# An Improved Failure Risk Assessment Method for Bilge System of the Large Luxury Cruise Ship under Fire Accident Conditions

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Review

- The same RC value implies that the risk factors’ actual ratings are identical. For example, consider a case where O, S, and D all equal two, and one where O = 4, S = 2, and D = 1. Following Equation (2), the two cases’ RCs are similar, and the risk ratings of the cases cannot be distinguished.
- Each risk parameter’s sensitivity to RC is the same. For example, let O, S, and D be 2, 2, 2, respectively in Equation (2). If O or S changes to 3, RC becomes 12. However, the influence of O, S, and D on risk rating should be different [7].

- The expert weight calculation model comprehensively considers the differences in experts’ expertise levels (i.e., qualification level, decision-making capacity, and decision-making preference). Furthermore, there are shortcomings in some of existing expert weight calculation methods. Therefore, the weighted expert weight calculation model is proposed.
- A new RC calculation method is proposed to solve the list of two problems. The RC calculation model incorporates a nonlinear aggregation of the risk parameters, utilizing a three-dimensional continuous matrix that serves to determine the risk factors’ ratings. Additionally, the weights of different risk parameters are also considered.

## 2. Preliminaries on Bilge System’s Failure Risk Assessment

#### 2.1. Hazard Identification for Risk Analysis

#### 2.2. Decision-Making for the Evaluation

#### 2.2.1. Evaluation Matrix Constructed by Experts

#### 2.2.2. Fuzzy Set for Decision-Making

#### 2.2.3. Extended Fuzzy TOPSIS to Determine the Risk Factors’ Weights

**Step 1.**Establish the evaluation set.

**Step 2.**Construct the fuzzy evaluation matrix $\tilde{E}$:

**Step 3.**Standardize the fuzzy evaluation matrix ${\left[{\tilde{x}}_{ij}\right]}_{n\times s}$ (yielding ${\left[{\tilde{z}}_{ij}\right]}_{n\times s}$).

**Step 4.**Calculate the fuzzy positive ideal solution ($FPI{S}_{j}$) and fuzzy negative ideal solution ($FNI{S}_{j}$) for each risk parameter following:

**Step 5.**Calculate each risk factor’s distance from $FPI{S}_{j}$ and $FPI{S}_{j}$.

**Step 6.**Calculate the closeness coefficient, which represents the distances from $FPI{S}_{j}$ and $FNI{S}_{j}$ simultaneously.

**Step 7.**Calculate the crisp weight of risk factors for each risk parameter [39].

#### 2.2.4. Fuzzy AHP to Determine the Risk Parameters’ Weights

**Step 1.**Construct a fuzzy pairwise comparison matrix.

**Step 2.**Calculate the fuzzy weight.

**Step 3.**Calculate the crisp weight.

**Step 4.**Measure the consistency.

## 3. Improved Calculation Model for Risk Ratings

#### 3.1. Expert Weight Calculation Model

#### 3.1.1. Experts’ Qualification Level

#### 3.1.2. Experts’ Decision-Making Capacity

**Step 1.**Perform defuzzification of the fuzzy pairwise comparison matrix $F$ from Equation (19) following Equations (28) and (29):

**Step 2.**Convert the non-reciprocal matrix ${F}^{*}$ to reciprocal matrix ${F}^{\mathsf{\Delta}}$:

**Step 3.**Calculate the matrix A from the reciprocal matrix ${F}^{\mathsf{\Delta}}$:

**Step 4.**Calculate the derived matrix A’s variance (${e}_{t}^{2}$):

**Step 5.**Determine the expert’s decision-making capacity:

#### 3.1.3. Expert Group Decision-Making Preferences

#### 3.2. Risk Coefficient Calculation Model

## 4. Case Study and Discussion

#### 4.1. The Evaluation Procedure

#### 4.1.1. Expert’s Evaluation Matrix Establishment

#### 4.1.2. Risk Coefficient Calculation

**Step 1.**Determining the risk parameter weights.

**Step 2:**Determining the risk factor weights

**Step 3.**Calculating the risk coefficients (RC)

_{6}) risk coefficient is the highest, highlighting the main bilge pump as one of the critical risk factors.

#### 4.2. Determination of Risk Ratings and Sensitivity Analysis

_{1}and I

_{2}) are identified in Figure 6a, while the method corresponding to Figure 6c detected only one high-risk factor (I

_{2}). Similar conclusions could be drawn by comparing Figure 6b,d. Both methods highlight I

_{2}as a high-risk factor, but the method using the expert weights (Figure 6b) detected additional factors. Further, all of the methods recognize I

_{6}as the highest-risk factor. These results demonstrate the utility of the expert weight calculation model to identify high-risk factors, revealing its moderate influence on the evaluation results.

_{3}, I

_{5}, I

_{7}, I

_{8}, I

_{9}). In contrast, Figure 6b identifies only six predominant risk factors, three of which are classified as medium-risk factors (I

_{1}, I

_{5}, I

_{9}). Similar conclusions can be drawn by comparing Figure 6c,d. These results prove the proposed risk coefficient calculation model’s influence on the evaluation results.

_{4}, I

_{5}, I

_{7}, I

_{8}, I

_{10}, I

_{11}, I

_{12},) that are low-risk in Figure 6d, while only four are low-risk (I

_{4}, I

_{10}, I

_{11}, I

_{12}) in Figure 6a. Therefore, the bilge branch line, valve, and electric control of the bilge system are also significant objects for the risk control option. In addition, the proposed models also identify a critical issue (i.e., another high-risk factor, I

_{1}). Furthermore, the influence of the expert weight calculation model on the evaluation results is not as pronounced as that of the risk coefficient calculation model in identifying medium-risk factors. However, the opposite is true when identifying high-risk factors.

#### 4.3. Risk Control Option

- Distributed power machinery: There are six MVZs in the VISTA cruise ship. Therefore, four bilge pumps connected to the bilge main are separated into different MVZs. Emergency bilge pump and rule bilge pump are located at MVZ2 and MVZ3, respectively. Moreover, No. 1 and No. 2 bilge/ballast pumps are located at MVZ1 and MVZ6 on the upper deck of the emergency bilge pump, respectively (see Figure 7). The oil bilge pump is located at MVZ4 (Figure 8). The spare pump is arranged in MVZ6 on Deck 4 (see Figure 9).

- 2.
- Redundancy: For the VISTA cruise ship’s rule bilge system, the redundant design is necessary to prevent the bilge main from being damaged and losing control of the bow and stern due to a fire accident. Redundant bilge main is fitted above the fuel tank at the stern and the end of the pipe tunnel at the bow, respectively (see Figure 9). However, the redundant bilge main cannot be fitted below the original bilge main.
- 3.
- Fire-resistant pipe: Of the rule bilge system elements, the bilge main is located at the engine room (high-risk area), at the bow (high-risk area with fuel tank), and the stern should be fire-resistant (see Figure 7 and Figure 9). The oily bilge system’s No. 1 oily bilge pipe is used for daily collecting oily bilge water, and No. 2 oily bilge pipe serves solely for collecting oily bilge water from the compartments with important equipment. Therefore, the bilge pipe for the overboard discharge and No. 1 oily bilge pipe should be fire-resistant to ensure the basic emission function in the event of serious fire accidents (see Figure 8).
- 4.
- Quarantine: Bilge main is fitted with isolation valves (e.g., butterfly valves) on both sides of watertight bulkheads (see Figure 7). When a fire accident occurs in one watertight compartment, the bilge main’s isolation valve can be used to prevent the bilge system outside of the damaged area from being affected. Moreover, the isolation valve must be easily accessible.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Risk Parameters | Linguistic Variables for the Risk Ratings | Description |
---|---|---|

O | Rare (level 1) | $0.0000\le O\le 0.0003$ |

Unlikely (level 2) | $0.0003\le O\le 0.003$ | |

Possible (level 3) | $0.003\le O\le 0.03$ | |

Likely (level 4) | $0.03\le O\le 0.3$ | |

Almost certain (level 5) | $0.3\le O\le 1.0$ | |

S | Insignificant (level 1) | No or only subsidiary damage, overall damage degree less than 20% |

Minor (level 2) | Slight subsidiary damage, overall damage degree 20–40% | |

Moderate (level 3) | Serious subsidiary damage, overall damage degree 40%–60% | |

Major (level 4) | Most of the system damaged, overall damage degree 60%–80% | |

Catastrophe (level 5) | The system almost destroyed, overall damage degree more than 80% | |

R | Very poor (level 1) | Extreme long response time, almost no possibility of recovery |

Poor (level 2) | Long response time, low possibility of recovery | |

Medium (level 3) | Timely response, moderate possibility of recovery | |

Strong (level 4) | Quick response, high possibility of recovery | |

Very strong (level 5) | Quick response, extremely high possibility of recovery |

Language Variables | Ratings of a Five-Level Scale |
---|---|

Equal importance | 1 |

Moderate importance | 2 |

Significant importance | 3 |

Very significant importance | 4 |

Extremely significant importance | 5 |

n | $\overline{\mathit{G}\mathit{C}\mathit{I}}$ |
---|---|

3 | 0.31 |

4 | 0.35 |

>4 | 0.37 |

Index | Categories | Score |
---|---|---|

Position | Closely related; Related; Unrelated to the evaluation object | 5, 2, 1 |

Professional qualifications | Professor; Associate professor; Other | 5, 2, 1 |

Education level | Doctor; Master; Other | 5, 2, 1 |

Relevant achievements or experience | Major; Moderate; Minor | 5, 2, 1 |

Judgment | Deep analysis; Reference data; Intuition | 5, 2, 1 |

Entire working experience | Above 15 years; 5–15 years; below 5 years | 5, 2, 1 |

Sailing experience | Above 12 years; 2–12 years; below 2 years | 5, 2, 1 |

Principal Dimensions | Value | Unit |
---|---|---|

Overall Length/Length between Perpendiculars | 323.6/287.1 | m |

Molded Depth | 11.4 | m |

Molded Breadth | 37.2 | m |

Maximum Draft | 8.5 | m |

Gross Tonnage | 133500.0 | GT |

Criteria | Sub-Criteria | Symbol |
---|---|---|

Power machinery | Oily bilge pump (reciprocating pump) | I_{1} |

Rule bilge pump (centrifugal pump) | I_{2} | |

Spare pump (screw pump) | I_{3} | |

Facility | Bilge holding tank | I_{4} |

Electric control of bilge system | I_{5} | |

Pipeline | Bilge main pipe | I_{6} |

Bilge branch pipe | I_{7} | |

Valve | I_{8} | |

Other piping accessories | I_{9} | |

Measuring instrument | Level gauge | I_{10} |

Pressure gauge | I_{11} | |

Flow gauge | I_{12} |

O | S | R | |
---|---|---|---|

I_{1} | (1,2,3) | (2,3,4) | (1,1,2) |

I_{2} | (2,2,3) | (3,4,4) | (1,1,2) |

I_{2} | (2,3,3) | (3,4,5) | (1,2,2) |

I_{4} | (1,1,2) | (1,2,2) | (1,2,3) |

I_{5} | (1,2,2) | (2,3,4) | (2,3,3) |

I_{6} | (3,3,4) | (3,4,5) | (1,1,2) |

I_{7} | (2,3,4) | (3,3,4) | (2,3,3) |

I_{8} | (3,3,4) | (2,3,4) | (2,2,3) |

I_{9} | (3,4,4) | (2,3,3) | (2,2,3) |

I_{10} | (2,2,3) | (1,2,2) | (3,3,4) |

I_{11} | (2,3,3) | (1,1,2) | (3,4,4) |

I_{12} | (2,3,3) | (1,1,2) | (3,4,4) |

O | S | R | |
---|---|---|---|

O | (1,1,1) | (1/5,1/4,1/2) | (1,2,3) |

S | (2,4,5) | (1,1,1) | (3,5,5) |

R | (1/3,1/2,1) | (1/5,1/5,1/3) | (1,1,1) |

Risk Parameter | Fuzzy Weight | Crisp Weight (Standardized) |
---|---|---|

O | (0.227, 0.277, 0.366) | 0.212 |

S | (0.703, 0.9471, 0.947) | 0.657 |

R | (0.162, 0.162,0.220) | 0.131 |

E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} | E_{8} | E_{9} | E_{10} | |
---|---|---|---|---|---|---|---|---|---|---|

Comprehensive score coefficient | 2.996 | 3.858 | 3.897 | 2.43 | 1.429 | 3.822 | 3.117 | 1.481 | 2.43 | 0.323 |

Expert weights | 0.111 | 0.143 | 0.144 | 0.09 | 0.053 | 0.141 | 0.115 | 0.055 | 0.09 | 0.058 |

E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} | E_{8} | E_{9} | E_{10} | |
---|---|---|---|---|---|---|---|---|---|---|

Derived matrix variance | 0.015 | 0.012 | 0.011 | 0.024 | 0.035 | 0.011 | 0.024 | 0.033 | 0.023 | 0.038 |

Expert weight | 0.128 | 0.149 | 0.168 | 0.078 | 0.054 | 0.168 | 0.076 | 0.057 | 0.080 | 0.048 |

E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} | E_{8} | E_{9} | E_{10} | |
---|---|---|---|---|---|---|---|---|---|---|

Expert weight | 0.149 | 0.134 | 0.122 | 0.092 | 0.087 | 0.201 | 0.067 | 0.054 | 0.044 | 0.050 |

Risk Factors | I_{1} | I_{2} | I_{3} | I_{4} | I_{5} | I_{6} | I_{7} | I_{8} | I_{9} | I_{10} | I_{11} | I_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Likelihood weight | 0.058 | 0.070 | 0.086 | 0.027 | 0.040 | 0.117 | 0.098 | 0.116 | 0.129 | 0.086 | 0.086 | 0.086 |

Severity weight | 0.107 | 0.142 | 0.116 | 0.027 | 0.099 | 0.166 | 0.083 | 0.103 | 0.098 | 0.026 | 0.019 | 0.014 |

Resilience weight | 0.161 | 0.161 | 0.127 | 0.115 | 0.048 | 0.161 | 0.048 | 0.064 | 0.064 | 0.021 | 0.015 | 0.015 |

E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} | E_{8} | E_{9} | E_{10} | |
---|---|---|---|---|---|---|---|---|---|---|

Expert weight | 0.109 | 0.164 | 0.171 | 0.072 | 0.088 | 0.131 | 0.067 | 0.084 | 0.054 | 0.060 |

Risk Factors | I_{1} | I_{2} | I_{3} | I_{4} | I_{5} | I_{6} | I_{7} | I_{8} | I_{9} | I_{10} | I_{11} | I_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Likelihood weight | 0.044 | 0.051 | 0.066 | 0.013 | 0.089 | 0.068 | 0.128 | 0.123 | 0.119 | 0.106 | 0.099 | 0.094 |

Severity weight | 0.135 | 0.126 | 0.096 | 0.037 | 0.100 | 0.135 | 0.110 | 0.100 | 0.081 | 0.037 | 0.026 | 0.026 |

Resilience weight | 0.147 | 0.171 | 0.105 | 0.027 | 0.096 | 0.182 | 0.043 | 0.088 | 0.094 | 0.013 | 0.018 | 0.016 |

Risk Factors | I_{1} | I_{2} | I_{3} | I_{4} | I_{5} | I_{6} | I_{7} | I_{8} | I_{9} | I_{10} | I_{11} | I_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Risk coefficient | 0.077 | 0.076 | 0.057 | 0.020 | 0.060 | 0.082 | 0.066 | 0.063 | 0.056 | 0.034 | 0.030 | 0.029 |

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**MDPI and ACS Style**

Liu, Z.; Guo, Z.; Li, Y.; Zhu, L.; Yuan, C.
An Improved Failure Risk Assessment Method for Bilge System of the Large Luxury Cruise Ship under Fire Accident Conditions. *J. Mar. Sci. Eng.* **2021**, *9*, 957.
https://doi.org/10.3390/jmse9090957

**AMA Style**

Liu Z, Guo Z, Li Y, Zhu L, Yuan C.
An Improved Failure Risk Assessment Method for Bilge System of the Large Luxury Cruise Ship under Fire Accident Conditions. *Journal of Marine Science and Engineering*. 2021; 9(9):957.
https://doi.org/10.3390/jmse9090957

**Chicago/Turabian Style**

Liu, Zhongzhi, Zhiwei Guo, Yongqing Li, Libao Zhu, and Chengqing Yuan.
2021. "An Improved Failure Risk Assessment Method for Bilge System of the Large Luxury Cruise Ship under Fire Accident Conditions" *Journal of Marine Science and Engineering* 9, no. 9: 957.
https://doi.org/10.3390/jmse9090957