hw 7 - ab 2 ac 3 dc 4 ad 5 db and 6 cb Suppose all branches...

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Homework 7 (12 March 2015) 1. Consider a six-engine descent system of a large crewed vehicle missions to Mars. The system is used to maintain balance of the vehicle. The system can land the vehicle safely as long as it experiences at most one engine-pair failure. As shown in Figure 1, the three engine-pairs are 1 4, 2 5, and 3 6. An engine-pair works only when both engines work. Assume that the six engines are identical and each has a probability p of successfully operating during landing. Determine the reliability of the system. Figure 1 Six-engine vehicle system 2. Figure 2 represents a four-node communications network. The four nodes, a , b , c , and d , represent the four stations. The six branches represent two-way communication links between each pair of stations. As shown in the figure, the six branches are numbered as: 1:

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Unformatted text preview: ab, 2: ac, 3: dc, 4: ad, 5: db and 6: cb. Suppose all branches are independent and identical with probability of success p. 1) Find all the four minimum cut-sets and all five minimum path-sets between a and b. 2) Hence, compute the lower bound and upper bound for the system reliability. 3) Write down the system structure function and simplify it. Figure 2 Reliability problem diagram a b c d 1 2 3 4 5 6 3. Three components A, B, C are connected in series. The reliabilities are given as: 0.8 A R  , 0.9 B R  , 0.95 C R  . (a) What is the system reliability? (b) If we have a redundant component D ( 0.9 D R  ) to be added in parallel with A, B, or C, which one will improve the system reliability most?...
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