Li He and Zhang Bangcheng from Changchun University of Technology, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, and Yang Xiaohong from the Second Aviation Academy of the Air Force, conducted research on reliability growth technology for CNC machine tools. They used the Mean Time Between Failures (MTBF) value for fault diagnosis of domestically produced CNC machine tools. Based on collected CNC lathe fault data, reliability analysis was performed, reliability evaluation indicators were calculated, and a fault interval distribution model was established. Failure Mode, Effects, and Criticality (FMECA) analysis was conducted on the CNC lathe, dissecting the failure mechanism, identifying weak points in the product, and proposing reliability improvement suggestions for components or subsystems. 1 Introduction CNC machine tools are fundamental equipment in modern manufacturing technology. Their quality and reliability directly affect a country's advanced manufacturing technology development level. With the development of advanced manufacturing technology, machine tools are required not only to have superior performance and high automation, but also to have maintainability, reliability, maintainability, and repairability—that is, machine tools must be trustworthy. The machinery manufacturing industry is rapidly developing towards precision, flexibility, integration, automation, and intelligence, leading to strong domestic demand for CNC machine tools and presenting the CNC machine tool industry with an excellent development opportunity. However, my country's machine tool industry faces extremely severe challenges and competition, urgently requiring it to narrow the gap with countries like Japan, the United States, and Switzerland. These challenges are mainly manifested in: high speed and high precision; machine tool reliability; appearance and manufacturing precision; self-development capabilities and product development cycles; and the overall societal integration and specialization. Among these, insufficient reliability is a major factor contributing to a lack of competitiveness; therefore, improving the reliability of domestically produced CNC machine tools has become a top priority. Research in reliability engineering theory and technology is based on a large amount of reliability information. Only with accurate and reliable data can reliability assessments and fault analyses be conducted on existing products, enabling reliability prediction, allocation, and design. Only through information analysis and processing can reliability improvement measures be proposed for product development, design, manufacturing, assembly, use, and maintenance, achieving reliability growth. Therefore, reliability information is a prerequisite for reliability engineering theory and technology research. 2. Statistical Analysis of CNC Machine Tool Data Reliability analysis is based on a large amount of reliability data. Reliability information is indispensable in product reliability testing, fault analysis, reliability design, use, and maintenance. To properly process and preserve past test data, prevent data loss or dispersion, and to analyze and process data as required, more conveniently and accurately calculate practical reliability indicators, it is urgent to establish a statistical analysis system adapted to the development requirements of CNC machine tools. For the above reasons, drawing on current research results in CNC machine tool reliability theory and related mathematical statistics knowledge, a CNC machine tool data statistical analysis system has been developed. The structure of the CNC machine tool data statistical analysis system is shown in Figure 1. 3. Assessment and Fault Analysis of Basic Reliability Status of CNC Lathes Throughout the entire product lifecycle, whether in the development, design, and manufacturing stages, or the use and maintenance stages, reliability data analysis is involved. Therefore, reliability testing technology and data collection and analysis are crucial and are important components of the fault reporting, analysis, and correction system. The data analysis part includes reliability test analysis, fault statistical analysis, FME(C)A, etc. 3.1 Failure Mode, Effects, and Criticality Analysis (FMECA) was used to analyze the failures of the S3-242/244 CNC lathe. This analysis clarified the proportion of each failure location, failure mode, and failure cause within the machine, providing an overall understanding of the failure patterns. Failure modes with significant impact on overall machine reliability were identified. In-depth failure mode and cause analysis was conducted on frequently failing components or subsystems. Criticality analysis revealed the weaknesses of the S3-242/244 CNC lathe, providing a basis for troubleshooting. The results of the failure analysis were communicated to the design, manufacturing, and user units, enabling them to implement countermeasures and measures to improve the reliability of the CNC lathe from all aspects of design, manufacturing, use, and maintenance. [IMG=Figure 1 Structure Diagram of CNC Machine Tool Data Statistical Analysis System]/uploadpic/THESIS/2007/11/2007111413230583628H.jpg[/IMG]Figure 1 Structure Diagram of CNC Machine Tool Data Statistical Analysis System[IMG=Table 1 Technical Parameters]/uploadpic/THESIS/2007/11/2007111413280199081Y.jpg[/IMG]Table 1 Technical Parameters[IMG=Figure 2 Typical Failure Rate Curve]/uploadpic/THESIS/2007/11/2007111413300754587D.jpg[/IMG]Figure 2 Typical failure rate curves and catastrophic failure analysis of the S3-242/244 CNC machine tool are crucial steps in quantifying the consequences of failures, based on Failure Mode and Effects Analysis (FMEA). The aim is to study the combined impact of each failure mode's severity level and severity numerical value or probability of occurrence to comprehensively evaluate its effects. Component catastrophic failure is a comprehensive assessment of the severity of a component's failure, reflecting the impact of a subsystem or component failure on the overall machine's performance, functionality, surrounding environment, and personnel safety. Through catastrophic failure analysis, key components affecting the reliability of the S3-242/244 CNC lathe can be identified, and weaknesses in the product can be pinpointed for targeted reliability improvement design. 3.2 Reliability Index Evaluation 3.2.1 Point Estimation of MTBF After various distribution type assumptions, parameter estimations, and hypothesis testing, the distribution type of failure interval time (MTBF) has been determined to be exponential. Based on this, the point estimate of MTBF is determined. The point estimate of MTBF is calculated by the following formula: (1) Where: f(t) is the probability density function of the fault interval time f(t) = 0.0044e[sup]-0.0044t[/sup] (2) Substituting formula (2) into formula (1), we get the estimated value MTBF = 227.27h 3.2.2 Interval estimation of MTBF The interval estimation of MTBF is to obtain a confidence interval of the reliability characteristic quantity MTBF based on the fault data. This interval includes the true value of the unknown parameter MTBF with a certain probability (i.e., confidence level). Usually, 90% is taken as the confidence level. 3.2.3 Mean time to repair (MTTR) and inherent availability A[sub]i[/sub] For repairable products, in addition to reliability, maintainability must also be considered. Some products are not easy to fail, but once a failure occurs, it takes a long time to repair. They may be in the repair state frequently, and the utilization rate is obviously not high. Therefore, we should not only pay attention to whether the product is easy to fail, but also whether the product is easy to repair. The corresponding maintainability index includes mean time to repair (MTBL), which is the mathematical expectation of repair time. 4. Implementation of Reliability Growth Technology for CNC Lathes Product reliability is determined by design and achieved through the manufacturing process. Due to the increasing complexity of products and the continuous adoption of new technologies, product design also requires a process of continuous deepening understanding and gradual improvement. Early prototypes of products often have numerous design and process defects and problems during testing or operation. Planned improvements to the design and processes are needed to eliminate failure modes, thereby improving the inherent reliability level of the product to meet usage requirements. Currently, reliability growth has become a crucial component of reliability engineering. In the decisive life stages of a product, such as research and development and production, only by using reliability growth technology for analysis, management, and engineering correction can various reliability activities be integrated into a whole and permeate the entire product lifecycle. Practice has proven that using reliability growth technology for testing, analysis, and management to improve product reliability is an effective method for saving research and development costs and shortening the development cycle. Furthermore, for products requiring reliability assessment or evaluation, if reliability growth technology is successfully applied during research and development or production, the resulting complete failure data can be used to assess or verify the product's reliability. Products vary greatly in structure and failure modes, necessitating the study of early failure mechanisms and the development of improvement measures based on these early failure modes. Research on the reliability of CNC lathes and their failure distribution patterns reveals that many early failures of CNC lathes are carried over to users. Frequent and high failure rates during the initial stages of field operation are a significant factor affecting the reputation of domestically produced CNC machine tools. To ensure that potential early failures are fully exposed and eliminated before CNC lathes leave the factory, stabilizing the product's failure rate and allowing it to directly enter a relatively stable period of occasional failures during user operation, early failure testing, analysis, and research on CNC lathes are of significant practical importance. 5. Reliability Evaluation and Comparative Analysis This paper conducts a reliability evaluation of a certain type of CNC lathe after implementing reliability growth technology. Analysis of the identified failure locations shows that the previously frequent failure sites—the spindle assembly and clamping accessories—have shifted to the Z-axis and X-axis feed systems; the causes of failure have changed from wear and breakage to loosening and jamming; and the main failure mode has changed from no movement during indexing and shifting to exceeding geometric accuracy standards. The reliability index MTBF value of the new round of CNC lathes has increased from the original 227h to 384h, improving the reliability level by 69.2%. 5.1 A Certain Type of CNC Lathe Under Evaluation 5.1.1 Product Description This type of CNC lathe adopts a 45° inclined high-rigidity bed, suitable for high-speed, heavy-duty cutting. The spindle has high precision and rigidity, enabling stepless speed regulation and constant speed cutting. It starts and stops quickly, and each lubrication point has an independent circulation device for quantitative lubrication, resulting in low temperature rise and thermal deformation. The tailstock sleeve extension and retraction can be controlled by a program. This type of CNC lathe can process straight lines, arcs, metric and imperial threads, and multi-start threads, and is particularly suitable for turning shaft and disc parts with complex shapes and high precision requirements. 5.1.2 Main Technical Parameters (Table 1) 5.2 Failure Interval Time Distribution Model of a Certain Type of CNC Lathe 5.2.1 Description of the Failure Interval Time Model Extensive statistical data shows that complex products generally exhibit the life characteristics described by the "bathtub" curve shown in Figure 2. Before T_B, the failure rate curve is called the early failure period, and it decreases. Once early failures are effectively eliminated, the product gradually operates normally, and the failure rate stabilizes. By T_B, the failure rate curve begins to flatten. The period from T_B to T_W is called the random failure period, and the failure rate is approximately constant. After T_W, the failure rate curve increases rapidly, and the product's failure rate rises rapidly after T_W. There are theoretical and statistical methods for determining the distribution type. For cases where the distribution is unclear, large-sample experiments should be conducted to determine the distribution type. For cases with existing experience, smaller-sample experiments can be conducted to hypothesize the distribution type, and then appropriate fit tests can be performed. When processing fault data from CNC lathes, most of the fault data follow Weibull, exponential, and log-normal distributions. Since this batch of data underwent early fault testing at the machine tool factory and has been used by the machine tool user for a year and a half, it has largely passed the early fault period, and the faults have stabilized, likely entering the period of occasional faults. Furthermore, probability theory shows that the probability density function curve of the log-normal distribution is unimodal, while the probability density function curve of the Weibull distribution is either unimodal or monotonically decreasing depending on its shape parameter. The probability density function curve of the exponential distribution is monotonically decreasing, and the single-parameter exponential distribution is the most widely used and simplest distribution in reliability engineering, with a constant failure rate. Based on these reasons, the exponential distribution is used to describe the distribution model of the fault interval time. 5.2.2 Parameter Estimation and Hypothesis Testing of the Fault Interval Time Distribution Model: A time-truncated experimental method was used, collecting 32 fault data points from 7 CNC lathes. When the fault interval time follows an exponential distribution, the method of moments was used for parameter estimation, and the d-test was used for hypothesis testing. The estimated value of parameter θ can be obtained from the calculation: Comparing the observed value of the test statistic D[sub]n[/sub] with the critical value D[sub]n ,α[/sub], for a given significance level α, the software calculates: D[sub]n[/sub]=0.142＜D[sub]32, 0.1[/sub]=0.216, therefore the distribution of failure interval time conforms to the above-assumed exponential distribution. 5.2.3 Determination of Fault Interval Time Distribution Model Substituting the calculated parameters into the characteristic function of the exponential distribution, the distribution model of the fault interval time of this type of CNC lathe is obtained: [IMG=Table 2 Fault Information Table]/uploadpic/THESIS/2007/11/2007111413390653705N.jpg[/IMG] Table 2 Fault Information Table [IMG=Figure 3 Fault Location Frequency Diagram]/uploadpic/THESIS/2007/11/20071114134209125242G.jpg[/IMG] Figure 3 Fault Location Frequency Diagram [IMG=Table 3 Fault Mode Frequency Table]/uploadpic/THESIS/2007/11/20071114134436565318.jpg[/IMG] Table 3 Fault Mode Frequency Table [IMG=Table 4 Table 4 Z-axis feed system fault mode frequency table [IMG=Table 5 Electrical system fault mode frequency table]/uploadpic/THESIS/2007/11/20071114134637399485.jpg[/IMG] Table 5 Electrical system fault mode frequency table The distribution function F(t) of the fault interval time is: F(t) = 1 - e[sup] - 0.0026t[/sup] (3) The probability density function f(t) is: f(t) = 0.0026e[sup] - 0.0026t [/sup] (4) The failure rate function λ(t) is: (5) 5.3 Fault Mode, Impact and Criticality Analysis of a Certain Type of CNC Lathe 5.3.1 Data Collection and Processing Table 2 is a fault information table obtained from sampling. It is the result of more than a year of data collection. Data that cannot truly reflect the faults of the CNC lathe has been removed. The judgment criteria and counting principles of fault data are followed to ensure the validity of data and information. 5.3.2 Overall Fault Analysis of CNC Lathe (1) Fault Location Analysis By analyzing the fault phenomena and causes, the frequency diagram of fault locations shown in Figure 3 is obtained. Based on the original fault table, it is known that the Z-axis feed system is the most frequently faulty part, mainly manifested as Z-axis overload alarm, Z-axis motor belt loosening, Z-axis jerking during jogging, and 414# alarm. The X-axis feed system also has many faults, mainly manifested as loose motor coupling, lead screw backlash, and tray backlash. In assessing other components and subsystems of the machine tool, there are also many faults in the electrical system, turret tool magazine, main drive system, spindle assembly, and cooling system. Therefore, the potential faults of these systems cannot be ignored. (2) Failure mode analysis From the failure mode frequency table in Table 3, it can be seen that the geometric accuracy exceeds the standard, accounting for a large proportion, reaching 21.88%. In addition to the backlash caused by the X-axis lead screw, the backlash of the X-axis slide will also cause the accuracy of the parts to be low during machining. Component damage also accounts for 15.63%, most of which are caused by the lead screw jamming. 5.3.3 Subsystem failure mode and cause analysis In the FMEA analysis of the subsystems below, the failure modes and causes of each subsystem or component are given in terms of frequency and frequency. Based on this, the failure mode frequency histogram and failure cause frequency histogram of each subsystem or component are drawn. The failure mode, failure cause analysis and cause classification analysis of the four subsystems with the most frequent failures in Table 4 are respectively carried out to explore the measures for reliability improvement design. (1) Z-axis feed system From the failure mode frequency table of the Z-axis feed system in Table 4, it can be seen that the failure modes of a certain type of CNC lathe Z-axis feed system are mainly component damage and loose preload mechanism and vibration of base components. Among them, component damage is the most frequent failure mode. The main causes of Z-axis feed system failures are jamming and loosening. (2) X-axis feed system [IMG=Table 6 Turret Tool Magazine Failure Mode Frequency Table]/uploadpic/THESIS/2007/11/20071114135814858149.jpg[/IMG] Table 6 Turret Tool Magazine Failure Mode Frequency Table [IMG=Table 7 CNC Lathe FMECA Table]/uploadpic/THESIS/2007/11/2007111414005154318L.jpg[/IMG] Table 7 CNC Lathe FMECA Table The X-axis feed system has only one failure mode: geometric accuracy exceeding the standard in the process type, which occurred 5 times. For this type of failure, there are many mechanical factors. The unstable machining accuracy is caused by the transmission error of the lathe and the repeatability of the tool holder. It is mainly caused by the loosening of the ball screw bearing nut and poor assembly. (3) Electrical System: From the electrical system failure mode frequency table (Table 5), we can see that the main failure mode is short circuit in the line and cable, accounting for 75%, followed by loose locking components, accounting for 25%. The main causes of failure are overload and component damage. (4) Turret Tool Magazine: From Table 6, we can see that in the failure modes of the turret tool magazine, geometric accuracy exceeding the standard accounts for 67%, and component damage accounts for 33%. The failures of the turret tool magazine are mainly caused by improper adjustment and component damage. 5.4 CNC Lathe Fatality Analysis: Fatality analysis is a key step in quantifying the consequences of failures for FMECA. That is, it analyzes the severity of the impact of various failure modes on the system function, and then determines the fatality of each part, component or system. The quantification of FMECA reflects the potential weaknesses of each key component of the system, so as to enable better improvement design of the CNC lathe. The formula for calculating the lethality of a component is: (6) Where: k is the number of failure modes of the component; n is the total number of times the component has all failure modes; n_i is the number of times the i-th failure mode of the component occurs; β_i is the probability that the component will be damaged due to failure mode i. The international draft calls this the conditional probability of loss of function. Its values ​​are as follows: β_i=1 indicates that the component will definitely be damaged; β_i=0.5 indicates that the component may be damaged; β_i=0.1 indicates that the component is unlikely to be damaged; β_i=0 indicates that the component has no effect. is the basic failure rate of the component, calculated using the average failure rate = N/∑_t. Where N is the total number of failures of the parts within the specified time; ∑[sub]t[/sub] is the cumulative working time of the parts within the specified time. The cumulative working time of the 7 CNC lathes of this type is 15955.159h. The FMECA table of this type of CNC lathe was established by calculation and analysis as shown in Table 7. Substituting β and λ into equation (6), the flammability table of the failure parts is obtained as shown in Table 8. It can be seen from the flammability table of the failure parts in Table 8 that the reliability of the Z-axis feed system and the X-axis feed system is the weakest and the parts that should be prioritized for reliability improvement design. Through statistical analysis of the failure parts, failure modes and flammability table of this type of CNC lathe, the influence of each failure part on this batch of CNC lathes can be quantitatively seen, and this can be used as the basis for a new round of product evaluation and comparative analysis to improve the reliability of this batch of lathes. [IMG=Table 8 Fatality Table of Fault Locations of a Certain Series of CNC Lathes]/uploadpic/THESIS/2007/11/2007111414045526425M.jpg[/IMG] Table 8 Fatality Table of Fault Locations of a Certain Series of CNC Lathes 5.5 Reliability Index Evaluation (1) Point Estimation of MTBF f(t) = 0.0026e[sup]-0.0026t[/sup] (7) Substituting the fault interval time probability density function of equation (7) into the following, we obtain the point estimate of MTBF of this type of CNC lathe: (2) Interval Estimation of MTBF The interval estimation of MTBF is to obtain a confidence interval of the reliability characteristic quantity MTBF based on the fault data. This interval includes the true value of the unknown parameter MTBF with a certain probability (i.e., confidence level). It is usually taken as 90% confidence level. The calculation shows that the two-sided confidence interval of MTBF is (284.79, 525.91) and the one-sided confidence lower limit of MTBF is 301.13. (3) Mean Time to Repair (MTTR) and Inherent Availability (A_i) The observed value of mean time to repair is the ratio of the total repair time to the number of products repaired. The observed value of mean time to repair of this type of CNC lathe is obtained by the following formula: Where: t_Mi is the actual repair time (h) of the i-th CNC lathe in the evaluation period. Inherent availability, also known as steady-state availability, is a generalized reliability characteristic that combines reliability and maintainability. Its expression is: It can be seen that the larger A_i is, the higher the effective working degree of the whole machine. The way to increase inherent availability is to increase MTBF and decrease MTTR. 6 Conclusions Based on the research of the basic theory and application technology of CNC machine tool reliability engineering, the following tasks were mainly completed: (1) On-site test research was conducted on the CNC lathe under test, fault data was collected, the types of CNC lathe reliability faults and fault criteria were determined, and a CNC lathe reliability database was established. (2) The software "CNC Machine Tool Data Statistical Analysis System" was developed and applied to the CNC lathe reliability information processing. The applicability and practicality of the software were verified through the fault information obtained from the survey. (3) The reliability of CNC lathes was studied in depth. Using the developed software, after the initial model selection, the distribution model of the fault interval time was determined through parameter estimation and hypothesis testing, and finally the reliability mathematical model of a certain type of CNC lathe was determined; the reliability characteristic quantity of the CNC lathe reliability evaluation system was given, the mean time between failures (MTBF) was estimated, the maintainability parameter mean repair time (MTTR) and the inherent availability (A[sub]i[/sub] in the availability characteristic quantity were estimated. (4) Failure Mode, Effects, and Criticality (FMECA) analysis was conducted on the CNC lathes under assessment. The proportions of various failure locations, failure modes, and failure causes of this type of CNC lathe were identified. The failure mechanism of the CNC lathe was thoroughly understood, the weak links of the product were identified, the overall occurrence of failures of this type of CNC lathe was grasped, and reliability improvement suggestions were put forward for the parts with frequent failures. The CNC machine tool data statistical analysis system developed can complete the data processing and management operations of CNC machine tool reliability tests, which greatly facilitates the analysis of machine tool reliability. It is fast, practical, and has basically achieved the purpose of serving reliability work after debugging. The reliability level of CNC lathes has increased significantly. Through the assessment of the new round of CNC lathes, the reliability level has increased by 67.1%, which shows that the reliability measures proposed for this type of CNC lathe are effective. At the same time, it reduces the time spent on machine tool maintenance, improves work efficiency, reduces production costs, and provides a favorable guarantee for orderly work progress. Proceedings of the Second Servo and Motion Control Forum Proceedings of the Third Servo and Motion Control Forum