Please provide steps for how you got the solution to the problem provided below, I am trying to understand the problem, not just see an answer. Thank you so much. A machine has two engines and a control module. It cannot operate with a malfunctioning control module, but only needs one engine, i.e., one engine is used for operation and one serves as a backup. At the beginning of a day, if machine is operational (i.e., at least one working engine and a working control module), 1 engine and the control unit will be used. During a day of operation one of 3 cases may happen: i. engine will malfunction with probability 0.0; ii. the control module will malfunction with probability 0.15; iii. no malfunctions will be observed with probability 0.8. If at the beginning of the day the machine cannot be operated (either both engines or the control module are malfunctioning), then repairs will be initiated, as follows: i. repair of each of the two engines will be attempted independently, succeeding with probability 0.9; ii. the control unit will be replaced with a new one (with probability 1). Model the the system as a Markov chain with states representing the status of each component (2 engines and control module) and transitions ones a day. Draw transition diagram and transition matrix. Each state should correspond to the status of the components, e.g., 2 engines and 1 module working, 1 engine and module working, etc.
Please provide steps for how you got the solution to the problem provided below, I am trying to understand the problem, not just see an answer. Thank you so much.
A machine has two engines and a control module. It cannot operate with a malfunctioning control module, but only needs one engine, i.e., one engine is used for operation and one serves as a backup. At the beginning of a day, if machine is operational (i.e., at least one working engine and a working control module), 1 engine and the control unit will be used. During a day of operation one of 3 cases may happen:
i. engine will malfunction with probability 0.0;
ii. the control module will malfunction with probability 0.15;
iii. no malfunctions will be observed with probability 0.8.
If at the beginning of the day the machine cannot be operated (either both engines or the control module are malfunctioning), then repairs will be initiated, as follows:
i. repair of each of the two engines will be attempted independently, succeeding with probability 0.9;
ii. the control unit will be replaced with a new one (with probability 1).
Model the the system as a Markov chain with states representing the status of each component (2 engines and control module) and transitions ones a day. Draw transition diagram and transition matrix. Each state should correspond to the status of the components, e.g., 2 engines and 1 module working, 1 engine and module working, etc.
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