A system has four components A,B,C,D connected to where A and B are connected in series (a line) and then connects to B and C which are connected in Parallel (splits off). They then reconnect forming the system.
Probability of success for each component
A=0.97
B=0.9
C=0.95
D=0.8
(function indepently) what's the probability of success?
I want to 0.97*0.9*(0.95+0.8)= but the parallel part confuses me
Probability of success for each component
A=0.97
B=0.9
C=0.95
D=0.8
(function indepently) what's the probability of success?
I want to 0.97*0.9*(0.95+0.8)= but the parallel part confuses me
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Probabilities can never be greater than 1, so that should be a warning bell that the (0.95+0.8) part is wrong.
Now You've omitted D in the question but I assume you meant to say C and D, not B and C. i.e. A, B and (C parallel D) in series.
For C and D, that part only fails if they both fail. So you multiply the failure probabilities and subtract from 1.
So p(C parallel D passes) = 1 - p(C parallel D fails)
= 1 - (1-0.95)(1-0.8)
= 1 - 0.05 * 0.2
= 1 - 0.01 = 0.99
Then for the system to pass all 3 components (A, B and (C parallel D)) must pass, so
p(pass) = 0.97 * 0.9 * 0.99
Now You've omitted D in the question but I assume you meant to say C and D, not B and C. i.e. A, B and (C parallel D) in series.
For C and D, that part only fails if they both fail. So you multiply the failure probabilities and subtract from 1.
So p(C parallel D passes) = 1 - p(C parallel D fails)
= 1 - (1-0.95)(1-0.8)
= 1 - 0.05 * 0.2
= 1 - 0.01 = 0.99
Then for the system to pass all 3 components (A, B and (C parallel D)) must pass, so
p(pass) = 0.97 * 0.9 * 0.99