call that a system of components, system of components, connected Consider the f
ID: 3314445 • Letter: C
Question
call that a system of components, system of components, connected Consider the followin connected in series, functions if all the components function. A d in parallel, functions if at least one component functions. series, funct functions g system where each component functions independently: (16 pts ( 4+4+4+4)) a) If each component has a probability pof functioning then what is the probability that the sub- system with components A and B functions? c) If each component has a probability p of functioning then what is the probability that the entire system functions? b) If each component has a probability p of functioning then what is the probability that the sub system with components C and D functions? abrlities d) if you are told that the four components have probab lity of functioing 0.99, 0.93, 0.97, and 0.96 but you would not be told which component has which probability of failing, what pairing(s) of the probabilities with the component letters would you "wish for" in order to result in the most reliable system?Explanation / Answer
a) Probability that the subsystem AB functions is computed as:
= Probability that each of the 2 components A and B works
= p*p
= p2
b) Probability that the subsystem CD works
= Probability that at least one of the two functions
= 1 - Probability that none of the two functions
= 1 - ( 1-p)2
= 2p - p2
c) Probability that the entire system functions is computed as:
= Probability that at least one of the two subsystems functions
= 1 - Probability that both the subsystems dont work
= 1 - ( 1 - p2)*( 1 - 2p + p2 )
This is the required expression here for the required probability .
d) For having the most reliable system, we would want the series components of the subsystems to have the maximum probability of functioning, therefore A and B should have the probabilities of functioning of 0.99 and 0.98 ( A and B are in equivalent positiond does not matter which of them has higher )
Also further C and D should have 0.97 and 0.96 ( C and D are in equivalent positiond does not matter which of them has higher )
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