The numbers inside the boxes of the interconnected system shown on the left are
ID: 3183360 • Letter: T
Question
The numbers inside the boxes of the interconnected system shown on the left are the individual probabilities that each element will fail to operate. In parts a) and b) assume that each element operates independent of all others, a) Determine the probability that the system will successfully operate, b) How does the answer to part a) change if one of the blocks with 0.4 failure probability is moved so it is in series with the block having failure probability 0.1? c) For the two elements connected in series, where each has individual failure to operate probability of 0.4, assume that when they are interconnected as shown, given that the first element (the one on the left) successfully operates, the second one (the one on the right) has probability of 0.7 to operate successfully. The remaining blocks operate independent of each other. Determine the probability that the system will successfully operate.Explanation / Answer
a. Probability that the system will operate successfully:-
(1-(0.20*0.10)) * 1-(0.40*0.40*0.10) * 1-(0.30*0.10) = 0.9353 = 93.53%
b. if the block of 0.40 is moved
(0.80*0.60*0.70) * (0.60*0.90) = 18.14%, so the new probability will shift to 18.14% from 93.53% with the change in position