Calculating Probability of Subsea Compressor System Failure

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Discussion Overview

The discussion centers around calculating the probability of failure for a subsea compressor system using Boolean Algebra. Participants explore the application of probability theory and Boolean logic to derive the correct probability based on given values and assumptions of independence among variables.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a Boolean expression for failure, F = A UBU(CUD), and provides specific probabilities for A, B, C, and D, seeking to calculate P[F].
  • Another participant suggests that the expression might be incorrectly stated and proposes an alternative form, F = A UBU(C∩D).
  • A participant describes their method of calculation using the associative law but finds discrepancies between their result and the provided answer.
  • Another participant affirms the method used by the first poster but suggests an alternative approach involving the probability of not failing.
  • A later reply indicates that the initial problem statement may have been incorrect, implying that the misunderstanding could have led to the confusion in calculations.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation of the Boolean expression and the method of calculation. There is no consensus on the correct approach or the validity of the initial problem statement.

Contextual Notes

Participants have not resolved the assumptions regarding the Boolean expression and its implications for the probability calculations. The discussion reflects uncertainty about the correct formulation and the resulting calculations.

abba02
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[SOLVED] Bolean Algebra

Question
The failure of a subsea compressor system is described by the following Boolean
Algebra statement:
F = A UBU(CUD)
If P[A] = 0.01; P = 0.0034; P[C] = 0.00067; P[D] = 0.002, calculate the probability
P[F] given independence between A,B,C,D.
ANSWER[0.013367]

ATTEMPTS AT PROBLEM
I have tried to use the associative expression to solve this but my answer is different from the given answer of .013367
 
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Welcome to PF!

Hi abba02! Welcome to PF! :smile:

(btw, this probably ought to be in the coursework and homework section)

Show us your attempt, and then we'll know how to help you. :smile:

[And are you sure it's not F = A UBU(C∩D)?]
 
My attempts to solve the problem

It is F = AUBU(CUD)
I had derived the below using the associative law. But after plugging in the values of A,B,C and D , my answer were still different from the given answer.
P(A) +P(B) +P(CUD)-P[A]P-P[A]P[CUD]-PP[CUD]+P[A]PP[CUD]
 
Last edited:
… looks good to me …

Hi abba02! :smile:

Yes, your method looks good to me! :smile:

(though it would be quicker to say P(notF) = P(notA)P(notB)P(notCUD))

ok, now try it with f = A UBU(C∩D), and see what you get.
 
Thanks, With your advise, I have got the solution to the problem. I think that the problem must have been stated wrongly.
 

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