A Variance Maximization Based Weight Optimization Method for Railway Transportation Safety Performance Measurement
Abstract
:1. Introduction
2. Study Area and Data Survey
3. Weight Optimization Method for Railway Transportation Safety Performance Measurement
3.1. Weight Interval Division
3.2. Expert Reliability Index Calculation
3.3. Calculation of Weight Interval Limits
3.4. Weight Optimization Model Based on Variance Maximization
- Step 1:
- according to the calculation Formulas (1)–(4) of the evaluation index and the basic data from the china railway yearbook, the evaluation index value of each evaluation object is obtained and the decision matrix of the evaluation index value is established.
- Step 2:
- according to the specific meaning of the evaluation indicators, the infinitude no dimension method is used to obtain a standard decision matrix
- Step 3:
- the fuzzy decision-making method is proposed to calculate the weight change interval (such as the value of ai and bi) based on the initial weight given by expert scoring. Moreover, this interval can be used as the constraint of the weight optimization model.
- Step 4:
- the numerical optimization algorithm is correspondingly proposed to solve the weight optimization model. Finally, the optimal weight vector is obtained for railway transportation safety performance measurement.
4. Case Study
4.1. Calculate the Value of Evaluation Index
4.2. Index Dimensionless Processing
4.3. Index Weight Constraints
4.4. Establishment of Weight Optimization Model
4.5. Results and Discussions
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Levels of Railway Incident (i) | Equivalent Conversion Factor (fi) |
---|---|
Special major incident | 100 |
Major incident | 15 |
Large incident | 5 |
General type A incident | 2 |
General type B incident | 1 |
General type C incident | 0.5 |
General type D incident | 0.2 |
Weight Interval Level | Fuzzy Numbers | ||
---|---|---|---|
ah | ch | bh | |
1 | 0.00 | 0.05 | 0.10 |
2 | 0.10 | 0.15 | 0.20 |
3 | 0.20 | 0.25 | 0.30 |
4 | 0.30 | 0.35 | 0.40 |
5 | 0.40 | 0.45 | 0.50 |
6 | 0.50 | 0.55 | 0.60 |
7 | 0.6 | 0.65 | 0.70 |
8 | 0.70 | 0.75 | 0.80 |
9 | 0.80 | 0.85 | 0.90 |
10 | 0.90 | 0.95 | 1.00 |
Educational Background | Working Years | Professional Level | qi |
---|---|---|---|
Graduate degree or above | more than 30 years | Senior engineers | 1.0 |
Bachelor’s degree | 20–30 years | Engineers | 0.9 |
Associate degree | 10–20 years | Assistant engineers | 0.8 |
High school graduate | 5–10 years | Skilled worker | 0.7 |
Less than high school | 1–5 years | Ordinary worker | 0.6 |
Railway Bureau | The Rate of Equivalent Incident(1/million ton*kilometer) | The Rate of the Locomotive Maintenance (%) | The Proportion of the Security Managers (%) | The Complaint Rate(1/million ton*kilometer) |
---|---|---|---|---|
Harbin Railway Bureau | 0.26 | 6.4 | 13.20 | 1.81 |
Shenyang Railway Bureau | 0.37 | 11.8 | 13.97 | 0.97 |
Beijing Railway Bureau | 0.18 | 5.4 | 16.40 | 3.13 |
Taiyuan Railway Bureau | 0.33 | 9.1 | 20.57 | 1.18 |
Hohhot Railway Bureau | 0.23 | 4.8 | 18.06 | 0.58 |
Zhengzhou Railway Bureau | 0.07 | 9.3 | 15.69 | 1.26 |
Wuhan Railway Bureau | 0.17 | 7.1 | 14.59 | 0.76 |
Xian Railway Bureau | 0.32 | 8.6 | 16.49 | 0.38 |
Jinan Railway Bureau | 0.05 | 8.0 | 19.70 | 1.19 |
Shanghai Railway Bureau | 0.01 | 6.8 | 15.13 | 1.00 |
Nanchang Railway Bureau | 0.33 | 6.9 | 19.12 | 8.04 |
Guangzhou Railway Group | 0.12 | 11.0 | 10.52 | 0.76 |
Nanning Railway Bureau | 0.47 | 10.8 | 15.20 | 1.60 |
Chengdu Railway Bureau | 0.39 | 8.4 | 14.63 | 2.21 |
Kunming Railway Bureau | 0.24 | 7.5 | 23.49 | 1.42 |
Lanzhou Railway Bureau | 0.17 | 10.0 | 16.05 | 1.12 |
Urumqi Railway Bureau | 0.25 | 10.1 | 25.89 | 0.74 |
Qingzang Railway Bureau | 0.16 | 8.2 | 19.09 | 3.83 |
Railway Bureaus | The Rate of Equivalent Incident | The Rate of the Locomotive Maintenance | The Proportion of the Security Managers | The Complaint Rate |
---|---|---|---|---|
Harbin Railway Bureau | 0.45 | 0.93 | 0.85 | 0.77 |
Shenyang Railway Bureau | 0.21 | 0.88 | 0.84 | 0.88 |
Beijing Railway Bureau | 0.62 | 0.94 | 0.82 | 0.61 |
Taiyuan Railway Bureau | 0.30 | 0.90 | 0.77 | 0.85 |
Hohhot Railway Bureau | 0.51 | 0.95 | 0.80 | 0.93 |
Zhengzhou Railway Bureau | 0.85 | 0.90 | 0.82 | 0.84 |
Wuhan Railway Bureau | 0.64 | 0.93 | 0.84 | 0.91 |
Xian Railway Bureau | 0.32 | 0.91 | 0.82 | 0.95 |
Jinan Railway Bureau | 0.89 | 0.92 | 0.78 | 0.85 |
Shanghai Railway Bureau | 0.98 | 0.93 | 0.83 | 0.88 |
Nanchang Railway Bureau | 0.30 | 0.93 | 0.79 | 0.00 |
Guangzhou Railway Group | 0.74 | 0.88 | 0.88 | 0.91 |
Nanning Railway Bureau | 0.00 | 0.89 | 0.83 | 0.80 |
Chengdu Railway Bureau | 0.17 | 0.91 | 0.84 | 0.73 |
Kunming Railway Bureau | 0.49 | 0.92 | 0.74 | 0.82 |
Lanzhou Railway Bureau | 0.64 | 0.89 | 0.82 | 0.86 |
Urumqi Railway Bureau | 0.47 | 0.89 | 0.71 | 0.91 |
Qingzang Railway Bureau | 0.66 | 0.91 | 0.79 | 0.52 |
Evaluation Index | Weight Interval [ai, bi] |
---|---|
The rate of equivalent incident | [0.3563, 0.5465] |
The rate of the locomotive maintenance | [0.1861, 0.3256] |
The proportion of the security managers | [0.0838, 0.2326] |
The complaint rate | [0.0980, 0.2672] |
Evaluation Index | The Average of the Weight Intervals | Optimized Weights |
---|---|---|
The rate of equivalent incident | 0.4450 | 0.5465 |
The rate of the locomotive maintenance | 0.2550 | 0.1861 |
The proportion of the security managers | 0.1625 | 0.0838 |
The complaint rate | 0.1375 | 0.1836 |
Railway Transportation Company | The Assessment Results with Initial Weights | The Assessment Results with Optimized Weights | ||
---|---|---|---|---|
Comprehensive Evaluation Value | Sorting Results | Comprehensive Evaluation value | Sorting Results | |
Harbin Railway Bureau | 0.684 | 12 | 0.6315 | 12 |
Shenyang Railway Bureau | 0.586 | 15 | 0.5115 | 15 |
Beijing Railway Bureau | 0.726 | 8 | 0.6933 | 7 |
Taiyuan Railway Bureau | 0.614 | 14 | 0.5523 | 14 |
Hohhot Railway Bureau | 0.734 | 7 | 0.6930 | 8 |
Zhengzhou Railway Bureau | 0.858 | 3 | 0.8570 | 3 |
Wuhan Railway Bureau | 0.785 | 5 | 0.7574 | 5 |
Xian Railway Bureau | 0.649 | 13 | 0.5870 | 13 |
Jinan Railway Bureau | 0.875 | 2 | 0.8806 | 2 |
Shanghai Railway Bureau | 0.926 | 1 | 0.9381 | 1 |
Nanchang Railway Bureau | 0.473 | 18 | 0.4013 | 17 |
Guangzhou Railway Group | 0.828 | 4 | 0.8118 | 4 |
Nanning Railway Bureau | 0.481 | 17 | 0.3816 | 18 |
Chengdu Railway Bureau | 0.549 | 16 | 0.4659 | 16 |
Kunming Railway Bureau | 0.690 | 10 | 0.6518 | 10 |
Lanzhou Railway Bureau | 0.767 | 6 | 0.7422 | 6 |
Urumqi Railway Bureau | 0.685 | 11 | 0.6484 | 11 |
Qingzang Railway Bureau | 0.717 | 9 | 0.6926 | 9 |
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Sun, D.; Jia, Y.; Qin, L.; Yang, Y.; Zhang, J. A Variance Maximization Based Weight Optimization Method for Railway Transportation Safety Performance Measurement. Sustainability 2018, 10, 2903. https://doi.org/10.3390/su10082903
Sun D, Jia Y, Qin L, Yang Y, Zhang J. A Variance Maximization Based Weight Optimization Method for Railway Transportation Safety Performance Measurement. Sustainability. 2018; 10(8):2903. https://doi.org/10.3390/su10082903
Chicago/Turabian StyleSun, Dongye, Yuanhua Jia, Lingqiao Qin, Yang Yang, and Juyong Zhang. 2018. "A Variance Maximization Based Weight Optimization Method for Railway Transportation Safety Performance Measurement" Sustainability 10, no. 8: 2903. https://doi.org/10.3390/su10082903