## Complex Architectures in the final element (I)

Calculating the probability of failure (PFDavg) in a complex architecture is not usually easy, especially if we do not know the concepts well. Let’s see in this case a complex architecture in the final element.

**Example: **Logic 4oo4 in the final element

From time to time we find Safety Instrumented Functions (SIF) in which several streams have to be closed, and which also use different types of valves and/or actuators.

**How do we calculate the probability of failure of the actuator subsystem?**

4oo4 means that we need to close the 4 flows for the SIF to act correctly, that is, we must add the 4 probabilities of failure to obtain the PFDavg of the final element. The problem is that the total PFDavg may be too high and not achieve the SIL that we need, although each leg of the 4oo4 does.

In the following table we see the result with SILcet:

FINAL ELEMENT | Design 1 | Design 2 |

F.E. Architecture | 4oo4 (1oo2/1oo2/1oo2/1oo1) | 4oo4 (1oo2/1oo2/1oo2/1oo2) |

Achieved SIL | SIL-1 | SIL-2 |

PFDavg | 2.10E-02 | 4.96E-03 |

RRF | 48 | 202 |

MTTFS | 14 years | 13 years |

In “Design 2” we modify the architecture of the last leg to 1oo2 and we see that we achieve SIL-2. As we see in the following table, the contribution to the probability of failure of the SIF is almost entirely due to the fourth leg of the final element since the architecture is 1oo1.

DESIGN 1 – FINAL ELEMENT | PFDavg | MTTFS (years) |

LEG 1 (1oo2) | 1.12E-03 | 64 |

LEG 2 (1oo2) | 1.12E-03 | 64 |

LEG 3 (1oo2) | 1.12E-03 | 64 |

LEG 4 (1oo1) | 1.72E-02 | 125 |

TOTAL F.E. | 2.05E-02 | 18.2 |

TOTAL SIF | 2.10E-02 | 14.2 |

Download SILcet COMPLEX ARCHITECTURES MANUAL.

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