Int J Performability Eng ›› 2019, Vol. 15 ›› Issue (1): 45-55.doi: 10.23940/ijpe.19.01.p5.4555
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Honghua Sun, Hongxia Chen(
), Qingyang Li, and Xudong Chen
Revised on
;
Accepted on
Contact:
Chen Hongxia
E-mail:chenhx@imut.edu.cn
About author:Honghua Sun is an associate professor in the School of Mechanical Engineering at Inner Mongolia University of Technology. She received her M.S. degree from Harbin Institute of Technology in 2008. Her current research interests include reliability data analysis and reliability evaluation.|Hongxia Chen is an associate professor in the School of Mechanical Engineering at Inner Mongolia University of Technology. She received her M.S. degree in 2008. Her current research interests include reliability data analysis and reliability evaluation.|Qingyang Li is a postgraduate student in the School of Mechanical Engineering at Inner Mongolia University of Technology. He received his bachelor’s degree from Inner Mongolia University of Technology in 2016. His current research interests include reliability data analysis and reliability evaluation.|Xudong Chen is a postgraduate student in the School of Mechanical Engineering at Inner Mongolia University of Technology. He received his bachelor’s degree from Inner Mongolia University of Technology in 2016. His current research interests include reliability data analysis and reliability evaluation.
Honghua Sun, Hongxia Chen, Qingyang Li, and Xudong Chen. Fuzzy Fault Tree Analysis based on Interpretive Structure Model and Binary Connection Numbers [J]. Int J Performability Eng, 2019, 15(1): 45-55.
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Figure 1
Applying ISM to establish a fault tree flow chart"
Table 1
Fault list"
| Fault code | Fault name | Fault code | Fault name |
|---|---|---|---|
| ${{X}_{1}}$ | Belt fault | ${{X}_{9}}$ | Bearing preload is too large |
| ${{X}_{2}}$ | Spindle system fault | ${{X}_{10}}$ | Bearing grinding injury |
| ${{X}_{3}}$ | Bearing galling | ${{X}_{11}}$ | Spindle does not drive |
| ${{X}_{4}}$ | Large cutting vibration | ${{X}_{12}}$ | Bearing damage |
| ${{X}_{5}}$ | Spindle overheating | ${{X}_{13}}$ | Bearing fault |
| ${{X}_{6}}$ | Loose headstock connection screws | ${{X}_{14}}$ | Proximity switch fault |
| ${{X}_{7}}$ | Bad bearing lubrication | ${{X}_{15}}$ | Bearing preload is not enough |
| ${{X}_{8}}$ | Chuck is not tightened |
Table 2
Element row sum in the Mmatrix"
| element | ${{X}_{1}}$ | ${{X}_{2}}$ | ${{X}_{3}}$ | ${{X}_{4}}$ | ${{X}_{5}}$ | ${{X}_{6}}$ | ${{X}_{7}}$ | ${{X}_{8}}$ |
|---|---|---|---|---|---|---|---|---|
| Row sum | 2 | 1 | 4 | 2 | 2 | 3 | 3 | 3 |
| element | ${{X}_{9}}$ | ${{X}_{10}}$ | ${{X}_{11}}$ | ${{X}_{12}}$ | ${{X}_{13}}$ | ${{X}_{14}}$ | ${{X}_{15}}$ | |
| Row sum | 3 | 3 | 2 | 3 | 3 | 3 | 4 |
Table 3
The order of Mmatrix element row sum"
| element | ${{X}_{2}}$ | ${{X}_{1}}$ | ${{X}_{4}}$ | ${{X}_{5}}$ | ${{X}_{11}}$ | ${{X}_{6}}$ | ${{X}_{7}}$ | ${{X}_{8}}$ |
|---|---|---|---|---|---|---|---|---|
| Row sum | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 |
| element | ${{X}_{9}}$ | ${{X}_{10}}$ | ${{X}_{12}}$ | ${{X}_{13}}$ | ${{X}_{14}}$ | ${{X}_{3}}$ | ${{X}_{15}}$ | |
| Row sum | 3 | 3 | 3 | 3 | 3 | 4 | 4 |
Figure 2
Interpretative structure model"
Figure 3
Thefault tree"
Table 4
Bottom eventtriangle fuzzy probability"
| Bottom event | TFM | Bottom event | TFM |
|---|---|---|---|
| ${{X}_{1}}$ | (0.014,0.016,0.018) | ${{X}_{9}}$ | (0.022,0.034,0.046) |
| ${{X}_{3}}$ | (0.014,0.017,0.020) | ${{X}_{10}}$ | (0.050,0.060,0.070) |
| ${{X}_{6}}$ | (0.018,0.022,0.026) | ${{X}_{12}}$ | (0.038,0.040,0.042) |
| ${{X}_{7}}$ | (0.008,0.011,0.014) | ${{X}_{14}}$ | (0.005,0.007,0.009) |
| ${{X}_{8}}$ | (0.018,0.03,0.042) | ${{X}_{15}}$ | (0.040,0.050,0.060) |
Table 5
Binaryconnection number of bottomevent"
| Bottom event | BCN | Bottom event | BCN |
|---|---|---|---|
| ${{X}_{1}}$ | 0.016+0.004i | ${{X}_{9}}$ | 0.034+0.024i |
| ${{X}_{3}}$ | 0.017+0.006i | ${{X}_{10}}$ | 0.060+0.020i |
| ${{X}_{6}}$ | 0.022+0.008i | ${{X}_{12}}$ | 0.040+0.004i |
| ${{X}_{7}}$ | 0.011+0.006i | ${{X}_{14}}$ | 0.007+0.004i |
| ${{X}_{8}}$ | 0.030+0.024i | ${{X}_{15}}$ | 0.050+0.020i |
Table 6
Probability importance of bottom event"
| Bottom event | I(h)(j) | Bottom event | I(h)(j) |
|---|---|---|---|
| ${{X}_{1}}$ | 0.7584-0.0869i | ${{X}_{9}}$ | 0.7726-0.0739i |
| ${{X}_{3}}$ | 0.7592-0.0856i | ${{X}_{10}}$ | 0.7939-0.0786i |
| ${{X}_{6}}$ | 0.7631-0.0846i | ${{X}_{12}}$ | 0.7774-0.0890i |
| ${{X}_{7}}$ | 0.7546-0.0851i | ${{X}_{14}}$ | 0.7515-0.0861i |
| ${{X}_{8}}$ | 0.7694-0.0737i | ${{X}_{15}}$ | 0.7856-0.0779i |
Table 7
Exact probability value of bottomevent"
| Bottom event | I(h)(j) | Bottom event | I(h)(j) |
|---|---|---|---|
| ${{X}_{1}}$ | 0.6804 | ${{X}_{9}}$ | 0.7052 |
| ${{X}_{3}}$ | 0.6823 | ${{X}_{10}}$ | 0.7224 |
| ${{X}_{6}}$ | 0.6869 | ${{X}_{12}}$ | 0.6975 |
| ${{X}_{7}}$ | 0.6781 | ${{X}_{14}}$ | 0.6743 |
| ${{X}_{8}}$ | 0.7021 | ${{X}_{15}}$ | 0.7147 |
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