Int J Performability Eng ›› 2019, Vol. 15 ›› Issue (1): 167-178.doi: 10.23940/ijpe.19.01.p17.167178
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Wenjie Dong(
), Sifeng Liu, Zhigeng Fang, and Yingsai Cao
Revised on
;
Accepted on
Contact:
Dong Wenjie
E-mail:dongwenjie@nuaa.edu.cn
About author:Wenjie Dong received his B.S. degree in industrial engineering from Shandong Jianzhu University, Jinan, China, in 2014, and he is currently working toward a Ph.D. in the College of Economics and Management at Nanjing University of Aeronautics and Astronautics, Nanjing, China. His research interests are reliability engineering and uncertainties.|Sifeng Liu is a professor in the College of Economics and Management at Nanjing University of Aeronautics and Astronautics, Nanjing, China. He received his Ph.D. in grey systems theory at Huazhong University of Science and Technology, Wuhan, China. He is the director of the Grey System Research Institute at Nanjing University of Aeronautics and Astronautics, the chairman of IEEE Grey System Society, and the vice chairman of IEEE SMC China (Beijing) Branch. His research interests include grey systems theory and complex equipment development and management. He is the editor-in-chief of two international journals: Grey Systems: Theory and Application and Journal of Grey Systems.|Zhigeng Fang is a professor in the College of Economics and Management at Nanjing University of Aeronautics and Astronautics, Nanjing, China. His research fields are grey systems theory and reliability management.|Yingsai Cao received his B.S. degree in management science and engineering from Nanjing University of Aeronautics and Astronautics, China, in 2014, and he is currently working toward a Ph.D. in the College of Economics and Management at Nanjing University of Aeronautics and Astronautics. His research interests are reliability engineering and complex equipment development and management.
Wenjie Dong, Sifeng Liu, Zhigeng Fang, and Yingsai Cao. Reliability Evaluation of Uncertain Multi-State Systems based on Weighted Universal Generating Function [J]. Int J Performability Eng, 2019, 15(1): 167-178.
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Figure 1
(a) A multi-state series system; (b) A multi-state parallel system"
Table 1
Relationship between system performance and component performances"
| Type of MSS | System performance | |
|---|---|---|
| Series system | Flow transmission MSS | $G_{s}^{(1)}=\min \{{{G}_{1}},{{G}_{2}},\cdots ,{{G}_{n}}\}$ |
| Task processing MSS | $G_{s}^{(2)}=\frac{1}{\sum\limits_{j=1}^{n}{(1/{{G}_{j}})}}$ | |
| Parallel system | Flow transmission MSS | $G_{s}^{(3)}=\sum\limits_{j=1}^{n}{{{G}_{j}}}$ |
| Task processing MSS | $G_{s}^{(4)}=\max \{{{G}_{1}},{{G}_{2}},\cdots ,{{G}_{n}}\}$ |
Figure 2
A general series-parallel system"
Figure 3
Structure of a steam turbine power generation system"
Table 2
Performance parameters of each component in the steam turbine power generation system"
| Component | Performance rate | Failure rate | Maintenance rate |
|---|---|---|---|
| 1 | ${{g}_{11}}=0$ | — | $\mu _{12}^{(1)}=120$ |
| ${{g}_{12}}=0.6$ | $\lambda _{21}^{(1)}=0.8$ | $\mu _{23}^{(1)}=150$ | |
| ${{g}_{13}}=0.9$ | $\lambda _{32}^{(1)}=1$ | — | |
| 2 | ${{g}_{21}}=0$ | — | $\mu _{12}^{(2)}=100$ |
| ${{g}_{22}}=0.8$ | $\lambda _{21}^{(2)}=1.5$ | $\mu _{23}^{(2)}=120$ | |
| ${{g}_{23}}=1.0$ | $\lambda _{32}^{(2)}=2$ | — | |
| 3 | ${{g}_{31}}=0$ | — | $\mu _{12}^{(3)}=100$ |
| ${{g}_{32}}=1.0$ | $\lambda _{21}^{(3)}=0.3$ | — |
Figure 4
Transfer relationship between performance rate of each component"
Figure 5
Availability of MSS"
Figure 6
Mean output performance of MSS"
Figure 7
Mean performance deficiency of MSS"
Table 3
Steady-state reliability indices values"
| Reliability indices System style | Stable availability | Stable output performance | Stable performance deficiency |
|---|---|---|---|
| Flow transmission MSS | 0.9933 | 0.8980 | 0.0017 |
| Task processing MSS | 0 | 0.4730 | 0.3770 |
| Fixed weight MSS | 0.9998 | 0.9675 | $1.8489\times {{10}^{-6}}$ |
| Variable weight MSS | 0.9966 | 0.9742 | $4.1884\times {{10}^{-4}}$ |
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