A system consists of five components, each can be operational or not. Each day one operational component is used and it will fail with probability 20%. Any time there no operational components at the end of a day, maintenance will be performed and all non-operational components will be repaired (with probability 1). The system does not perform any other tasks on the day of repairs.Model the system as a Markov chainWrite down equations for determining long-run proportions.Suppose that you are interested in the average number of days that the system is under repair. Explain how you would find it using your model.

Ans- We can model this system as a Markov chain with 6 states, where state i represents the number…

Answered: A system consists of five components,…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A system consists of five components, each can be operational or not. Each day one operational component is used and it will fail with probability 20%. Any time there no operational components at the end of a day, maintenance will be performed and all non-operational components will be repaired (with probability 1). The system does not perform any other tasks on the day of repairs.
1. Model the system as a Markov chain
2. Write down equations for determining long-run proportions.
3. Suppose that you are interested in the average number of days that the system is under repair. Explain how you would find it using your model.

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