Expressing Fault Tree Analysis in BBN

[uppglassmel]

Hello,

I am interested in using BBN to modify probabilities that are being fed into a Fault Tree event node. Hence, I would like to also incorporate the Fault Tree Analysis as part of the BBN node.

I have seen some researchers (J.E. Vinnem et al "Risk Modelling of maintenance work on major process equipment on offshore petroleum installations") where they have configured Fault Tree gates in HUGIN by having inputs as "1" or "0" according to the states of the child node such they it resemble a AND-gate or OR-gate.

I have done the same, but my outcome node's results are only "1" or "0" because the values in the conditional probability tables(meant to describe the node as AND or OR gates) are propagated as the actual probabilities.

Do you have any advice what I can do ( my model is attached).

I mean to model C1 as a outcome node, with C2 (0.7 False, 0.3 True) and C3 (0.7 False, 0.3 True) as the input nodes. Based on C1 having the nature of an AND-gate, if I feed evidence that C2 and C3 is true, then I would like to see C1 being reflected as (0.3 X 0.3 = 0.09 that True will occur).

Thank you in advance, I hope I have been clear

Mel

[Anders L Madsen]

Hello,

If you want P(C1=true|P2=true,P3=true)=0.3*0.3=0.09, then you can achieve this using a "noisy-add" gate as demonstrated in the attached model. You set P2_input=true and P3_input=true to get the desire result.

Hope this helps.

[uppglassmel]

Hej Anders,

Thank you for showing me the 'noisy-add' gate, it worked for an OR-gate as well.

Attached it here in case someone else might be interested in it

Very appreciative of your time!

Mel

[uppglassmel]

Hi Anders,

I would like to find out, if I have a node C4 with three states (Correct, Defective, Failure) can the NOISY-ADD still be used to implement a multi-state node as a Fault Tree encoded in a BBN.

As an AND gate:
How C4 should affect C1 is that when C4 = Defective or C4 =Failure, C1 should be simulated as

and P(C1=true|C2=true,C3=true, C4=Defective)=0.3*0.3*0.0099=0.000891

and P(C1=true|C2=true,C3=true, C4=Failure)=0.3*0.3*0.0001=0.000009

and that P(C1=False) whenever either one of or all of C4, C3, C2 takes on (False, Correct)

e.g. P(C1=False|C2=False,C3=False, C4=correct)=0.7*0.7*0.99=0.4851,



And also, as an OR gate, how should one encode it?

P(C1=False) when either C4,C3 and C2 takes on (Correct, False)
P(C1=True) when either C4,C3 and C2 takes on (Defective, Failure, True)


Thank you for your time

[Anders L Madsen]

Hi Mel,

The "generalization" of OR / AND is MAX / MIN. If you encode false/correct as 0, true/failure as 1, and defective as 2 using Numbered nodes and use MIN/MAX instead of AND/OR, then you should be able to encode the desired CPTs.

The idea is that there must be an order on the states and this is enforced by the use of the Numbered node where 0 would reflect the absence of a cause and higher values reflect a more significant presence of the cause.

Let me know if this works for you.
Anders

[uppglassmel]

Hej Anders,

Thank you for the tips, I will try it out!

Appreciate your time

/Mel