not only affected by the earlier process but also by the 5M1E (i.e., Man, Machine, Material, Method, Measurement, Environment) of the current process [19] and other uncertainty factors. Therefore, this model has its own limitations. The error transfer model based on the partial correlation coefficient can quantitatively reflect the correlation of machining error between processes, but it cannot combine the error transmission with the inherent machining error of the process.