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Posted by **April** on Sunday, January 24, 2010 at 11:06pm.

My possible answers are:

.7559

.2441

.8217

.8128

I have tried and asked and no one is getting any of these. Help, please!

- math -
**Dr Russ**, Monday, January 25, 2010 at 6:31amMy understanding of your question means that you have a fault tree with 'machine unavailable' as the top event and the Boolean algebra expression for the top event being

A OR B OR C OR D

because failure of any one of the four components results in machine failure.

As an approximation (because it will be missing the AB components and therefore slightly too high - the probability of A OR B is [P(A)+P(B)-P(A)*P(B)])

is 0.07+0.07+0.05+0.08 = 0.27, which is slightly high so the unavailability is likely to be the 0.2441 value, hence the probability that it is working is

1-0.2441 = 0.7559.

You will need to workout an exact value for your answer and the best way to do this is to sequentially use the [P(A)+P(B)-P(A)*P(B)] expression. What I mean is combine A OR B, then combine the result of this with C and so on.

- math -
**Dr Russ**, Monday, January 25, 2010 at 7:29amJust to confirm.

If you go through the maths steps as I indicated I got

0.2439854, so allowing for the occasion rounding error this is close to 0.2441.

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