A nsk analyst is tring to reduce the likelihood of event D He has determined tha

Question

A nsk analyst is tring to reduce the likelihood of event D He has determined that the fault tree above applies in this situation where events A B and C are independent Furthermore he knows that P A = 0.53 and P -0.52 e does not yet know the value of PIC). He has two options for reducing the value of P(D). The first option will reduce P(C) to half of its value, while the second option will reduce both P(A) and P(B) to 0.75 of their current values. He realizes that for high values of P(C) the first option will reduce the probability more, whereas for low values the second option is more effective. What is the value of P(C) for which the two options are equally effective? (Answer to 2 decimal places).

Explanation / Answer

Let P(c)=x, here P(A)=0.53 P(B)=0.52.

Here we have two options.According to first option X reduced by 1/2.So new value of P(C)=x/2

Now A and B are connected by AND gate so the probability will be P(A)*P(B)=0.28 and then it is connected with C by OR gate.So P(D)=0.28+x/2

Now for second option P(A) and P(B) reduced by .75 so new value of them will be P(A)=0.40 and P(B)=0.39

So by second option P(D)=0.40*0.39 +x =0.16+x

Two option will be equally effective if this two equation will same.

So, 0.16 +x = 0.28 +x/2

so x=0.24

So the value of P(C) is 0.24 for which the two options are equally effective.

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