Consider a system consisting of four components, as pictured in the diagram show
ID: 3328714 • Letter: C
Question
Consider a system consisting of four components, as pictured in the diagram shown below. Components 1 and 2 form a series subsystem, as do Components 3 and 4. The two subsystems are connected in parallel. Suppose that P(1 works) = .1, P(2 works) = .1, P(3 works) = .1, and P(4 works) = .1 and that the four components work independently of one another.
(a) The 1Â2 subsystem works only if both components work. What is the probability of this happening?
(b) What is the probability that the 1Â2 subsystem doesn't work?
That the 3Â4 subsystem doesn't work?
(c) The system won't work if the 1Â2 subsystem doesn't work and if the 3Â4 subsystem also doesn't work. What is the probability that the system won't work?
That it will work?
(d) How would the probability of the system working change if a 5Â6 subsystem were added in parallel with the other two subsystems? (Give the answer to four decimal places.)
It ---Select--- increases decreases .
(e) How would the probability that the system works change if there were three components in series in each of the two subsystems? (Give the answer to four decimal places.)
It ---Select--- increases decreases .
Explanation / Answer
a) Probability that the subsystem 12 works is computed as:
= P( 1 works ) * P( 2 works )
= 0.1*0.1
= 0.01
Therefore 0.01 is the required probability here.
b) Probability that subsystem does not work
= 1 - Probability that the subsystem 12 works
= 1 - 0.01
= 0.99
Therefore 0.99 is the required probability here.
Probability that the subsystem 34 does not work is computed as:
= 1 - P(3 works ) P(4 works)
= 1 - 0.1*0.1
= 0.99
Therefore 0.99 is the required probability here.
c) Probability that the whole system does not work is computed as:
= 1 - Probability that both subsystems does not work
= 1 - 0.99*0.99
= 0.0199
Therefore 0.0199 is the required probability here that the whole system works
Now probability that the whole system does not work is computed as:
= 1 - Probability that the whole system works
= 1 - 0.0199
= 0.9801
Therefore 0.9801 is the required probability here that the whole system does not work
d) Clearly if another parallel subsystem is added, the probability of the system to work would increases as the system gets one more option to work.
e) In each series subsystem will have another element added, the probability of a subsystem to work will decrease and therefore the probability of the system to work would also decrease.