# A Proactive Decision-Making Model for Evaluating the Reliability of Infrastructure Assets of a Railway System

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## Abstract

**:**

## 1. Introduction

- (1)
- The extension of the criticality evaluation factors to include factors like maintainability (MT), safety and environmental impact protection (SEP), and costs of maintenance (CM), which have not been used as reliability and criticality factors in the evaluation of failure modes or when determining the root cause of failure under the reliability evaluation literature as well as for railway infrastructure asset evaluation.
- (2)
- The use of an expert-based approach for determining the root cause of failure in the railway infrastructure assets, which is the first of its kind in this area of research, as it can provide a solution to complex problems by reasoning through large bodies of knowledge and specific human expertise otherwise referred to as experts in this study.
- (3)
- The study also contributes to the reliability study of the railway infrastructure assets by proposing a new PMCDM model that holistically addresses the uncertainties in the evaluation process by using a multi-dimensional membership function that includes real membership, imaginary membership, real non-membership, and imaginary non-membership functions.
- (4)
- Unlike the currently existing reliability management model, the new PMCDM model accounts for some of the reliability quantitative parameters that are otherwise ignored in the currently existing reliability management model.
- (5)
- The new model is flexible and can be used in the evaluation of decision-making problems.

## 2. Methods

#### 2.1. Formation of the PMCDM Model

#### 2.1.1. Interval-Valued Intuitionistic Fuzzy Set (IVIFS)

**Definition 1**

**.**If $X(\ne \varnothing )$ is a given set and $D\left[0,\text{}1\right]$ is a set of all closed subintervals of an interval [0, 1], then IVIFS of A in X is expressed as follows:

**Definition 2**

**.**Let ${\phi}_{i}=\left([{d}_{i},{e}_{i}]\right),[f,{g}_{i}])$ represent the interval-valued intuitionistic fuzzy number (IVIFN) of the interval-valued intuitionistic fuzzy Dombi Heronian mean (IVIIFDHM) operator, which has been selected specifically for the formation of the PMCDM model. For all $i=(\mathrm{1,2},\mathrm{3,4},\dots ..,p)$, the IVIIFDHM operator of dimension n is a mapping IVIIFDHM of ${\mathsf{\Omega}}^{n}\to \mathsf{\Omega}$ such that

#### 2.1.2. Reliability Quantitative Parameters

- Failure rate

- (i)
- Estimation: Failure data obtained from the field are, in most cases, used to estimate the failure rate of a particular system by using statistical analysis techniques [29]. To ensure the accuracy of the failure rate, it is advised that the analyst have a good understanding of equipment and system operation, understand the procedures for data collection, understand the key environmental and physical parameters and variables impacting the failure rates, understand how the equipment is operated at the system level, and finally, understand the type of failure data required.
- (ii)
- Historical data about the device or system under consideration: Many engineering facilities maintain several rules of engagement, including the internal databases of failure information on the devices or systems they operate or produce [30]. With the failure information, the failure rate can be calculated for each device or system. For new devices or systems, the historical data for similar devices or systems can serve as a useful estimate [31].
- (iii)
- Prediction: Time lag is one of the many drawbacks associated with failure rate estimations of engineering systems. According to Mettas [32], failure rate data are concerning; however, when they are available, the system or devices for which the failure information is required have become obsolete. Due to this drawback, failure-rate prediction methods are often deployed to obtain data for the design and maintainability of systems and devices. These methods may be used on newly designed devices to predict the device’s failure rates and failure modes. Two of the most prominent approaches that have found application recently include the life cycle testing method and the failure modes, effects, and diagnostic analysis (FMEDA) method.

**Definition 3.**

- Availability

**Definition 4.**

#### 2.2. PMCDM Model Algorithm and Framework

- Step 1: Request expert opinion from at least two persons with corresponding work experience on the subject matter to evaluate the reliability of the infrastructure assets of a railway system by prioritizing the failure modes of the system. The experts, who should come from both academia and industry, should have at least a first degree in engineering; this is mainly to ensure the integrity of the assessment process.
- Step 2: The identified set of failure modes is subject to some reliability-based criteria. Ask the experts to evaluate the failure modes using a linguistic scale that has a corresponding IVIFN equivalent (see Table 1).
- Step 3: With the gathered experts’ opinions and evaluations, construct the linguistic intuitionistic fuzzy decision matrix of the experts $(M={(x}_{ij}{)}_{mxn}$). Using the IVIFN values in Table 1, convert the $M={(x}_{ij}{)}_{mxn}$ to a numerical matrix. The numerical form of the matrix is given in Equation (9) and is based on the IVIFN.

- Step 4: With the numerical matrix in place, which is provided by the individual experts, the IVIIFDHM operator in Equation (4) is then used for the aggregation of the experts’ preference opinions and evaluation. The aggregation, which allows for the integration of some reliability quantitative parameters like fuzzy failure rate and availability function into the model, is used for the construction of the comprehensive intuitionistic decision matrix $CM={(y}_{ij}{)}_{mxn}$.
- Step 5: Using the intuitionistic entropy originally proposed by Ye [35], the weighted vector of the reliability criteria is computed from $CM={(y}_{ij}{)}_{mxn}$ by using the following mathematical formation:

- Step 6: With the weighted vector, construct a weighted normalization matrix for the reliability criteria. From the matrix, determine the maximum and minimum values and then use them as the intuitionistic fuzzy positive and negative ideal (CIFNI) solution, respectively.
- Step 7: Determine the closeness coefficient values for the failure modes using Equation (11).$${cc}_{i}=\frac{{S}^{-}}{({S}^{-}+{S}^{+})}$$
- Step 8: Rank the failure modes in descending order using the results obtained in Step 7.

## 3. Results and Discussion

#### Numerical Implementation of the Model

- The IVIFS allow for the representation of uncertainty inherent in railway infrastructure reliability assessment.
- The IVIFS-based MCDM model offers greater flexibility in handling multiple criteria and decision factors relevant to railway infrastructure reliability.
- The proactive nature of IVIFS-based MCDM models allows decision-makers to anticipate and mitigate potential reliability issues before they escalate.
- The model involves a complex mathematical computation; consultants, academics, or experts of some sort are identified as the most probable eventual end-users of the developed model, where they may become involved with companies to aid its usage.
- The model may be ideal for a company that wants to ensure flexibility, adjustability, and agility in the management of their product reliability and decision-making process.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Oyefuga, B.; Egbetokun, A. Rebuilding Rail Infrastructure in Nigeria—Policy, Problems and Prospects. In Autumn Conference and Annual Meeting of the Korean Society for Railway; The Korean Society for Railway: Seoul, Republic of Korea, 2016; pp. 1–13. [Google Scholar]
- Wojuade, C.A. Potentials of Light Rail Transit in Nigeria. Int. J. Manag. Sci. Bus. Res.
**2016**, 5, 271–277. [Google Scholar] - Agbaeze, E.K. Boosting Railway System Infrastructure in Nigeria: The Public-Private Partnership Option. J. Bus. Adm. Manag. Sci. Res.
**2014**, 3, 39–48. [Google Scholar] - Ayoola, T.A. Establishment of the Nigerian Railway Corporation. J. Retracing Africa
**2016**, 3, 21–42. [Google Scholar] - Ogochukwu, C.G.; Ogochukwu, O.F.; Ogorchukwu, I.M.; Ebuka, I.A. Assessment of the performance of railway transportation in Nigeria from 1970 to 2010. Sci. Afr.
**2022**, 15, e01120. [Google Scholar] [CrossRef] - Yeh, C.T.; Lin, Y.K.; Yeng, L.C.L.; Huang, P.T. Reliability evaluation of a multistate railway transportation network from the perspective of a travel agent. Reliab. Eng. Syst. Saf.
**2021**, 214, 107757. [Google Scholar] [CrossRef] - Garmabaki, A.H.S.; Marklund, S.; Thaduri, A.; Hedström, A.; Kumar, U. Underground pipelines and railway infrastructure–failure consequences and restrictions. Struct. Infrastruct. Eng.
**2020**, 16, 412–430. [Google Scholar] [CrossRef] - Yu, Z.; Lei, N.; Mo, Y.; Xu, X.; Li, X.; Huang, B. Feature Extraction Based on Self-Supervised Learning for Remaining Useful Life Prediction. J. Comput. Inf. Sci. Eng.
**2024**, 24, 021004. [Google Scholar] [CrossRef] - Song, Z.; Hackl, C.M.; Anand, A.; Thommessen, A.; Petzschmann, J.; Kamel, O.; Braunbehrens, R.; Kaifel, A.; Roos, C.; Hauptmann, S. Digital Twins for the Future Power System: An Overview and a Future Perspective. Sustainability
**2023**, 15, 5259. [Google Scholar] [CrossRef] - Sresakoolchai, J.; Kaewunruen, S. Railway infrastructure maintenance efficiency improvement using deep reinforcement learning integrated with digital twin based on track geometry and component defects. Sci. Rep.
**2023**, 13, 2439. [Google Scholar] [CrossRef] - He, Y.; Zhang, Y.; Yao, Y.; He, Y.; Sheng, X. Review on the Prediction and Control of Structural Vibration and Noise in Buildings Caused by Rail Transit. Buildings
**2023**, 13, 2310. [Google Scholar] [CrossRef] - Zhang, C.; Kordestani, H.; Shadabfar, M. A combined review of vibration control strategies for high-speed trains and railway infrastructures: Challenges and solutions. J. Low Freq. Noise Vib. Act. Control
**2023**, 42, 272–291. [Google Scholar] [CrossRef] - Zhu, Z.; Feng, Y.; Yang, X.; Li, H.; Zou, Y. An efficient parallel computing method for random vibration analysis of a three-dimensional train-track-soil coupled model using Seed-PCG algorithm. J. Cent. South Univ.
**2024**, 31, 302–316. [Google Scholar] [CrossRef] - Zoeteman, A. Life cycle cost analysis for managing rail infrastructure. Eur. J. Transp. Infrastruct. Res.
**2001**, 1, 391–413. [Google Scholar] [CrossRef] - Kefalidou, G.; Golightly, D.; Sharples, S. Identifying rail asset maintenance processes: A human-centric and sensemaking approach. Cogn. Technol. Work
**2018**, 20, 73–92. [Google Scholar] [CrossRef] - Dinmohammadi, F.; Alkali, B.; Shafiee, M. Risk Evaluation of Railway Rolling Stock Failures Using FMECA Technique: A Case Study of Passenger Door System. Urban Rail Transit
**2016**, 2, 128–145. [Google Scholar] [CrossRef] - Al-Douri, Y.K.; Tretten, P.; Karim, R. Improvement of railway performance: A study of Swedish railway infrastructure. J. Mod. Transp.
**2016**, 24, 22–37. [Google Scholar] [CrossRef] - Dindar, S.; Kaewunruen, S.; An, M.; Gigante-Barrera, A. Derailment-based Fault Tree Analysis on Risk Management of Railway Turnout Systems. IOP Conf. Ser. Mater. Sci. Eng.
**2017**, 245, 1–8. [Google Scholar] [CrossRef] - Jafarian, E.; Rezvani, M.A. Application of fuzzy fault tree analysis for evaluation of railway safety risks: An evaluation of root causes for passenger train derailment. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit
**2012**, 226, 14–25. [Google Scholar] [CrossRef] - Khalid, N.I.M.; Najdi, N.F.N.; Adlee, N.F.K.; Misiran, M.; Sapiri, H. Assessing railway accident risk through event tree analysis. AIP Conf. Proc.
**2019**, 2138, 0300231–0300238. [Google Scholar] [CrossRef] - Quiroga, L.M.; Schnieder, E. Monte Carlo simulation of railway track geometry deterioration and restoration. Proc. Inst. Mech. Eng. Part O J. Risk Reliab.
**2012**, 226, 274–282. [Google Scholar] [CrossRef] - Che Hassan, C.R.; Puvaneswaran, B.; Aziz, A.R.; Noor Zalina, M.; Hung, F.C.; Sulaiman, N.M. Quantitative risk assessment for the transport of ammonia by rail. Process Saf. Prog.
**2010**, 29, 60–63. [Google Scholar] [CrossRef] - Chen, Y. Improving Railway Safety Risk Assessment Study. Ph.D. Dissertation, University of Birmingham, Birmingham, UK, 2012. [Google Scholar]
- Shang, H. Maintenance Modelling, Simulation and Performance Assessment for Railway Asset Management. Ph.D. Dissertation, Université de Technologie de Troyes, Troyes, France, 2015. [Google Scholar]
- Ye, J. Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Syst. Appl.
**2009**, 36, 6899–6902. [Google Scholar] [CrossRef] - Atanassov, K.T. Intuitionistic fuzzy sets. Fuzzy Sets Syst.
**1986**, 20, 87–96. [Google Scholar] [CrossRef] - Wu, L.; Wei, G.; Wu, J. Some Interval-Valued Intuitionistic Fuzzy Dombi Heronian Mean Operators and their Application for Evaluating the Ecological Value of Forest Ecological Tourism Demonstration Areas. Int. J. Environ. Res. Public Health
**2020**, 17, 829. [Google Scholar] [CrossRef] [PubMed] - Finkelstein, M. Introduction. In Failure Rate Modelling for Reliability and Risk; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2008; pp. 1–84. [Google Scholar]
- Goble, W.M.; van Beurden, I. Combining field failure data with new instrument design margins to predict failure rates for SIS Verification. In Proceedings of the 2014 International Symposium—Beyond Regulatory Compliance, Making Safety Second Nature, Hilton College Station-Conference Center, College Station, TX, USA, 28–30 October 2014; pp. 1–15. [Google Scholar]
- Aikhuele, D.O. A Study of product development engineering and design reliability concerns. Int. J. Appl. Ind. Eng.
**2018**, 5, 79–89. [Google Scholar] [CrossRef] - Aikhuele, D.O.; Turan, F.M. Need for reliability assessment of parent product before redesigning a new product. Curr. Sci.
**2017**, 112, 10–11. [Google Scholar] - Mettas, A. Design for Reliability: Overview of the Process and Applicable Techniques. Int. J. Perform. Eng.
**2010**, 6, 577–586. [Google Scholar] - Garg, H.; Sharma, S.P.; Rani, M. Weibull fuzzy probability distribution for analyzing the behaviour of pulping unit in a paper industry. Int. J. Ind. Syst. Eng.
**2013**, 14, 395–413. [Google Scholar] [CrossRef] - Garg, H.; Rani, M.; Sharma, S.P. Reliability analysis of the engineering systems using intuitionistic fuzzy set theory. J. Qual. Reliab. Eng.
**2013**, 2013, 943972. [Google Scholar] [CrossRef] - Ye, J. Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Appl. Math. Model.
**2010**, 34, 3864–3870. [Google Scholar] [CrossRef] - Aikhuele, D.O. A hybrid-fuzzy model with reliability-based criteria for selecting consumables used in welding dissimilar aluminum alloys joint. Eng. Appl. Sci. Res.
**2019**, 46, 79–85. [Google Scholar] [CrossRef] - Aikhuele, D.O. Intuitionistic fuzzy hamming distance model for failure detection in a slewing gear system. Int. J. Syst. Assur. Eng. Manag.
**2021**, 12, 884–894. [Google Scholar] [CrossRef]

**Figure 1.**Railway infrastructure assets [24].

Linguistic Terms | IVIFN |
---|---|

Minor (M) | ([0.1, 0.2], [0.1, 0.4]) |

Important (I) | ([0.2, 0.5], [0.2, 0.3]) |

Significant (S) | ([0.3, 0.5], [0.1, 0.3]) |

Major (Ma) | ([0.4, 0.3], [0.1, 0.2]) |

E1 | E2 | E3 | E1 | E2 | E3 | E1 | E2 | E3 | E1 | E2 | E3 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

FF | MT | SEP | CM | |||||||||

FB | I | S | M | M | M | I | Ma | 1 | M | Ma | Ma | M |

BDR | I | I | S | S | Ma | I | Ma | S | M | M | M | I |

DTS | Ma | S | I | Ma | Ma | M | M | M | I | I | I | Ma |

IC | Ma | I | S | M | I | M | M | I | M | S | Ma | I |

PPM | Ma | S | M | Ma | Ma | M | Ma | S | I | Ma | I | M |

TC | Ma | Ma | Ma | Ma | S | I | I | M | S | I | S | M |

SP | I | I | I | S | S | S | Ma | Ma | Ma | S | S | M |

LB | S | S | Ma | M | I | M | M | I | M | I | S | M |

FCW | Ma | Ma | M | Ma | S | M | I | I | I | S | Ma | I |

FPB | M | M | M | Ma | I | M | I | I | Ma | S | S | S |

LAR | M | M | I | Ma | Ma | Ma | S | S | S | Ma | Ma | Ma |

ARD | Ma | S | M | S | S | S | Ma | S | M | Ma | Ma | M |

DD | S | Ma | I | S | S | Ma | M | M | I | I | S | M |

GOP | S | S | S | I | I | Ma | Ma | Ma | Ma | M | I | M |

LP | Ma | I | M | I | S | M | Ma | Ma | M | S | Ma | I |

FF | MT | SEP | CM | |
---|---|---|---|---|

FB | ([0.169, 0.065], [0.254, 0.101]) | ([0.261, 0.090], [0.261, 0.086]) | ([0.125, 0.085], [0.257, 0.111]) | ([0.095, 0.130], [0.335, 0.122]) |

BDR | ([0.155, 0.053], [0.211, 0.115]) | ([0.109, 0.063], [0.261, 0.131]) | ([0.111, 0.085], [0.335, 0.111]) | ([0.261, 0.090], [0.261, 0.086]) |

DTS | ([0.106, 0.064], [0.261, 0.133]) | ([0.095, 0.130], [0.335, 0.122]) | ([0.261, 0.090], [0.261, 0.086]) | ([0.122, 0.063], [0.211, 0.130]) |

IC | ([0.107, 0.064], [0.257, 0.133]) | ([0.257, 0.089], [0.257, 0.087]) | ([0.257, 0.089], [0.257, 0.087]) | ([0.109, 0.063], [0.261, 0.131]) |

PPM | ([0.111, 0.085], [0.335, 0.111]) | ([0.095, 0.130], [0.335, 0.122]) | ([0.106, 0.064], [0.261, 0.133]) | ([0.125, 0.085], [0.257, 0.111]) |

TC | ([0.077, 0.115], [0.335, 0.183]) | ([0.106, 0.064], [0.261, 0.133]) | ([0.170, 0.065], [0.254, 0.099]) | ([0.169, 0.065], [0.254, 0.101]) |

SP | ([0.183, 0.053], [0.183, 0.115]) | ([0.115, 0.053], [0.335, 0.115]) | ([0.077, 0.115], [0.335, 0.183]) | ([0.101, 0.063], [0.335, 0.130]) |

LB | ([0.101, 0.063], [0.335, 0.130]) | ([0.257, 0.089], [0.257, 0.087]) | ([0.257, 0.089], [0.257, 0.087]) | ([0.169, 0.065], [0.254, 0.101]) |

FCW | ([0.095, 0.130], [0.335, 0.122]) | ([0.111, 0.085], [0.335, 0.111]) | ([0.183, 0.053], [0.183, 0.115]) | ([0.109, 0.063], [0.261, 0.131]) |

FPB | ([0.335, 0.183], [0.335, 0.077]) | ([0.125, 0.085], [0.257, 0.111]) | ([0.122, 0.063], [0.211, 0.130]) | ([0.115, 0.053], [0.335, 0.115]) |

LAR | ([0.261, 0.090], [0.261, 0.086]) | ([0.077, 0.115], [0.335, 0.183]) | ([0.115, 0.053], [0.335, 0.115]) | ([0.077, 0.115], [0.335, 0.183]) |

ARD | ([0.111, 0.085], [0.335, 0.111]) | ([0.115, 0.053], [0.335, 0.115]) | ([0.111, 0.085], [0.335, 0.111]) | ([0.095, 0.130], [0.335, 0.122]) |

DD | ([0.109, 0.063], [0.261, 0.131]) | ([0.101, 0.063], [0.335, 0.130]) | ([0.261, 0.090], [0.261, 0.086]) | ([0.169, 0.065], [0.254, 0.101]) |

GOP | ([0.115, 0.053], [0.335, 0.115]) | ([0.122, 0.063], [0.211, 0.130]) | ([0.077, 0.115], [0.335, 0.183]) | ([0.257, 0.089], [0.257, 0.087]) |

LP | ([0.125, 0.085], [0.257, 0.111]) | ([0.169, 0.065], [0.254, 0.101]) | ([0.095, 0.130], [0.335, 0.122]) | ([0.109, 0.063], [0.261, 0.131]) |

FF | MT | SEP | CM | CC_{i} | Ranking | |
---|---|---|---|---|---|---|

CR | 0.3453 | 0.3460 | 0.2474 | 0.2206 | ||

FB | ([0.058, 0.022], [0.088, 0.035]) | ([0.090, 0.031], [0.090, 0.030]) | ([0.203, 0.191], [0.147, 0.597]) | ([0.021, 0.029], [0.074, 0.027]) | 0.529 | 3 |

BDR | ([0.054, 0.018], [0.073, 0.040]) | ([0.038, 0.022], [0.090, 0.045]) | ([0.214, 0.203], [0.170, 0.597]) | ([0.058, 0.020], [0.058, 0.019]) | 0.816 | 1 |

DTS | ([0.037, 0.022], [0.090, 0.046]) | ([0.033, 0.045], [0.116, 0.042]) | ([0.162, 0.149], [0.064, 0.597]) | ([0.027, 0.014], [0.046, 0.029]) | 0.349 | 15 |

IC | ([0.037, 0.022], [0.089, 0.046]) | ([0.089, 0.031], [0.089, 0.030]) | ([0.163, 0.150], [0.065, 0.597]) | ([0.024, 0.014], [0.058, 0.029]) | 0.471 | 10 |

PPM | ([0.038, 0.030], [0.116, 0.038]) | ([0.033, 0.045], [0.116, 0.042]) | ([0.212, 0.198], [0.163, 0.597]) | ([0.027, 0.019], [0.057, 0.024]) | 0.531 | 2 |

TC | ([0.027, 0.040], [0.116,0.063]) | ([0.037, 0.022], [0.090, 0.046]) | ([0.189, 0.177], [0.119, 0.597]) | ([0.037, 0.014], [0.056, 0.022]) | 0.478 | 14 |

SP | ([0.063, 0.018], [0.063, 0.040]) | ([0.040, 0.018], [0.116, 0.040]) | ([0.232, 0.217], [0.201, 0.597]) | ([0.022, 0.014], [0.074, 0.029]) | 0.482 | 13 |

LB | ([0.035, 0.022], [0.116, 0.045]) | ([0.089, 0.031], [0.089, 0.030]) | ([0.163, 0.150], [0.065, 0.597]) | ([0.037, 0.014], [0.056, 0.022]) | 0.515 | 4 |

FCW | ([0.033, 0.045], [0.116, 0.042]) | ([0.038, 0.030], [0.116, 0.038]) | ([0.181, 0.165], [0.099, 0.597]) | ([0.024, 0.014], [0.058, 0.029]) | 0.497 | 11 |

FPB | ([0.116, 0.063], [0.116, 0.027]) | ([0.043, 0.030], [0.089, 0.038]) | ([0.203, 0.188], [0.143, 0.597]) | ([0.025, 0.012], [0.074, 0.025]) | 0.508 | 7 |

LAR | ([0.090, 0.031], [0.090, 0.030]) | ([0.027, 0.040], [0.116, 0.063]) | ([0.214, 0.202], [0.169, 0.597]) | ([0.017, 0.025], [0.074, 0.040]) | 0.498 | 10 |

ARD | ([0.038, 0.030], [0.116, 0.038]) | ([0.040, 0.018], [0.116, 0.040]) | ([0.214, 0.203], [0.170, 0.597]) | ([0.021, 0.029], [0.074, 0.027]) | 0.494 | 12 |

DD | ([0.038, 0.022], [0.090, 0.045]) | ([0.035, 0.022], [0.116, 0.045]) | ([0.162, 0.149], [0.064, 0.597]) | ([0.037, 0.014], [0.056, 0.022]) | 0.501 | 9 |

GOP | ([0.040, 0.018], [0.116, 0.040]) | ([0.042, 0.022], [0.073, 0.045]) | ([0.232, 0.217], [0.201, 0.597]) | ([0.057, 0.020], [0.057, 0.019]) | 0.502 | 8 |

LP | ([0.043, 0.030], [0.089, 0.038]) | ([0.059, 0.023], [0.088, 0.035]) | ([0.219, 0.207], [0.179, 0.597]) | ([0.024, 0.014], [0.058, 0.029]) | 0.512 | 6 |

P and Q | CC_{i} | Ranking | P and Q | CC_{i} | Ranking | |
---|---|---|---|---|---|---|

FB | P = 0.002, q = 0.0001 | 0.529 | 3 | P = 0.002, q = 0.999 | 0.550 | 2 |

BDR | 0.816 | 1 | 0.840 | 1 | ||

DTS | 0.349 | 15 | 0.425 | 15 | ||

IC | 0.471 | 14 | 0.473 | 14 | ||

PPM | 0.531 | 2 | 0.503 | 5 | ||

TC | 0.478 | 13 | 0.501 | 8 | ||

SP | 0.482 | 12 | 0.496 | 12 | ||

LB | 0.515 | 4 | 0.502 | 6 | ||

FCW | 0.497 | 10 | 0.500 | 9 | ||

FPB | 0.508 | 6 | 0.504 | 4 | ||

LAR | 0.498 | 9 | 0.498 | 11 | ||

ARD | 0.494 | 11 | 0.496 | 12 | ||

DD | 0.501 | 8 | 0.500 | 9 | ||

GOP | 0.502 | 7 | 0.502 | 6 | ||

LP | 0.512 | 5 | 0.506 | 3 |

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**MDPI and ACS Style**

Aikhuele, D.O.; Sorooshian, S.
A Proactive Decision-Making Model for Evaluating the Reliability of Infrastructure Assets of a Railway System. *Information* **2024**, *15*, 219.
https://doi.org/10.3390/info15040219

**AMA Style**

Aikhuele DO, Sorooshian S.
A Proactive Decision-Making Model for Evaluating the Reliability of Infrastructure Assets of a Railway System. *Information*. 2024; 15(4):219.
https://doi.org/10.3390/info15040219

**Chicago/Turabian Style**

Aikhuele, Daniel O., and Shahryar Sorooshian.
2024. "A Proactive Decision-Making Model for Evaluating the Reliability of Infrastructure Assets of a Railway System" *Information* 15, no. 4: 219.
https://doi.org/10.3390/info15040219