Applying weightages, multiplying outcomes of a node with a numeric factor to create another node, FTA in Genie

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mlfee
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Joined: Wed Mar 29, 2017 10:28 am

Applying weightages, multiplying outcomes of a node with a numeric factor to create another node, FTA in Genie

Post by mlfee » Sat Apr 14, 2018 1:09 pm

Hello all or Marek/Shooltz

I am interested in trying out the model proposed by Roed (https://www.sciencedirect.com/science/a ... via%3Dihub) on using BBN as a way of modelling organisational and management factors to ultimately adjust a failure probability feeding into a Fault Tree Analysis.

Some background:

In the BBN model part, the BBN nodes would have 6 states in 1 node, each state referring to different grades (A,B,C,D,E,F)

In the final node (“Failure”) that is being fed into a FTA, it is a node with 2 states only (State 1 = Failure, State 0= Success)

In the BBN model part, the conditional probabilities are elicited by expert judgement. The elicitation is based on an exponential function of the distance between the child node states and the parent states, as well as a weighted average to the parent state. I have used excel to generate the Zj values, and subsequently for the CPT as well as I couldn’t figure out how to use Equation Nodes in GeNIe to do it. It also seemed easier for me on Excel.

(See eqn 4.1, 4.2, if interested)

In the GeNIe file "Summary_Roed", Nodes 3,1,2 ( and the copies of it) refer to the above paragraph’s description .

I would like to know how I can model the following segments in Genie:

Qn 1: How do I multiply probabilities of the states of a node with a number(an adjustment factor) and a weightage, and have an output as a single value?

For the BBN part( Node 3 – Node 4 or Copy of Node 3 to Node 5 in GeNIe file “Summary_Roed”) leading to the binary nodes, the author proposed the following:

(See Equation 4.3)

Pik refers to the probabilities of each parent state, Q refers to adjustment factors ( See Table 2) below.

So I would like to be able to multiply the probability of each state in Node 3/ Copy of Node 3 to its corresponding Adjustment factors Q, do you have any advice or suggestion how I may use equation nodes to do that?

At Node 4 in “Summary_Roed”, I would like P(Node 3 =A) = 0.10 to be multiplied by the adjustment factor Q =0.1.. and P(Node3=B)= 0.51 multiplied by Q=0.55 etc up to P(Node3=F). The outcome of equation (4.3) is
Pj=(a factor, say 1.54) X Pbasis, where PBasis is a probability of failure from reliability databases etc. Since the overall intention is for Node 4 to feed in Factor Value node, it does not matter if Node 4 is calculated as a single value already, or as adjusted/recalculated States A to F.

If Node 4 is reflected as having outcomes of updated States A to F, how may I apply weightages from Node 4 to Factor Value node? ( If Node 4 is a ndoe with a single value, I understand I can use equation nodes to reflect that)

Now, the only solution in my mind is to have an equation node and manually type in the P(Node 3 =A, B,C,D,E,F) values multiplied by its adjustment factors and weightages to obtain a factor value…but that seems like a very crude method!

QN 2: Is my Fault Tree modelled correctly in GeNIe, and how can I update model with the Factor Value node in Qn1 into the Fault Tree?

I have also modelled the adjustment factor node to update a Pbasis = 0.05. It is in the model “AND_OR_gates..”.

May I also ask for advice how I may incorporate an updated FTA Node 2 ( by a simple factor value) to the Fault Tree Model? Right now, it is just a separate 2-node system to update the failure probabilities, and then I manually type in the updated probabilitites in FTA Node 2

Is my fault tree model done correctly? Am I using Noisy Add functions correctly or at all?

(In my Fault Tree Model, I am using the “input nodes” to reflect State 1 as an observation, in order to calculate as if it is a Fault Tree Model)

Thank you for your time
Attachments
RoedEqns_Table2.pdf
(76.8 KiB) Downloaded 99 times
Summary_Roed.xdsl
Roed's Model
(13.75 KiB) Downloaded 178 times
AND_OR_gates_noisy_add_sample.xdsl
FTA Model in GeNIe
(5.78 KiB) Downloaded 181 times

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