3. Consider the three component system shown below. Components 1, 2, and 3 fail with rates...

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3. Consider the three component system shown below. Components 1, 2, and 3 fail with rates 21, 22, 23, respectively, and they are repaired with rates µ1, µ2, µ3, respectively. a. Draw a Markov diagram for this system, indicating the states, the number j of each state, and for each state, which components are up (KU) and which are down (KD), where k is the component number 1, 2, or 3. Also indicate the state transitions and corresponding transition rates. b. Express the probability of failure in terms of the long-run state probabilities pj. 04 3. Consider the three component system shown below. Components 1, 2, and 3 fail with rates 21, 22, 23, respectively, and they are repaired with rates µ1, µ2, µ3, respectively. a. Draw a Markov diagram for this system, indicating the states, the number j of each state, and for each state, which components are up (KU) and which are down (KD), where k is the component number 1, 2, or 3. Also indicate the state transitions and corresponding transition rates. b. Express the probability of failure in terms of the long-run state probabilities pj. 04

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Solutions Step 1 a The Markov diagram for the threecomponent system can be represented as follows State 0 000 21 22 23 v v v State 1 100 State 2 010 State 3 001 u1 u2 u3 v v v State 4 110 State 5 101 ... View the full answer