Research Article
Fuzzy Risk Graph Model for Determining Safety Integrity Level
Table 3
Transformation of crisp intervals into Fuzzy intervals.
| | Transformation indices | Lower mean value | Upper mean value | Geometric mean of | Lower boundary
of the core | Upper boundary
of the core | Left spread of | Right spread of | Lower boundary
of the support
| Modified value
of
| Upper boundary
of the support
| Modified value
of
|
| | Symbols | | | | | | | | | | | |
| | Consequence | | Minor | 1.0E-09 | 1.0E-07 | 1.0E-08 | 3.162E-09 | 3.162E-08 | 4.325E-09 | 1.368E-07 | −1.162E-09 | 1.0E-09 | 1.684E-07 | — | | Moderate | 0.01 | 0.1 | 3.162E-02 | 1.778E-02 | 5.623E-02 | 1.557E-02 | 8.753E-02 | 2.217E-03 | — | 1.438E-01 | — | | Critical | 0.1 | 1 | 3.162E-01 | 1.778E-01 | 5.623E-01 | 1.557E-01 | 8.753E-01 | 2.217E-02 | — | 1.438E+00 | — | | Catastrophic | 1 | 10 | 3.162E+00 | 1.778E+00 | 5.623E+00 | 1.557E+00 | 8.753E+00 | 2.217E-01 | — | 1.438E+01 | 10 |
| | Exposure | | Rare | 0 | 10 | 5.0E+00 | 2.50E+00 | 7.50E+00 | 5.0E+00 | 5.0E+00 | −2.50E+00 | 0 | 1.250E+01 | — | | Frequent | 10 | 100 | 5.50E+01 | 3.250E+01 | 7.750E+01 | 4.50E+01 | 4.50E+01 | −1.250E+01 | 7.50E+00 | 1.225E+02 | 100 |
| | Avoidance | | Not likely | 0 | 90 | 4.50E+01 | 2.250E+01 | 6.750E+01 | 4.50E+01 | 4.50E+01 | −2.250E+01 | 0 | 1.125E+02 | 9.250E+01 | | Possible | 90 | 100 | 9.50E+01 | 9.250E+01 | 9.750E+01 | 5.0E+00 | 5.0E+00 | 8.750E+01 | — | 1.025E+02 | 100 |
| | Demand rate | | Very low | 1.0E-02 | 0.03 | 5.477E-04 | 7.401E-05 | 4.054E-03 | 1.280E-04 | 5.189E-02 | −5.401E-05 | 1.0E-05 | 5.595E-02 | — | | Low | 0.03 | 0.3 | 9.487E-02 | 5.335E-02 | 1.687E-01 | 4.670E-02 | 2.626E-01 | 6.652E-03 | — | 4.313E-01 | — | | Relatively high | 0.3 | 1 | 5.477E-01 | 4.054E-01 | 7.401E-01 | 2.107E-01 | 5.198E-01 | 1.946E-01 | — | 1.260E+00 | 1 |
| | SIL (RRF = 1/ PFD) | | NSSR (a) | 1 | 10 | 3.162E+00 | 1.778E+00 | 5.623E+00 | 1.557E+00 | 8.753E+00 | 2.217E-01 | 1 | 1.438E+01 | — | | SIL1 | 10 | 100 | 3.162E+01 | 1.778E+01 | 5.623E+01 | 1.557E+01 | 8.753E+01 | 2.217E+00 | — | 1.438E+02 | — | | SIL2 | 1.0E+02 | 1.0E+03 | 3.162E+02 | 1.778E+02 | 5.623E+02 | 1.557E+02 | 8.753E+02 | 2.217E+01 | — | 1.438E+03 | — | | SIL3 | 1.0E+03 | 1.0E+04 | 3.162E+03 | 1.778E+03 | 5.623E+03 | 1.557E+03 | 8.753E+03 | 2.217E+02 | — | 1.438E+04 | — | | SIL4 | 1.0E+04 | 1.0E+05 | 3.162E+04 | 1.778E+04 | 5.623E+04 | 1.557E+04 | 8.753E+04 | 2.217E+03 | — | 1.438E+05 | — | | NR | 1.0E+05 | 1.0E+06 | 3.162E+05 | 1.778E+05 | 5.623E+05 | 1.557E+05 | 8.753E+05 | 2.217E+04 | — | 1.438E+06 | 1.0E+06 |
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