Reliability Prediction for New Prefabricated Track Structures Based on the Fuzzy Failure Modes, Effects, and Criticality Analysis Method

: This paper aims to address the problems of safety and durability in China’s ballastless track structures, particularly the lack of accurate analysis and methods for predicting the reliability of the new type of prefabricated track structure during the design phase. We propose a reliability prediction method for a new prefabricated track structure, the modular assembled track structure with built-in position retention. By adopting the fuzzy Failure Modes, Effects, and Criticality Analysis (fuzzy FMECA) method, a comprehensive assessment of fault severity, fault occurrence probability, and fault detection difficulty is conducted on the CRTS II slab track structure and the modular assembled track structure with built-in position retention. Consequently, a fault mode hazard assessment model for the new prefabricated track structure is constructed. Based on the assessment model and using a similar product method, a reliability prediction model for the new prefabricated track structure is established, and reliability prediction for the track structure is conducted. The research results indicate that the modular assembled track structure with built-in position retention has lower hazard levels and higher reliability compared to the CRTS II slab track structure. This study provides a scientific basis for the design optimization of new prefabricated track structures, helping to improve their safety and reliability, reduce operating and maintenance costs, and thereby promote the green and low-carbon development of the railway.


Introduction
The ballastless track structure of high-speed railway refers to the track structure that replaces the ballast with a monolithic foundation such as a concrete or asphalt mixture.Due to its various advantages such as good stability, long-lasting geometric dimensions, low maintenance workload, high durability, small secondary dead load of bridges, small clear area of tunnels, and high comprehensive economic benefits [1][2][3], it has become the preferred choice for high-speed railway track structures worldwide.Currently, the primary method for ballastless track construction involves prefabricating track slabs in factories, while the base slab and filling layer are constructed on-site [4].However, several issues exist in this method, including heavy on-site wet work, difficulty in precision control, poor quality stability, and high construction costs [5][6][7], which hinder the green and low-carbon progress of the railway industry.
The new prefabricated track structure involves prefabricating track components in factories and transporting them to the construction site for rapid assembly.Compared to traditional ballastless track structures, it boasts advantages like convenient construction, a shorter construction period, better stability, and reduced labor force requirements.The structure comprises high-precision prefabricated track slabs, fastening systems, elastic pads, and other connecting components, facilitating efficient and precise track laying.Its defining feature is the utilization of prefabricated components for on-site assembly.This approach not only increases construction efficiency but also meets the rigorous demands of highspeed, heavy-duty, high-volume, and high-density railway transportation.Consequently, it significantly improves wheel-rail contact and optimizes stress and strain distribution across various track components, thereby effectively prolonging the lifespan of the equipment and postponing the maintenance cycles.Through a combination of factory production and on-site assembly, the application of prefabricated track structures is becoming increasingly widespread in modern railways [8], urban rail transit [9], and other related fields.
The National Engineering Research Center of High-speed Railway Construction Technology (Changsha, China) has proposed a new track structure, namely, the modular assembled track structure, with built-in position retention [10].This structure aims to tackle the issues inherent in traditional track structures, improve the assembly rate, stability, and safety of the track structure, and reduce labor costs, construction costs, as well as operation and maintenance costs on site.This promotes the further advancement of rail transit technology.Accurate analysis and prediction of the reliability of the new prefabricated track structure during the schematic design phase can help identify possible failure modes, causes, and impacts during use.This determination of reliability levels aids in selecting the optimal scheme, thereby enhancing the safety and durability of the rail transit system while reducing operational and maintenance costs.This promotes green and low-carbon development in the railway industry.
Reliability refers to the ability of a product to perform its intended function under specified conditions and within a specified time interval [11].The core of engineering structure reliability research is to solve the scientific measurement problem of structural safety under random conditions [12].Traditional reliability analysis methods are mainly in two categories, probability-based methods and model-based methods [13].
(1) Probability-based methods: In 1926, Mayer first systematically discussed the idea of using probability theory to study the safety of structures in his book Structural Safety.Since then, related research has continued to emerge.Probability-based methods can be further divided into two categories: precise method and approximation method.
The precise method, also known as the full probability method [14], involves solving the structural failure probability through the probability density function of precise resistance and load models.The approximation method serves as a substitute for the precise method and includes techniques such as the First-Order Second-Moment (FOSM) central point method [15], the FOSM design point method [16], and the JC method [17].Probability-based methods rely on probability theory and statistical analysis to assess the likelihood of a system operating successfully under given conditions.These methods typically provide precise quantification of uncertainties and offer comprehensive reliability evaluations.However, they often require a significant amount of historical data or performance parameters from similar systems to establish probability models.However, in the schematic design phase of the new prefabricated track structure, it is difficult to obtain historical data or performance parameters of similar systems, which restricts the application of this precise method.(2) Model-based methods: Model-based methods predict product failure times through deterministic Physics of Failure (PoF) models [18], assuming that uncertainties affecting failure times stem from random variations in model parameters.Product reliability is then estimated using analytical methods or Monte Carlo simulation [19,20].The accuracy of these results heavily relies on the precision and completeness of the established model.However, in the schematic design phase of the new prefabricated track structure, due to a lack of sufficient information to establish an accurate model, the application of these methods has also been somewhat limited.
Since traditional methods are not available, the main reliability prediction methods used in the schematic design phase are the performance parameter method and the similar product method [21].The performance parameter method [22] is based on statistical analysis of the relationship between performance parameters and the reliability of a large number of similar systems, deriving empirical formulas and coefficients.The similar product method [23] utilizes the experience and data from existing similar products to predict the reliability of new products.However, for new prefabricated track structures, due to a lack of performance parameters from similar systems, these two methods have certain limitations in predicting their reliability.
Therefore, this paper proposes a reliability prediction method for prefabricated track structures based on fuzzy Failure Modes, Effects, and Criticality Analysis (fuzzy FMECA [24]).It integrates the expert survey method, similar product method, fuzzy comprehensive evaluation method, and FMECA [25].The outline of this paper is as follows: Section 2 introduces the principles of the fuzzy FMECA method.Section 3 uses the fuzzy FMECA method to conduct a comprehensive assessment of fault severity, fault occurrence probability, and fault detection difficulty for the CRTS II slab track structure and the modular assembled track structure with built-in position retention.Consequently, a fault mode hazard assessment model for the new prefabricated track structure is constructed.Section 4 utilizes the similar product method to establish a reliability prediction model for the new prefabricated track structure and carries out reliability prediction for the track structure, verifying the effectiveness of the proposed method.

The Fuzzy FMECA Method
FMECA is a method used to identify and assess potential failure modes in a system or product, their impact on the system or product, and to determine corresponding countermeasures and optimization plans [23].FMECA is a fundamental task for identifying the weak links and critical items in the reliability of a new prefabricated track structure system.Through FMECA, basic information for evaluating and improving system reliability can be systematically obtained, providing data support for enhancing the overall performance of the track structure [26,27].
However, in engineering practice, fault information often exhibits complex, uncertain, and even fuzzy characteristics.Traditional FMECA methods may have limitations when dealing with such information, unable to meet the high requirements of accuracy and reliability in evaluation work.To more accurately process this fuzzy information and improve the accuracy and reliability of evaluation results, relevant theories and methods of fuzzy mathematics are introduced based on FMECA, leading to the development of the fuzzy FMECA method [28].
The analysis steps for the fuzzy FMECA method [29] are as follows.

Construct the Factor Set
The factor set is a collection of factors that influence the evaluation object and is represented as where u i represents the ith influencing factor.

Constructing the Evaluation Set
The evaluation set is a collection of rating levels that experts may assign to each potential influencing factor.The rating levels can be quantitative values or qualitative descriptions.The evaluation set is represented as where v i represents the jth rating level.

Constructing the Fuzzy Evaluation Matrix
The evaluation team consists of h experts.Each expert can assign only one rating level to the ith influencing factor of failure mode k.The number of experts who assigned each rating level is recorded as h k ij , and the corresponding membership degree is denoted as r k ij .Therefore, the evaluation set for the ith influencing factor of failure mode k is The fuzzy evaluation matrix for failure mode k is

Constructing the Weight Vector
The weight vector, denoted as W, consists of the weights representing the importance of each influencing factor on the failure mode.The determination of factor weights can be done through subjective weighting methods or objective weighting methods.Subjective weighting methods rely on expert experience and judgment, such as the Delphi method or the Analytic Hierarchy Process (AHP).Objective weighting methods are based on data and mathematical models such as entropy weighting or principal component analysis.In this paper, the entropy weighting method is used to construct the weight vector.The entropy weighting method is a multi-criteria weight determination method based on information entropy theory, which transforms the information entropy between indicators into weight coefficients.The specific steps are as follows.

Calculate the Entropy Value
The entropy value measures the amount of information in a random variable.A lower entropy value suggests less uncertainty and less impact on the evaluation, while a higher entropy value indicates greater uncertainty and a stronger influence on the results.Taking the fuzzy evaluation matrix R k for failure mode k as an example, the entropy value for the ith influencing factor is calculated as

Construct the Weight Vector
The weight vector W is used to represent the weight vector for failure mode k.The weight for the ith influencing factor of failure mode k, denoted as w k i , is calculated as

Determine the Criticality
The criticality of a failure mode refers to the severity of the potential harm it may cause to the system, equipment, product, or service.It is a relative measure of the consequences and the occurrence probability of the failure mode.The criticality of failure mode k is denoted as C k and can be calculated as The product criticality refers to the expected number of specific types of product failures caused by the failure modes of a product under specific operating conditions.The specific type is represented by the severity category of the product failure mode.For a specific severity category and operating phase, the product criticality is the sum of the criticalities of the failure modes in that severity category.The product criticality for product r, denoted as C r , where k represents the number of failure modes for product r, can be calculated as

Composition of Track Structures
The composition of the CRTS II slab track structures is similar for embankment, tunnel, and bridge sections.It consists of steel rails, fasteners, prefabricated track slabs, CA (cement asphalt) mortar layer, and base plates (see Figure 1 [30]).the modular assembled track structure with built-in position retention [10] mainly consists of steel rails, fasteners, prefabricated track slabs, an intermediate layer with elastic damping pads, base plates, and prefabricated limit pressure rings (see Figure 2).

Determine the Criticality
The criticality of a failure mode refers to the severity of the potential harm it may cause to the system, equipment, product, or service.It is a relative measure of the consequences and the occurrence probability of the failure mode.The criticality of failure mode k is denoted as  and can be calculated as The product criticality refers to the expected number of specific types of product failures caused by the failure modes of a product under specific operating conditions.The specific type is represented by the severity category of the product failure mode.For a specific severity category and operating phase, the product criticality is the sum of the criticalities of the failure modes in that severity category.The product criticality for product r, denoted as  , where k represents the number of failure modes for product r, can be calculated as 3. Fuzzy FMECA for New Prefabricated Track Structures

Composition of Track Structures
The composition of the CRTS II slab track structures is similar for embankment, tunnel, and bridge sections.It consists of steel rails, fasteners, prefabricated track slabs, CA (cement asphalt) mortar layer, and base plates (see [30]). the modular assembled track structure with built-in position retention [10] mainly consists of steel rails, fasteners, prefabricated track slabs, an intermediate layer with elastic damping pads, base plates, and prefabricated limit pressure rings (see ).

FMECA of Track Structures
The main steps of the FMECA for track structures include defining the system to be analyzed, drawing functional and reliability block diagrams, identifying failure modes, causes, effects, and detection methods, filling out the FMECA analysis table, and obtaining expert ratings for the failure severity, the failure occurrence, and the difficulty of fault

FMECA of Track Structures
The main steps of the FMECA for track structures include defining the system to be analyzed, drawing functional and reliability block diagrams, identifying failure modes, causes, effects, and detection methods, filling out the FMECA analysis table, and obtaining expert ratings for the failure severity, the failure occurrence, and the difficulty of fault detection.The rating criteria [31] are outlined in Tables 1-3.Following guidelines from the Guide to failure mode, effects and criticality analysis [32] and the Guide to failure modes, effects and criticality analysis for space products [33], and considering project-specific circumstances, FMECA is conducted on the key components of the track structure.The results of the CRTS II slab track structure analysis are provided in Appendix A, while the results for the modular assembled track structure with built-in position retention are provided in Appendix B.

Fuzzy FMECA of Track Structures
Based on the principles and steps of fuzzy FMECA described in Section 2, a fuzzy FMECA is conducted for the CRTS II slab track structure and the modular assembled track structure with built-in position retention.The analysis process is as follows:

Construction of Factor Set
Construct a factor set U consisting of three influencing factors: the failure severity, the failure occurrence, and the difficulty of fault detection, denoted as u 1 , u 2 , u 3 , respectively.Thus, U = {u 1 , u 2 , u 3 }.

Construction of Evaluation Set
A panel of five experts from China Railway Guangzhou Group Co., Ltd.(Canton, China), National Engineering Research Center of High-speed Railway Construction Technology, and Central South University forms the evaluation team.The expert information is shown in Table 4. Based on the rating criteria in Tables 1-3, the experts assign scores for each failure mode of the two track structures.The membership values are calculated using Equation (3).The membership values for the CRTS II slab track structure are shown in Table 5, while those for the modular assembled track structure with built-in position retention are shown in Table 6.

Determining Criticality
Using Equation ( 8), the criticality value for failure mode MA3 of the CRTS II slab track structure can be calculated as C 3 = 3.550.
Similarly, the criticality value for other failure modes can be determined, as shown in Table 7.Using Equation ( 9), the overall criticality value for the CRTS II slab track structure can be calculated as C 0 = 34.7464,and the overall criticality value for the modular assembled track structure with built-in position retention can be calculated as C 1 = 33.5803.

Reliability Prediction for New Prefabricated Track Structures
Reliability prediction refers to the quantitative estimation of system reliability during the schematic design phase, aiming to forecast the reliability performance of the system under practical use.Reliability prediction is typically based on factors such as historical reliability data of similar products, system composition and structural characteristics, and operating environment to estimate the reliability of system components and the overall system.Reliability prediction is a comprehensive process that starts from the bottom, progresses from local to global, and from small to large.

Reliability Prediction Model Based on a Similar Product Method
The basic principle of the similar product method [23] is as follows: assuming that a new model product is similar to an old model product, it can be assumed that they have the same ratio between their failure rates and the number of defects.If the number of defects in the old model product is d 0 and the failure rate is λ 0 , then we have where k is the ratio between the failure rate and the number of defects.
If the number of defects in the new model product is d r and the failure rate is λ r , then we have λ r = kd r (11) Furthermore, considering the reliability function Based on Equations ( 10)-( 12), the reliability R r of the new model product and the reliability R 0 of the old model product satisfy In FMECA work, failure modes and severity are important indicators for assessing and predicting product reliability.Failure mode refers to the manifestation of product failures, while severity represents the comprehensive importance of failure modes.The similar product method is a commonly used reliability prediction method, but the concept of the number of defects is difficult to apply in practice.Therefore, severity can be used as a substitute for the number of defects.The new reliability prediction model becomes

Reliability Prediction
According to the Key Supported Project of the National Natural Science Foundation of China and the High-Speed Railway Joint Fund, U1434204, Research Report on the Long-Term Behavior of Ballastless Track-Bridge System for High-Speed Rail [34], the initial reliability indicators for the CRTS II slab track structure are 5.890 for the track slab, 3.964 for the CA mortar layer, and 3.273 for the baseplate.
The calculated value of failure probability P f and the reliability indicator β satisfy [35] where Φ(•) represents the standard normal distribution function.
The relationship between failure probability F(t) and reliability R(t) is [36] The reliability R s (t) of a series system and the reliability R i (t) of a unit satisfy [14]   R s The track slab, CA mortar layer, and baseplate of the CRTS II slab track structure are regarded as a series system.Based on Equations ( 15)-( 17), the reliability of the CRTS II slab track structure is R 0 = 0.9994.Based on the analysis in Section 3 of this paper, the overall criticality value of the CRTS II slab track structure is C 0 = 34.7464and the overall criticality value of the modular assembled track structure with built-in position retention is C 1 = 33.5803.Based on Equation ( 14), the reliability of the modular assembled track structure with built-in position retention can be predicted to be R 1 = 0.9994.

Discussion
Based on the aforementioned research, this paper describes an in-depth analysis of various fault modes and their hazard levels for the key components of the modular assembled track structure with built-in position retention.Accordingly, the optimization suggestions are proposed to further enhance the reliability of the new prefabricated track structure as follows: (1) For the EPDM interlayer, considering the failure mode of severe rupture or deformation of the EPDM interlayer (MB7), during the structural design phase, it is essential to comprehensively consider multiple factors such as stress concentration caused by train loads, temperature changes, and corrosive environmental factors to improve the durability of the interlayer.Strict quality control of the interlayer products should be implemented to ensure they meet relevant quality requirements.During the construction phase, special attention should be paid to the construction quality of this part to ensure installation precision and craftsmanship quality.
(2) For the UHPC limiting ring, considering the failure mode of crushing of the UHPC limiting ring (MB12), in the UHPC material selection phase, it is crucial to fully consider the surface resistance to mechanical impact and wear, as well as stress concentration problems caused by train loads and temperature changes, to enhance the durability of the position retention ring.The structural form and dimensions of the position retention ring should be optimized to reduce the frequency of faults.Similarly, strict quality control during the construction of this part should be implemented to ensure it meets the design requirements.
(3) For failure modes M2 and M6, although these fault modes are common issues in almost all track structures, including the new prefabricated track structure, this paper still recommends strengthening the design optimization of these parts.If economically feasible, materials with higher strength and better durability should be preferred.Sufficient attention should also be given to the construction quality of these parts to ensure their long-term stable operation.

Conclusions
This study conducted reliability analysis and prediction of a new type of prefabricated track structure using the fuzzy FMECA method, and the main conclusions are as follows: 1.
The overall criticality value of the two track structures was calculated using the fuzzy FMECA method.The overall criticality value of the CRTS II slab track structure was 34.7464, while the overall criticality value of the modular assembled track structure with built-in position retention was 33.5803, which indicates that the latter has lower criticality.

2.
A reliability prediction model based on the similar product method was established, and the reliability of the modular assembled track structure with built-in position retention was quantitatively estimated.According to the reliability prediction model, the reliability of the modular assembled track structure with built-in position retention is 0.9994, which indicates a high level of reliability.
This study provides a scientific basis and relevant recommendations for the design optimization of a new type of prefabricated track structure, which helps to improve their safety and reliability, reduce operation and maintenance costs, and thereby promote the green and low-carbon development of the rail transit industry.
The data on the number of faults and the period of the CRTS II slab track structure analyzed in this study are not publicly available due to the data safety policies of the railway operation and maintenance companies.Therefore, we will further conduct scaled and full-scale experiments on the mechanical properties, failure processes, and durability of the CRTS II slab track structure and the new prefabricated track structure to obtain firsthand data on their reliability-related performance.This will help us to further improve the proposed reliability prediction method for the new type of prefabricated track structure in this work.Additionally, applying the reliability prediction method proposed in this study to other types of track structures is also a task that needs to be carried out in the future.

Figure 1 .
Figure 1.Structure diagram of the CRTS II slab track.(a) cross section of 1/2 track structure, (b) narrow joint, (c) longitudinal connection of the slack adjuster.

Figure 1 .
Figure 1.Structure diagram of the CRTS II slab track.(a) cross section of 1/2 track structure, (b) narrow joint, (c) longitudinal connection of the slack adjuster.

17 Figure 2 .
Figure 2. Structure diagram of the built-in limit module assembly track.

Figure 2 .
Figure 2. Structure diagram of the built-in limit module assembly track.

Table 6 .
Membership values for modular assembled track structure with built-in position retention.

Table 3 .
Difficulty of fault detection (D) rating criteria.

Table 4 .
Details of the experts.

Table 5 .
Membership values for the CRTS II slab track structure.

Table 7 .
Criticality values for track structure failure modes.