A novel FMECA method for CNC machine tools based on D-GRA and data envelopment analysis | Scientific Reports

Nov 05, 2024

Scientific Reports volume 14, Article number: 26596 (2024) Cite this article

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Failure Modes, Effects, and Criticality Analysis (FMECA) is a commonly used method for analyzing system reliability. It is frequently applied in identifying weak points in the reliability of CNC machine tools. However, traditional FMECA has issues such as vague descriptions of risk factors, equal treatment of risk factors, and unclear directions for improving weak points. In response to the issue of vague descriptions of risk factors, this paper further expands severity (S) into machine hazard (M) and personal hazard (P), and subdivides detectability (D) into functional structural complexity (D1) and detection cost (D2). In addressing the issue of treating risk factors equally, this paper integrates Distance Analysis Method (DAM) and Grey Relational Analysis (GRA) to propose Distance-Grey Relational Analysis (D-GRA). Subsequently, based on the D-GRA method, the weights of each risk factor were determined by comprehensively considering expert system scores and actual economic loss indicators. In response to the issue of unclear improvement directions for weak points, this paper introduces the BCC model. It treats common failure modes of CNC machine tools as decision-making units within the BCC model, refines risk factors as input indicators, and evaluates the efficiency values of each decision-making unit based on various actual losses as output indicators. Through efficiency value analysis, it proposes improvement directions for weak points. Then, based on the weights of risk factors and the efficiency values of failure modes, a modified calculation method for the new Risk Priority Number (RPN) is proposed to amend the traditional RPN, This paper takes the electric spindle system of a certain machining center as an example, applies the proposed method to rank common failure modes with the new RPN, and compares it with other RPN calculation methods to verify the rationality of the proposed approach. Finally, it presents improvement directions for reliability enhancement.

With the advancement of science and technology and the rapid development of the manufacturing industry, CNC machine tools have become an indispensable key equipment in industrial production1,2,3,4,5. However, due to the complexity and high automation of CNC machine tools, their reliability issues are becoming increasingly prominent. Therefore, it is of great significance to conduct reliability analysis on CNC machine tools and achieve reliability growth6. By conducting reliability analysis on the key components of the system, potential faults and problems can be discovered in a timely manner, and corresponding measures can be taken to repair and improve them, thereby improving the reliability of the equipment and reducing the downtime and downtime costs of the equipment7.

FMECA (Failure Mode, Effects and Criticality Analysis) is a reliability analysis method for CNC machine tools, which is often used to analyze the critical failure modes of CNC machine tools8,9. The traditional FMECA analysis flow chart is shown in Fig. 1. FMECA systematically analyzes the possible failure modes and failure effects by the correspondence between the functional layer and the structural layer of each component of the CNC machine tool, and sorts them according to their degree of harm, so as to take corresponding preventive or improvement measures10.

Traditional FMECA analysis flowchart.

In recent years, FMECA has achieved many results in the application research of system-level products. Mu et al.11 applied FMECA to a five-axis linkage blade machining center. Through FMECA analysis, they found the high-frequency subsystems of 67 machining centers in a machine tool factory that failed, determined the weak links in the reliability of the machining centers, and proposed improvement measures and suggestions for the reliability of the machining centers based on the weak links. Nagesh et al.12 used FMECA to analyze the failure mode of CNC gear hobbing machine tools, determined the priority of preventive measures by sorting RPN, and combined the failure mode with high RPN value with machine learning to evaluate the health of the tool so that it can be replaced in time before any problems occur. These studies improved the traditional FMECA by improving the calculation method of RPN, but they all have problems such as the lack of subdivision of risk factors or insufficient subdivision. Subdividing risk factors can more clearly express the degree of harm of different risk factors. In order to study the relative importance of each influencing factor, many researchers introduced weight relationships between risk factors when implementing FMECA. Qian et al.13 used the FMECA method based on fuzzy comprehensive evaluation to analyze the reliability of the threshing and cleaning system. By quantifying the expert evaluation results and using the analytic hierarchy process (AHP) to assign weights, the accuracy and objectivity of the evaluation were improved. This method can effectively identify key failure modes. Liu et al.14 used the triangular fuzzy soft set method to fuse the evaluation information of the evaluators’ language variables through AND operation, calculated the weight of the fusion index of each risk factor, and finally ranked the severity of the failure mode through the failure mode comparison decision table to determine the severity ranking of the risk factors. The above studies have improved the rationality of RPN in the traditional FMECA method by considering the weight relationship between risk factors, but they still have many shortcomings, such as: the expert system scoring is still subjective and cannot be linked to objective indicators such as economic losses. If the subjectivity of the expert system scoring is weakened by objective indicator data, more reasonable analysis results can be obtained. Through FMECA, key failure modes can be identified and preventive measures can be proposed. Preventive measures are to avoid or reduce the harm caused by potential failure modes during the use phase of the product. In fact, improvements made during the design phase of the product can avoid economic losses caused by potential failure modes to a greater extent. In recent years, many experts and scholars have done a lot of research on preventive measures and improvement directions. Nikhil et al.15 improved the expert scoring system and RPN calculation in FMECA based on fuzzy theory, and proposed a new F-RPN method. This method determines preventive measures by fuzzifying the expert system score. Subsystems with higher F-RPN values are monitored in real time and predictive maintenance is performed, and subsystems with lower F-RPN values are preventively maintained. Finally, the rationality of the proposed fault prevention scheme is verified by taking CNC machine tools as an example. Liu et al.16 identified the weak links of mechanical equipment based on FMECA and proposed a new equipment design method that considers five characteristics. Finally, the analysis results are directly fed back to equipment designers to continuously optimize and improve the design method. However, the above studies did not consider the impact of objective evaluation indicators on the improvement direction. If objective evaluation indicators can be introduced to give a targeted improvement direction for system reliability, the analysis results will be more scientific and reasonable. Therefore, in summary, the research on FMECA still has the following limitations:

1. Insufficient consideration of risk factors. Traditional CNC machine tool FMECA only considers severity (S), occurrence (O) and detectability (D) when calculating the risk priority number RPN, without considering the impact of specific factors under each risk factor. For example, severity (S) can be divided into hazards to machine tools and hazards to human body. In fact, when the occurrence and detectability are the same, the hazard to human body must be given more attention than the hazard to the machine tool itself17,18,19. Therefore, the factors need to be further refined, especially in today’s increasingly refined industry division of labor, the refined factors will make the FMECA analysis results more and more accurate.

2. Insufficient consideration of the weight of risk factors. Traditional CNC machine tool FMECA ignores the relative importance of various risk factors. RPN is obtained by multiplying only S, O, and D, three parameters obtained by expert experience evaluation, and the subjectivity of the expert system is too strong20,21,22. At the same time, if one of the parameters is too high, the disturbance to the final multiplication RPN result will be large, the robustness of RPN to other factors will be poor, and it will not be able to reflect the degree of influence of each factor on the result.

3. Failure to give a targeted direction for improving system reliability based on actual conditions. Past methods only analyzed the impact of each failure mode on the product, but failed to propose a targeted direction for improving system reliability based on actual conditions23,24. In fact, based on the results of FMECA analysis, studying the improvement direction of CNC machine tool products based on the main failure modes is more practical for improving the reliability of CNC machine tools.

For problem 1, this paper expands the severity (S) into machine tool hazards (M) and personal hazards (P), and subdivides the detectability (D) into functional structure complexity (D1) and detection cost (D2), refines the risk factors in the design stage of CNC machine tools and gives scoring criteria. For question 2, this paper improves the traditional grey relational analysis (GRA), proposes the distance-grey relational analysis (D-GRA), and introduces the economic loss index into D-GRA to modify the expert system score and determine the weight of each risk factor. Then, the “efficiency value” of each failure mode is evaluated in combination with the BCC model. The impact of different risk factors on the analysis results is carried out based on the “efficiency value”. For question 3, this paper characterizes the ability of different failure modes to cause economic losses according to the “efficiency value” of each failure mode, and then determines the main failure modes that need to be focused on. Then, the improvement direction of the main failure mode is proposed based on the risk factors, and the improvement measures are globalized based on the perspective of asset management. The method flow of this paper is shown in Fig. 2.

New FMECA method based on D-GRA and BCC model.

The subsequent arrangement of this paper is as follows: Sect. 2 establishes a new FMECA method model based on the D-GRA method and BCC model; Sect. 3 applies and validates the proposed new method through practical cases, conducts targeted analysis to determine improvement directions for weak links, and compares it with traditional methods to validate the rationality of this paper’s approach; Sect. 4 concludes the findings.

Traditional FMECA in CNC machine tools is limited by relying solely on three parameters (S, O, and D) when calculating the Risk Priority Number (RPN). Therefore, the analysis results may not accurately describe the types of failure hazards. However, the explicit identification of failure hazard types can lead to a more refined expression of the severity of hazards25,26,27. Moreover, traditional FMECA fails to consider the complexity of structural design, which often impacts the reliability level of a product, especially in terms of the difficulty in detecting faults28. Therefore, building upon traditional FMECA in CNC machine tools, this paper further subdivides the conventional risk factors (S, O, and D). Specifically, severity (S) is expanded into machine hazard (M) and personal hazard (P), while detectability (D) is further subdivided into functional structural complexity (D1) and detection cost (D2). The refined indicators of risk factors for CNC machine tool FMECA proposed in this paper are illustrated in Fig. 3. Classifying and analyzing the refined risk factors proposed in this paper, Tables 1, 2, 3, 4 and 5 provide the scoring levels for each risk factor.

Optimization Indicators for Risk Factors.

In traditional FMECA of CNC machine tools, RPN is calculated by multiplying three risk factors (i.e., S, O, and D). There is no relative influence of each risk factor on the final result29. However, the weight of each risk factor is obtained by multi-factor comprehensive decision-making method, and then the RPN value is obtained by calculating the weighted sum of each factor to reflect the relative importance of each factor30. Among the many multi-factor comprehensive decision-making methods, grey relational analysis (GRA) and distance analysis method (DAM) are widely used. However, GRA is a calculation method that uses the correlation calculation formula to treat each sample equally. It is suitable for linear correlation analysis but has poor objectivity31. DAM generalizes all samples and has good objectivity but does not consider the actual situation. It may cause “dimensional disaster” and make the analysis results unreliable32. Therefore, the distance-grey relational analysis method (D-GRA) formed by improving GRA based on DAM has the advantages of objective comparison results and the ability to analyze the actual situation. In D-GRA, the input is usually the original data matrix, which contains the observation values of multiple samples under different indicators, and the output is the gray correlation matrix between samples, which reflects the correlation and difference between different risk factors. Through the D-GRA method, we can have a deeper understanding of the interaction between different risk factors of the system and provide a more accurate basis for decision-making.

In methodology, D-GRA must first preprocess the data to eliminate the influence of different dimensions on the analysis results. Then, according to the research purpose and actual situation, the Euclidean distance matrix between samples is calculated. On the basis of the distance matrix, combined with the correlation calculation formula of GRA, the gray correlation between samples is calculated. Finally, the results are analyzed, and the samples are sorted or classified according to the calculated gray correlation to reveal the correlation and difference between samples. The sorting or classification results can intuitively show the similarity or difference between samples. Therefore, this paper introduces D-GRA into FMECA of CNC machine tools to calculate the weights of different risk factors.

In order to weaken the subjectivity of expert scoring, this paper introduces the actual economic loss index to modify the expert scoring system. By associating the actual losses caused by each failure mode under different risk factors with the expert scoring system, the subjectivity of expert scoring can be objectively reduced. The economic loss index data needs to be obtained by surveying multiple factories. Table 6 gives the specific definition of the economic loss index. By analyzing the expert scoring matrix and the economic loss matrix, the weights of each risk factor in this method are obtained. The specific steps are as follows:

Step 1: Determine the reference matrix X and the comparison matrix Y;

Among them, xij is the score value of the j-th risk factor of the i-th failure mode in CNC machine tool FMECA;

The economic loss table is established based on the economic loss data obtained from a survey of a certain machining center and is used as the comparison matrix Y.

Among them, yij is the value of the j-th economic loss indicator corresponding to the i-th fault mode;

Step 2 Normalization of data, using the interval relative value method to normalize the reference matrix X and the comparison matrix Y, and calculate the difference sequence matrix ∆ij;

Among them, minxi represents the minimum value of the i-th risk factor in all fault mode ratings in matrix X, and maxxi represents the maximum value of the i-th risk factor in all fault mode ratings in matrix X. The same principle applies to other formulas in this paper;

Step 3: Calculate the correlation coefficient matrix Z;

Among them, \(\:\rho\:\) is the resolution coefficient, ranging between [0,1], typically set to 0.5;

Step 4: To eliminate the influence of the association degree, perform equal weight processing on the correlation coefficient matrix Z. Use distance analysis for directional alignment and dimensionless processing to obtain matrix B;

Step 5: Perform depolarization processing and calculate the distance from each sample point to the reference sample point using the Euclidean formula;

Step 6: Calculate the relative proximity Ck of each sample point to the optimal sample point;

Step 7: Normalize Ck to obtain Wk. Here, w represents the weight vector, and finally, the importance of each risk factor is determined by sorting the associated degrees;

The reason for using the D-GRA method to calculate weights is that this method can effectively handle complex system problems with multiple factors and dimensions. The failure mode assessment of CNC machine tools involves multiple risk factors, and there is mutual influence between the factors. The D-GRA (distance grey correlation analysis) method can objectively measure the importance of each factor by calculating the grey correlation between each risk factor and the ideal solution, and reflect its relative weight. This method is particularly suitable for situations where data is incomplete or information is uncertain, and can better adapt to the needs of failure mode analysis of CNC machine tool systems, ensuring that the weight distribution is more scientific and reasonable.

Through the above steps, using the D-GRA method, on the basis of rating and scoring each risk factor of each failure mode, the weight of each risk factor is calculated, making preliminary preparations for the subsequent RPN calculation.

In order to be closer to the actual work, FMECA in this article introduces economic loss indicators as an objective basis for evaluating the degree of harm of each failure mode, and adopts data envelopment analysis to achieve this goal. Data Envelopment Analysis (DEA) is a non-parametric evaluation method used to evaluate the efficiency of multiple input and output variables33,34,35.

Common DEA methods include CCR (Charnes Cooper Rhodes Model) and BCC (Banker Charnes Cooper Model). The theoretical basis of the BCC model is mainly based on linear programming and convex analysis. It evaluates the relative efficiency of each decision making unit (DMU) by evaluating the input scale and technical effectiveness of the DMU. The BCC model constructs a linear programming model to find the optimal input-output combination of each DMU, thereby determining its efficiency value. Previously, the BCC model was often used in enterprise efficiency evaluation, financial institution efficiency evaluation, and project evaluation and selection36,37,38,39. The methodological description of the BCC model is shown in the Fig. 4.

Methodological description of the BCC model.

Considering that the BCC model is not affected by scale efficiency compared to the CCR model and can handle complex problems with multiple indicators, it is more applicable in this paper. Therefore, this paper adopts the BCC model based on constraint conditions. By substituting the output indicators and input indicators into the BCC model envelope analysis to obtain the efficiency value θ, the efficiency value θreflects the degree of system performance, especially in terms of resource utilization and output efficiency40.

This paper divides the machine tool main system into several key subsystems for research. Each failure mode of each subsystem is called a decision unit of the BCC model. By analyzing the efficiency value θ of each failure mode, the ability of each failure mode in the subsystem to cause economic damage is understood.

For decision-making unit j0, the following model is provided:

In Eq. 2.15, it is assumed that each subsystem has n fault modes, that is, n decision-making units in total, Where eij(l) represents the value of the l-th input indicator (risk factor) of the j-th output indicator (economic loss table) of the i-th fault mode, and frj(t)represents the value of the t-th input indicator (risk factor) of the r-th output indicator (economic loss table) of the j-th decision-making unit. Among them:

In Eq. 2.16, ℇ is a non-Archimedean infinitesimal quantity used to ensure the robustness of the model. δ1, δ2 are parameters with a value of 0 or 1. If they take different values, they correspond to different DEA models. When δ1 = 0, the efficiency of the CCR model can be obtained; When δ1 = 1, δ2 = 0, the efficiency of the BCC model can be obtained; ai(l) represents the relative weight of the l-th output index of the i-th input index, and br(t) represents the relative weight of the t-th output index of the r-th input index, \(\dot{S}^{ - }\) and \(\dot{S}^{ + }\) represent the slack variables of the input and output respectively. λ represents the weight coefficient of the decision-making unit.

Let Φ0, λ0, \(\lambda _{{{\text{n}} + {\text{1}}}}^{0}\), \(\dot{S}^{ - }\) and \(\dot{S}^{ + }\) be the optimal solution of the BCC model, If Φ0 = 1 and \(\sum _{{{\text{l}} = {\text{1}}}}^{{{\text{Li}}}} a_{{\text{i}}} ^{{\text{l}}} \ldots_{{\text{i}}} ^{{{\text{l}} - 0}} = 0,i = {\text{1}},{\text{2}}, \ldots ,{\text{m}}\), \(\sum _{{{\text{t}} = {\text{1}}}}^{{{\text{Tr}}}} b_{{\text{r}}} ^{{\text{t}}} \ldots_{{\text{r}}} ^{{{\text{t}} - 0}} = 0,r = {\text{1}},\;{\text{2}}, \ldots ,{\text{s}}\), then the decision-making unit j0 is said to be DEA effective, and the reciprocal of Φ0 is the efficiency value of the decision-making unit j0 .

The efficiency value θ usually ranges from 0 to 1, where 1 represents the highest efficiency. The efficiency value θof each decision-making unit reflects its performance relative to the highest performance. The closer the value is to 1, the closer the unit is to the highest performance; High efficiency values indicate potential problem areas. The higher the value, the greater the ability of this failure mode to cause economic losses and the greater the need to invest more resources in improvements; Depending on the areas with higher efficiency values, specific improvement measures can be developed41. For example: For those failure modes that are more efficient and have greater impact, more resources can be invested in improvements to improve the reliability of the overall system.

In this paper, the risk factor score table considering the weight is used as the input index, and the economic loss table obtained through the survey is substituted into the BCC model as the output index. The efficiency value θ of each decision-making unit j0can be obtained through envelope analysis42.

In summary, this section proposes the FMECA method for CNC machine tools based on D-GRA and BCC models. The basic steps are as follows:

Step 1: Divide the CNC machine tools into hierarchies: determine the functions, composition and agreed levels of the analyzed system, determine the correspondence between them and the reliability block diagram, and formulate an FMEA table.

Step 2: Define the risk factors of CNC machine tool FMECA: This article defines the degree of occurrence (O), machine tool hazard (M), personal hazard (P), functional structure complexity (D1) and detection cost (D2) as risk factors.

Step 3: Conduct expert scoring on different failure modes; invite an expert group to score each risk factor of different failure modes according to the scoring rules in Tables 1, 2, 3, 4 and 5 to form an expert scoring table.

Step 4: Risk factor weight allocation; use D-GRA to calculate the weight values of the five risk factors of occurrence (O), machine tool hazard (M), personal hazard (P), functional structure complexity (D1) and detection cost (D2) .

Step 5: Establish the BCC model and solve it: This article uses the degree of occurrence (O), machine tool hazard (M), personal hazard (P), functional structure complexity (D1) and detection cost (D2) as input indicators. The economic losses obtained through investigation, such as maintenance and replacement costs (R), employee safety and labor costs (E), production efficiency losses (G), product quality issues (Q), and customer satisfaction losses (C), from a certain machining center are taken as output indicators to establish the BCC model. Then, the efficiency values θ of different fault modes are calculated using the Data Envelopment Analysis method.

Step 6: Determine the direction of reliability improvement; sort the efficiency values θ of different failure modes. The sorting results can determine the failure modes that need improvement. Distribute the weights obtained in step 4 to the expert scoring table in step 3 to obtain an expert scoring table considering the weights. Based on this table, the reliability improvement direction of the failure mode that needs improvement is determined.

Step 7: Calculate the RPN value of each failure mode and sort it; based on the characteristics of the efficiency value θ above, this paper proposes a new RPN calculation method based on the weighted score of risk factors and using the BBC model to obtain the efficiency value θ for correction, the calculation method is as follows:

Among them, xij0l− is the score of the i-th risk factor of the \(\:{j}_{0}\)-th failure mode, and ail is the relative weight of the i-th economic loss of the l-th risk factor.

The new FMECA method proposed in this study is applicable to systems with “serial relationships”. In such systems, the failure of a single component will cause the entire system to stop operating. This structure is widely present in most CNC machine tools and their key subsystems. Taking the spindle system of most models as an example, as a typical serial structure, its operation depends on the coordinated work of multiple components, and the failure of a single component will cause the failure of the entire system function. The applicability of this method is not limited to the spindle system, but can also be extended to other key components of machine tools based on the serial system structure or similar complex systems, providing a reference for improving the overall reliability of the system.

Although the method in this paper expands the traditional FMECA by incorporating factors such as economic benefits to more comprehensively adjust the evaluation results of the failure mode, it also has certain limitations, such as not considering the impact of environmental factors such as temperature and humidity on the operation of the system. For some industries, especially those machine tools operating in extreme or changing environments, these environmental conditions may have a significant impact on the performance of the machine tools. Therefore, in cases where environmental factors seriously affect the operation of equipment, the current method may not be applicable to these enterprises.

At present, most subsystems of various types of CNC machine tools are in series, that is, if a certain component is damaged, the entire system cannot realize the corresponding function. The method proposed in this paper is applicable to all complex systems of CNC machine tools in series. In order to make the analyzed cases more realistic, this paper selected 96 CNC machine tool companies of the same model for data research, and counted the frequency of different failures in the spindle system of this model of machine tool within 1 month and the economic losses caused. The frequency of different failures is shown in the Fig. 5 below, and the economic losses caused are shown in Table 7. Based on the statistical results, we selected 96 companies with more than 20 failures in a month for analysis.

The frequency of spindle system failures of 96 CNC machine tools of the same model within one month.

This paper takes the electric spindle system of a machining center as an example and analyzes it using the proposed new FMECA method. Based on the analysis results, the reliability weaknesses faced by this model of electric spindle are determined, and improvement measures are proposed based on the hazard ranking results of the method proposed in this paper.

Step 1 The electric spindle of CNC machine tools is one of the key components in CNC machine tools and is used to drive cutting tools for machining operations43,44,45. The electric spindle plays a vital role in CNC machine tools. Its performance and stability directly affect the processing quality and efficiency. The structural level, functional level and corresponding relationship diagram of the CNC machine tool electric spindle system is shown in Fig. 6.

CNC machine tool electric spindle subsystem division.

The spindle systems are numbered according to the sequence from left to right and from top to bottom in the diagram. For example, in Fig. 6, the pivot 01 in Principal axis 01 corresponds to 0101 in Fig. 7, and so on. After analysis, it is evident that if a subsystem of the CNC machine tool spindle fails, it will affect the operation of the entire system, with the subsystems being interconnected in series. The reliability block diagram of the CNC machine tool spindle subsystems is illustrated in Fig. 7.

CNC machining center spindle system reliability block diagram.

Based on statistical analysis of the spindle system operation, 13 frequently occurring fault modes during spindle system operation were identified, and an FMEA table was developed as shown in Table 8.

Based on statistical analysis of the electric spindle operation, the common 13 fault modes during the operation of the spindle system are listed in Table 8. Expert groups filled in the expert system scoring table for various indicators according to Tables 1, 2, 3, 4 and 5, scoring potential fault modes, forming an evaluation matrix as shown in Table 9.

Following the steps of the D-GRA method to determine the weights of the five risk factors. Firstly, various CNC workshops were surveyed, taking the processing of a specific part order as an example, extensively documenting the economic losses caused by each fault mode, resulting in an economic loss table as shown in Table 7.

Step 1: Define the reference matrix X using the values of the risk factors corresponding to each fault mode in the expert scoring table. Define the comparison matrix Y using the actual economic losses caused by each fault mode as recorded in the economic loss Table

Step 2: Perform data normalization using the interval relative value method on both the reference matrix and the comparison matrix, and calculate the difference sequence matrix.

Step 3: Calculate the grey relational coefficient matrix. Identify the maximum and minimum values in the difference sequence matrix to form the grey relational coefficient matrix Z.

Step 4: Normalize and homogenize the grey relational coefficient matrix Z using the distance analysis method to obtain matrix B.

Step 5: Select the optimal sample B+ and the worst sample B− from the normalized and homogenized indicators.

Optimal sample

Worst sample

Step 6: Depolarization and calculating the distance of each sample from the reference sample points.

Step 7 Calculate the relative proximity Ck between the sample point and the optimal sample point.

Step 8: Normalize Ck to obtain Wk, and draw a weight table of each risk factor.

Get the weight vector W=(0.1865, 0.1806, 0.2027, 0.2145, 0.2157), i.e., b1 = 0.1865, b2 = 0.1806, b3 = 0.2027, b4 = 0.2145, b5 = 0.2157. Table 10 shows the specific risk factor weights.

This study fully considers the impact of the weights of different risk factors. The subdivided factors, namely functional structure complexity (D1), detection cost (D2), occurrence (O), machine tool hazard (M), and personal hazard (P), are multiplied by their respective weights and used as input indicators for the BCC model. This forms the weighted expert evaluation table, as shown in Table 11.

Based on the research results from a certain machining center, the maintenance and replacement costs (R), employee safety and labor costs (E), production efficiency losses (G), product quality issues (Q), and customer satisfaction losses (C) are taken as output indicators. The study employs data envelopment analysis to delve into the relationship between various risk factors and actual losses in the factory. According to the BCC model formula (2.15), the evaluation efficiency values θ for each failure mode are calculated as shown in Table 12.

The efficiency value θ calculated by each decision-making unit in the above table is used to modify the traditional RPN. The input indicators of the BCC model established in this study are the product of refined risk factors and their respective weights, while the output indicators are objective results obtained from investigating various types of losses. The efficiency values θ obtained through envelopment analysis serve as corrective factors derived from analyzing the relationship between the actual economic losses and the severity of the hazards associated with each fault mode. In the original BCC model, the efficiency value θ of each decision-making unit reflects the extent to which its performance approaches the highest level. A value closer to 1 indicates that the unit is closer to achieving optimal performance. In this paper, high efficiency values indicate potential problematic areas. The higher the value, the greater the economic harm caused by a component in that failure mode.

Using efficiency values θ as correction factors to adjust the traditional Risk Priority Number (RPN) can help to correct the subjectivity of the expert rating system from an economic perspective. From Table 12, it can be observed that the efficiency values θ for FM7, FM6, FM8, FM9, and FM4 are relatively high, at 0.9492, 0.8970, 0.7854, 0.6852, and 0.5375, respectively. This indicates that these five fault modes have a relatively high capability of causing economic harm. Taking FM7 and FM8 as examples, it is observed that there is not much difference in the expert ratings between FM7 and FM8. This indicates that in the expert system’s cognition, the degree of harm between FM7 and FM8 is not significantly different. However, there is a significant difference in economic losses between them. This demonstrates the effectiveness of efficiency values θ as correction factors.

The sorting results of efficiency values θ can reflect the direction of reliability design improvement. Taking FM6 (breakage of internal locking nut assembly) as an example, the efficiency value θ of FM6 in Table 12 ranks second, indicating that among all the fault modes included in the calculation, FM6 has a significant economic impact and requires special attention. In Table 11, the highest-rated risk factors for FM6 are detection cost, machine tool hazard, and functional structure complexity. These values are derived from the correlation between expert system ratings and objective economic losses. A higher value indicates a higher economic loss caused by this risk factor. Among them, detection cost and machine tool hazard appear to be excessive, while functional structure complexity indicates a relatively smaller hazard, suggesting that there is still some safety margin. This also suggests that if the intention is to reduce the RPN of this failure mode, measures should be taken to reduce detection costs, mitigate machine tool hazards, and decrease the complexity of the fault location. For failure modes with higher efficiency values θ, corresponding reliability improvement design measures are proposed based on the risk factors that significantly affect their evaluation efficiency. These measures are organized into a reliability design improvement table, as shown in Table 13 below.

Improvement measures proposed for CNC machine tool spindle systems include the introduction of fault detection systems and the implementation of regular maintenance plans. The feasibility and practicality of these measures have been recognized by many companies. For example, in terms of the feasibility of improvement measures, the introduction of a fault detection system is one of the effective means to ensure reliability. The fault detection system provides enterprises with a means of real-time monitoring, which can warn of potential faults in advance, thereby avoiding sudden shutdowns of equipment during operation. Combined with current sensor technology and intelligent systems, the implementation of this improvement measure is highly feasible, especially in enterprises with a good data foundation, where the fault detection system can effectively reduce downtime and maintenance costs. Regular maintenance plans, as a preventive maintenance measure, can perform necessary inspections and repairs on equipment before a fault occurs to ensure that the equipment remains in the best working condition. The feasibility of such plans has been verified in many industries, especially in high-load and continuous production scenarios, where regular maintenance helps reduce the occurrence of sudden failures.

However, in actual applications, there are also some potential challenges. Although these measures can improve the overall reliability of the equipment, the implementation of these measures requires enterprises to invest a certain amount of money. For example, the introduction of a fault detection system requires not only the purchase of relevant hardware equipment, but also the training of operators and integration into the existing production management system. For small and medium-sized enterprises, the initial investment cost may become a major challenge. In addition, although reducing the number of components can theoretically reduce the failure rate, it must be carefully designed and verified to ensure that it does not affect the normal function of the equipment. Data and technical support also have high requirements for enterprises. The implementation of the fault detection system relies on a large amount of operating data and failure mode analysis. For some enterprises with insufficient data accumulation or low technical level, they may face problems such as insufficient data acquisition and lack of analysis ability, which will affect the effectiveness of the fault detection system. The effective operation of regular maintenance plans and fault detection systems cannot be separated from the support and adaptation of operators. This means that enterprises need to train existing employees to ensure that they have mastered the monitoring, maintenance and emergency handling capabilities of the equipment. The training cost and the time it takes for employees to adapt to the new system are also potential challenges that enterprises need to consider during the implementation process.

Although these improvement measures are technically feasible and have significant advantages in improving equipment reliability, enterprises still need to comprehensively consider factors such as cost, technical support and personnel training during actual implementation. Through reasonable planning and phased implementation, these challenges can be overcome, thereby achieving effective improvements to the CNC machine tool spindle system.

The new RPN values proposed in this article are calculated and sorted according to formula (2.17), as shown in Table 14.

In the current study, we proposed a variety of improvement measures for the key failure modes of CNC machine tools, which improved the operating efficiency and reliability of machine tools to a certain extent. However, these measures focus more on single problems or technical improvements and do not fully reflect the global perspective of asset management. According to asset management theory, equipment management is not limited to daily maintenance and fault repair, but also requires comprehensive management of equipment from the perspective of the entire life cycle. The goal of asset management is to achieve the optimal use and value maximization of equipment through comprehensive management of equipment planning, procurement, operation, maintenance and disposal. As pointed out in the literature46,47,48, asset management strategies can help enterprises make more comprehensive resource allocation and optimization decisions throughout the equipment life cycle, thereby improving the long-term reliability and economy of equipment.

In this study, the improvement measures for bearing burnout are taken as an example, which can be further expanded to the global optimization of asset management. For example, the fault detection system can be integrated with the asset management system to aggregate the detected fault signals and equipment operation data into a centralized database, thereby realizing all-round monitoring of equipment status. Through the accumulation of historical data, enterprises can accurately predict the service life, performance degradation trend, and failure frequency of equipment, and make optimized maintenance plans and equipment update decisions based on this. This global management approach can not only reduce unplanned downtime, but also reduce the company’s capital expenditure by extending the service life of equipment.

The global nature of asset management is also reflected in its adaptability to external environmental factors. For equipment operating in complex or extreme environments, asset management can provide more targeted maintenance and adjustment measures. For example, changes in temperature and humidity may have a significant impact on the normal operation of equipment. The asset management system can combine environmental monitoring data to adjust the maintenance cycle and operating parameters of the equipment in real time to ensure that the equipment remains efficient and stable under different working conditions. The introduction of a global asset management perspective makes the method in this article not only applicable to the current CNC machine tool spindle system, but can also be extended to other key machine tool components and complex systems, helping enterprises to maximize economic benefits.

To validate the effectiveness of the proposed method, this study compared the RPN values of different failure modes under the traditional method, the method proposed in Ref49, and the method proposed in this study. The results were sorted and presented in Fig. 8. Figure 9 presents the normalized RPN values obtained from the three methods. Overall, the three methods exhibit similar trends. However, based on the economic loss analysis proposed in this study, there are some changes in the relative ranking of RPN values for certain failure modes. Taking the failure mode FM6 (internal locking nut assembly fracture) as an example, in our method, the RPN value for FM6 is relatively higher compared to the other methods, indicating that the actual hazard of FM6 is higher than the assessment results from the expert system. Through the analysis of the output indicators for FM4, FM5, and FM6, it can be observed that the economic losses caused by FM6 are significantly higher than those of FM4 and FM5. In the method proposed in this paper, the efficiency value θ for FM6 is 0.8970, while for FM4 and FM5, the efficiency values θ are 0.5375 and 0.5293, respectively. After applying the BCC model to correct the RPN values based on the efficiency values θ, the relative relationships between FM4, FM5, and FM6 become clearer in Fig. 9.

Although the traditional method and the method in Ref49 can also express the relationship between different failure modes, the accuracy of the description still needs to be improved. In practical terms, addressing FM6 may involve replacing damaged components, performing precise adjustments and calibration, and increasing the inventory of spare parts to resolve the issue. On the other hand, FM4 may only require re-tightening bolts and inspecting related components, while FM5 might involve replacing damaged tools and mechanical parts. Compared to the series of maintenance, replacement, and calibration operations required for FM6, addressing FM4 and FM5 is relatively easier and has a smaller impact. In summary, the approach presented in this paper, which considers weights and adjusts the Risk Priority Number (RPN) based on the efficiency values θ evaluated by the BCC model, enables a more detailed identification of fault risks. It can be observed that this method yields rankings closer to the actual design situation compared to traditional methods. By considering more factors, it better aligns with reality.

RPN solution results for different failure modes under traditional method, literature method in Ref49 and this method.

RPN ranking diagram of different failure modes after image normalization using traditional method and literature method in Ref49.

The analysis conducted in this paper, comparing the RPN values obtained directly by summing up the risk factors, the RPN values obtained by weighted addition of risk factors, and the new RPN values derived through the proposed research method, reveals that the RPN values calculated in this study consider the weights of different risk factors and the refined risk factors such as system complexity. Consequently, these values are closer to real-world scenarios and are more suitable for reliability analysis of complex systems like machine tools.

This paper proposes the D-GRA method, combined with the BCC model, to improve the evaluation indicators of traditional FMECA in the design phase of CNC machine tools. It addresses the shortcomings of non-refined risk factors and the neglect of risk factor weights in the RPN calculation formula. Additionally, it provides targeted reliability improvement measures for fault modes with significant economic impact. The main conclusions are as follows:

In addressing the limitations of traditional FMECA in accurately describing fault hazards during the design phase of CNC machine tools, this paper separates the hazards to the machine and human safety. The severity (S) is divided into machine hazard (M) and personal hazard (P). To overcome the shortcomings of traditional FMECA in neglecting structural complexity, the detectability (D) is expanded into functional structural complexity (D1) and detection cost (D2) for separate analysis. Rating tables for each indicator have been established. Note that the rating data should be treated as continuous data.

Addressing the issue of neglecting the relative importance of risk factors in the design phase of CNC machine tools in traditional FMECA, this paper integrates the Distance Analysis Method (DAM) with the traditional Grey Relational Analysis (GRA) to develop the Distance-Grey Relational Analysis (D-GRA). By introducing economic loss indicators as an objective basis, the subjectivity of expert system ratings is mitigated. Combining detailed expert rating matrices with economic loss matrices, the weights of various risk factors are determined. This approach objectively reflects the relative importance of each risk factor by assigning appropriate weights to them.

Addressing the shortcomings of traditional FMECA, which does not evaluate the impact of each fault on the product at the end of the CNC machine tool design phase and hence fails to suggest directions for improving machine reliability, this paper introduces the BCC model to calculate the efficiency value θ for each failure mode and correct the traditional RPN values. Based on the efficiency value θ, this method identifies failure modes that cause significant economic losses and provides targeted reliability improvement directions. This offers specific and reasonable suggestions for product design and optimization, fundamentally preventing the occurrence of failure modes that could lead to substantial economic losses.

The efficiency value is obtained through the BCC model, and the traditional RPN calculation method is improved. Taking into account the score value, weight value and efficiency value of the refined failure mode of the risk factor, a new RPN calculation method is proposed. The new RPN is sorted to obtain a risk priority number ranking result that is closer to the actual situation, and the improvement direction is globalized from the perspective of asset management. Based on the analysis of specific cases, the example shows that the failure mode hazard score obtained by the new method proposed in this paper is basically consistent with the traditional method, but it takes into account specific risk factors such as the complexity of the structure, and is more comprehensive and effective.

All data generated or analyzed during this study are included in this published article.

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First of all, we are most grateful to the editors for their constructive suggestions. In addition, I would like to thank the authors of this paper’s references, whose work has made great contributions to the completion of this paper. Finally, we would like to thank the sponsors of this study, which was funded by the Youth Growth Technology Program of Jilin Provincial Department of Science and Technology (20220508004RC).

School of Mechanical and Aerospace Engineering, Jilin University, Key Laboratory of CNC Equipment Reliability, Ministry of Education, Changchun, 130022, Jilin Province, People’s Republic of China

Hailong Tian, Yuzhi Sun, Chuanhai Chen, Zeyi Zhang, Tianyi Liu, Jialong He & Lijuan Yu

China FAW Motor Corporation Limited, Changchun, 130022, Jilin Province, People’s Republic of China

Tianyu Zhang

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Hailong Tian: Conceptualization, Project administration.Yuzhi Sun: Methodology, Writing – review & editing, Writing – original draft.Chuanhai Chen: Resources, Supervision.Zeyi Zhang: Investigation.Tianyi Liu: Formal analysis. Tianyu Zhang: Validation. Jialong He: Resources, Supervision. Lijuan Yu: Validation.

Correspondence to Yuzhi Sun or Jialong He.

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Tian, H., Sun, Y., Chen, C. et al. A novel FMECA method for CNC machine tools based on D-GRA and data envelopment analysis. Sci Rep 14, 26596 (2024). https://doi.org/10.1038/s41598-024-77920-7

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Received: 21 June 2024

Accepted: 28 October 2024

Published: 04 November 2024

DOI: https://doi.org/10.1038/s41598-024-77920-7

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