Reliability Modelling of CNC Machine Tools Based on the Improved Maximum Likelihood Estimation Method

Abstract

The existing standard reliability models for computerized numerical control (CNC) machine tools are not satisfactory and they fall short of predicting failure rates or lifetime of key functional parts of CNC machine tools. This is attributed to two reasons: the small sample size of failure data and a large truncated ratio of the censored failure data. Improved correction method (ICM), maximum likelihood estimation (MLE), and empirical maximum likelihood estimation (EMLE) are presented and compared with each other in this study. In order to improve the shortage of reliability models developed by the traditional methods, an improved maximum likelihood estimation method (IMLE) is proposed through enlarging censored failure data. Moreover, the correction factors of mean ratio to extend censored time are designed, by which the censored failure data can be close to the true time between failures (TBF). Furthermore, a solution method of correction factors considering amount of calculation is proposed to meet the requirements of calculation precision. Finally, verification by the orthogonal experiment is simulated to verify the proposed model. The verifying test results show that the proposed method can be applied in reliability modelling for not only CNC machine tools but also the key functional parts of CNC machine tools.

Optimization of Manufacturing Production and Process

“…By studying the kinematic configuration of CNC machine tools, it is found that it directly affects the nonlinear errors generated in the process of free-form surface machining [11], and has a direct impact on processing energy consumption and design of the supporting CNC system [12]. The moving parts of CNC machine tools and the mechanism of each feed axis also have a significant impact on the overall rigidity [13], positioning error [14], maintainability [15], and other indicators of CNC machine tools, which determine machining accuracy and work reliability [16]. The spindle of CNC machine tools can be analyzed and optimized by finite element analysis [17].…”

A review of prognostics and health management of machine tools

“…firstly, often machine tools are customized systems, produced in small batches. This severily hampers the collection of large failure datasets [121,123,48];…”

Accuracy reliability analysis of CNC machine tools considering manufacturing errors degrees

“…In terms of reliability evaluation of the whole machine tool, Yang et al 18 proposed a bootstrap interval estimation method for the reliability of CNC machine tools, which makes full use of the timed censoring data of machine tools, the maximum likelihood estimation method is improved, the mean value of the censoring time is extended, and the censored failure data closer to the time between failures (TBF) is made. The reliability analysis of the traditional method of machine tools follow the reliability analysis method of electronic products, but the structure, performance, function, and other characteristics of machine tools are different from electronic products, which leads to confusion about failure mode and failure cause, and the separation of function failure and performance failure.…”