# Risk Assessment of Bauxite Maritime Logistics Based on Improved FMECA and Fuzzy Bayesian Network

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

- (1)
- Maritime Logistics Risk.

- (2)
- Risk Assessment Methods in Maritime Logistics.

- (3)
- Research Gap.

## 3. Construction of Risk Assessment Model for Bauxite Maritime Supply Chain Based on FBN

#### 3.1. Determination of Risk Characterization Parameters

#### 3.1.1. Construction of Risk Characterization Parameter System

#### 3.1.2. Risk Parameter Weighting Based on AHP-Entropy Weight Method

- (1)
- AHP

- (2)
- Entropy method

- (3)
- Determine the overall weight

#### 3.2. Determining the Magnitude of Risk Index Based on Fuzzy Logic

#### 3.2.1. Fuzzy Rating Indication

#### 3.2.2. Fuzzy Rating Result Calculation

- (1)
- Calculate the arithmetic mean of the trapezoidal fuzzy numbers as ${\stackrel{~}{R}}_{m}=\left({a}_{im}^{j},{b}_{im}^{j},{c}_{im}^{j},{d}_{im}^{j}\right)$, among:$${a}_{im}{}^{j}=\frac{1}{n}{\displaystyle \sum _{k=1}^{n}{a}_{ik}^{j}}{b}_{im}{}^{j}=\frac{1}{n}{\displaystyle \sum _{k=1}^{n}{b}_{ik}^{j}}{c}_{im}{}^{j}=\frac{1}{n}{\displaystyle \sum _{k=1}^{n}{c}_{ik}^{j}}{d}_{im}{}^{j}=\frac{1}{n}{\displaystyle \sum _{k=1}^{n}{d}_{ik}^{j}}$$
- (2)
- Calculate and measure the distance between ${R}_{k}\mathrm{and}{\stackrel{~}{R}}_{m}$.$$d({R}_{k},{\tilde{R}}_{m})=\frac{1}{4}(\left|{a}_{ik}^{j}-{a}_{im}^{j}\right|+\left|{b}_{ik}^{j}-{b}_{im}^{j}\right|+\left|{c}_{ik}^{j}-{c}_{im}^{j}\right|+\left|{d}_{ik}^{j}-{d}_{im}^{j}\right|)$$
- (3)
- Calculate the similarity between ${R}_{k}$ and ${\stackrel{~}{R}}_{m}$. For trapezoidal fuzzy numbers ${R}_{k}=({a}_{ik}^{j},{b}_{ik}^{j},{c}_{ik}^{j},{d}_{ik}^{j})$, if ${\stackrel{~}{R}}_{m}=({a}_{im}^{j},{b}_{im}^{j},{c}_{im}^{j},{d}_{im}^{j})$ is their mean value, then$$s({R}_{k},{\tilde{R}}_{m})=1-\frac{d({R}_{k},{\tilde{R}}_{m})}{{\displaystyle \sum _{k=1}^{n}}d({R}_{k},{\tilde{R}}_{m})}$$
- (4)
- Fuzzy number assembly.

#### 3.3. Identification of Failure Mode of Bauxite Ocean Maritime Logistics

#### 3.4. Constructing a Fuzzy Rule Database System Based on a Confidence Structure

#### 3.5. Bayesian Network Construction

_{1}, S

_{1}, and D

_{2}, the probability of child node ${C}_{m}\left(m=1,2,\cdots ,5\right)$ is $\left(0.75,0.25,0,0,0\right)$, or it can be expressed as $P\left({C}_{m}|{O}_{1},{S}_{1},{D}_{1}\right)=\left(0.75,0.25,0,0,0\right)$. Therefore, the fuzzy rule library of the confidence structure can be transformed into the form of the conditional probability distribution.

#### 3.6. Use the Utility Function to Sort the Criticality

#### 3.7. Maritime Logistics System Risk Assessment

- (1)
- The steps of the DS evidence fusion method based on weight distribution and the matrix analysis are as follows: assuming that the matrix $A=\left({a}_{1},{a}_{2},{a}_{3},{a}_{4},{a}_{5}\right),B=\left({b}_{1},{b}_{2},{b}_{3},{b}_{4},{b}_{5}\right),C=\left({c}_{1},{c}_{2},{c}_{3},{c}_{4},{c}_{5}\right)$, multiply A by B, transpose of the matrix, and obtain the matrix M
_{1}.$${M}_{1}={A}^{T}\times B=\left(\begin{array}{ccc}{a}_{1}\times {b}_{1}& \cdots & {a}_{1}\times {b}_{5}\\ \vdots & & \vdots \\ {a}_{5}\times {b}_{1}& \cdots & {a}_{5}\times {b}_{5}\end{array}\right)$$ - (2)
- In the matrix M
_{1}, the sum of the non-main diagonal elements is the degree of conflict between the risk factors A and B.

_{1}should be multiplied with matrix C to obtain matrix M

_{2}.

_{1}and M

_{2}. Following the same steps, a limited number of remaining risk factors can be merged, and the conflict degree K of all risk factors can be obtained.

- (3)
- Use the improved synthetic formula for weight distribution to calculate the following.

#### 3.8. Sensitivity Analysis

**Axiom**

**1.**

**Axiom**

**2.**

## 4. Risk Assessment of Bauxite Maritime Logistics

#### 4.1. Failure Mode Criticality Assessment

#### 4.2. Risk Assessment of Bauxite Maritime Logistics System

#### 4.3. Sensitivity Analysis Results

## 5. Conclusions

- (1)
- A systematic risk assessment model is proposed, which can carry out a risk assessment of the system from the local and overall dimensions and can effectively improve the scientificity and accuracy of the risk assessment of the system in an uncertain environment.
- (2)
- The improved FMECA can effectively overcome the limitations of the traditional FMECA method, making it more suitable for the field of risk analysis, and improving the reliability and rationality of the risk assessment.
- (3)
- The improved ER theory is used to realize the assessment of the overall system risk of maritime logistics, which provides a new perspective for the field of risk assessment.
- (4)
- The proportional method combined with parameter weights is applied to construct the fuzzy rule base, and to rationalize the confidence distribution in the fuzzy rule base.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Experts | Position | Company | Working Experience |
---|---|---|---|

1 | A professor, head of port management studies | A university in China | Involved in maritime transport safety management and maritime supply chain management |

2 | Senior operational managers | A leading port in China | Involved in port safety and operational services |

3 | A qualified master mariner | A shipping company in China | Involved in bauxite international transportation |

4 | Senior security officers | A bauxite company in China | Involved in bauxite customs and transport security |

Risk Parameter | Local Weight | Overall Weight | ||
---|---|---|---|---|

Occurrence likelihood (O) | 0.30 | 0.30 | ||

Difficulty of detection (D) | 0.25 | 0.25 | ||

Severity of consequences (S) | Time delay/disruption (ST) | 0.45 | 0.25 | 0.11 |

Additional cost (SC) | 0.53 | 0.24 | ||

Safety and security loss (SF) | 0.22 | 0.10 |

Grade | Linguistic Variables | Definition | Fuzzy Number |
---|---|---|---|

O_{1} | Low | Occurs less than once a year | (0, 0, 1, 2) |

O_{2} | Relatively low | Expected to happen every few months | (0.5, 2, 3, 4.5) |

O_{3} | Medium | Expected at least once a month | (3, 4, 6, 7) |

O_{4} | Relatively high | Expected at least once a week | (5.5, 7, 8, 9.5) |

O_{5} | High | Expected at least once a day | (8, 9, 10, 10) |

Grade | Linguistic Variables | Definition | Fuzzy Number |
---|---|---|---|

D_{1} | Easy | Can be easily found through risk inspection | (0, 0, 1, 2) |

D_{2} | Relatively easy | Can be detected through regular risk inspection | (0.5, 2, 3, 4.5) |

D_{3} | Medium | Not easily detected by regular risk inspection | (3, 4, 6, 7) |

D_{4} | Relatively hard | May be detected through rigorous risk inspection | (5.5, 7, 8, 9.5) |

D_{5} | Difficult | Unable or difficult to pass rigorous risk inspections | (8, 9, 10, 10) |

Grade | Linguistic Variables | Definition | Fuzzy Number |
---|---|---|---|

ST_{1} | Short | Delay time less than 6 h | (0, 0, 1, 2) |

ST_{2} | Relatively short | The delay time does not exceed 5% of the planned transportation time | (0.5, 2, 3, 4.5) |

ST_{3} | Medium | The delay time exceeds the planned transportation time by 5–20% | (3, 4, 6, 7) |

ST_{4} | Relatively long | The delay time exceeds the planned transportation time by 20–40% | (5.5, 7, 8, 9.5) |

ST_{5} | Long | The delay time exceeds 40% of the planned transportation time | (8, 9, 10, 10) |

Grade | Linguistic Variables | Definition | Fuzzy Number |
---|---|---|---|

SC_{1} | Few | No more than 1% of the total cost | (0, 0, 1, 2) |

SC_{2} | Relatively few | 2–5% over the total cost | (0.5, 2, 3, 4.5) |

SC_{3} | Medium | Over 6–20% of the total cost | (3, 4, 6, 7) |

SC_{4} | Relatively many | 21–40% over the total cost | (5.5, 7, 8, 9.5) |

SC_{5} | Much | More than 40% of the total cost | (8, 9, 10, 10) |

Grade | Linguistic Variables | Definition | Fuzzy Number |
---|---|---|---|

SF_{1} | Light | The goods, equipment, or system are slightly damaged, but the functions are complete, and the maintenance is convenient and fast; the number of minor injuries does not exceed 2 | (0, 0, 1, 2) |

SF_{2} | Relatively light | The equipment or system is slightly damaged, and the maintenance is more convenient; the damage rate of the goods is 1–5%; three people or more have been slightly injured | (0.5, 2, 3, 4.5) |

SF_{3} | Medium | Equipment or system is medium-damaged, and maintenance is not convenient; the proportion of cargo damage reaches 5–10%; 1–2 people are medium-injured | (3, 4, 6, 7) |

SF_{4} | Relatively serious | The equipment or system is seriously damaged and inconvenient to maintain; the damage rate of goods reaches 10–20%; 1–2 people are seriously injured | (5.5, 7, 8, 9.5) |

SF_{5} | Severe | The equipment or system is seriously damaged, and transportation cannot be carried out; the proportion of goods damaged is more than 20%; personnel deaths occur | (8, 9, 10, 10) |

Symbol | Failure Mode |
---|---|

FM_{1} | Worker riots |

FM_{2} | Port congestion |

FM_{3} | Improper operation by the crew |

FM_{4} | Piracy or terrorist attack |

FM_{5} | Terrible sea conditions |

FM_{6} | Bauxite-free surface effect |

FM_{7} | Ship facilities and equipment failure |

Rules | Antecedent Attributes (Input) | Criticality C (Output) | ||||||
---|---|---|---|---|---|---|---|---|

O | S | D | Low | Relatively Low | Medium | Relatively High | High | |

1 | Low | Light | Easy | 1 | 0 | 0 | 0 | 0 |

2 | Low | Light | Relatively easy | 0.75 | 0.25 | 0 | 0 | 0 |

3 | Low | Light | Medium | 0.75 | 0 | 0.25 | 0 | 0 |

4 | Low | Light | Relatively difficult | 0.75 | 0 | 0 | 0.25 | 0 |

5 | Low | Light | Difficult | 0.75 | 0 | 0 | 0.25 | |

6 | Low | Relatively light | Easy | 0.55 | 0.45 | 0 | 0 | 0 |

… | … | … | … | … | … | … | … | … |

123 | High | Severe | Medium | 0 | 0 | 0.25 | 0 | 0.75 |

124 | High | Severe | Relatively difficult | 0 | 0 | 0 | 0.25 | 0.75 |

125 | High | Severe | Difficult | 0 | 0 | 0 | 0 | 1 |

C | O_{1} | … | O_{5} | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

S_{1} | … | S_{5} | … | S_{5} | |||||||||

D_{1} | D_{2} | … | D_{5} | … | D_{1} | … | D_{5} | … | D_{1} | D_{2} | … | D_{5} | |

C_{1} | 1 | 0.75 | … | 0.75 | … | 0.55 | … | 0.3 | … | 0.25 | 0 | … | 0 |

C_{2} | 0 | 0.25 | … | 0 | … | 0 | … | 0 | … | 0 | 0.25 | … | 0 |

C_{3} | 0 | 0 | … | 0 | … | 0 | … | 0 | … | 0 | 0 | … | 0 |

C4 | 0 | 0 | … | 0 | … | 0 | … | 0 | … | 0 | 0 | … | 0 |

C_{5} | 0 | 0 | … | 0.25 | … | 0.45 | … | 0.7 | … | 0.75 | 0.75 | … | 1 |

Risk Factor | Identification Framework | ||||
---|---|---|---|---|---|

L | RL | M | RH | H | |

FM_{1} | a_{1} | a_{2} | a_{3} | a_{4} | a_{5} |

FM_{2} | b_{1} | b_{2} | b_{3} | b_{4} | b_{5} |

FM_{3} | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} |

Risk Parameter | Linguistic Variables | Trapezoidal Fuzzy Number | Prior Probability Distribution |
---|---|---|---|

O | L, RL, L, L | (0.083, 0.333, 1.333, 2.417) | (0, 0, 0.285, 0.460, 0.255) |

D | M, RL, M, RH | (3, 4.175, 5.825, 7) | (0, 0.265, 0.471, 0.265, 0) |

ST | H, RH, H, H | (7.583, 8.667, 9.667, 9.917) | (0, 0, 0, 0.426, 0.574) |

SC | H, RH, RH, H | (6.75, 8, 9, 9.75) | (0, 0, 0.053, 0.474, 0.474) |

SF | H, RH, M, H | (6.3, 7.455, 8.64, 9.29) | (0, 0, 0.154, 0.475, 0.371) |

Failure Mode | Criticality Assessment Fuzzy Subset | CI Value | Rank | ||||
---|---|---|---|---|---|---|---|

Low (%) | Relatively Low (%) | Medium (%) | Relatively High (%) | High (%) | |||

FM_{1} | 17.20 | 19.40 | 14.50 | 27.40 | 21.40 | 54.222 | 2 |

FM_{2} | 21.60 | 32.30 | 24.30 | 14.30 | 7.65 | 38.816 | 4 |

FM_{3} | 39.10 | 34.90 | 13.40 | 11.30 | 1.27 | 25.561 | 7 |

FM_{4} | 14.20 | 14.60 | 21.30 | 32.90 | 17.00 | 56.117 | 1 |

FM_{5} | 10.70 | 41.00 | 40.40 | 7.96 | 0 | 36.527 | 5 |

FM_{6} | 21.90 | 34.90 | 29.10 | 12.90 | 1.27 | 34.439 | 6 |

FM_{7} | 3.48 | 34.00 | 45.40 | 17.20 | 0 | 44.135 | 3 |

Number | Combination | CI Value | Change Value | Serial Number | Combination | CI Value | Change Value |
---|---|---|---|---|---|---|---|

1 | Initial | 54.222 | - | 17 | O D ST | 59.692 | 5.47 |

2 | O | 57.192 | 2.97 | 18 | O D SC | 59.917 | 5.695 |

3 | D | 56.097 | 1.875 | 19 | O D SF | 59.817 | 5.595 |

4 | ST | 54.597 | 0.375 | 20 | O ST SC | 58.317 | 4.095 |

5 | SC | 54.822 | 0.6 | 21 | O ST SF | 58.217 | 3.995 |

6 | SF | 54.722 | 0.5 | 22 | O SC SF | 58.292 | 4.07 |

7 | O D | 59.067 | 4.845 | 23 | D ST SC | 56.972 | 2.75 |

8 | O ST | 57.567 | 3.345 | 24 | D ST SF | 56.972 | 2.75 |

9 | O SC | 57.792 | 3.57 | 25 | D SC SF | 57.197 | 2.975 |

10 | O SF | 57.692 | 3.47 | 26 | ST SC SF | 55.597 | 1.375 |

11 | D ST | 56.472 | 2.25 | 27 | O D ST SC | 59.942 | 5.72 |

12 | D SC | 56.697 | 2.475 | 28 | O D ST SF | 59.942 | 5.72 |

13 | D SF | 56.597 | 2.375 | 29 | O D SC SF | 60.167 | 5.945 |

14 | ST SC | 55.097 | 0.875 | 30 | O ST SC SF | 58.567 | 4.345 |

15 | ST SF | 55.097 | 0.875 | 31 | D ST SC SF | 57.472 | 3.25 |

16 | SC SF | 55.572 | 1.35 | 32 | O D ST SC SF | 60.442 | 6.22 |

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## Share and Cite

**MDPI and ACS Style**

Sun, J.; Wang, H.; Wang, M.
Risk Assessment of Bauxite Maritime Logistics Based on Improved FMECA and Fuzzy Bayesian Network. *J. Mar. Sci. Eng.* **2023**, *11*, 755.
https://doi.org/10.3390/jmse11040755

**AMA Style**

Sun J, Wang H, Wang M.
Risk Assessment of Bauxite Maritime Logistics Based on Improved FMECA and Fuzzy Bayesian Network. *Journal of Marine Science and Engineering*. 2023; 11(4):755.
https://doi.org/10.3390/jmse11040755

**Chicago/Turabian Style**

Sun, Jiachen, Haiyan Wang, and Mengmeng Wang.
2023. "Risk Assessment of Bauxite Maritime Logistics Based on Improved FMECA and Fuzzy Bayesian Network" *Journal of Marine Science and Engineering* 11, no. 4: 755.
https://doi.org/10.3390/jmse11040755