The above image is the diagram from the slide where F1 and F2 are the Overall Sy

Question

The above image is the diagram from the slide where F1 and F2 are the Overall System failure

Perform the following tasks:

Write a MATLAB function that returns the state transition matrix for the above two-bus, three-processors system given the bus failure rate (1), processor failure rate (2) and time interval (t) as inputs.

Given 1 = 2×10-4 failures/hr and 2 = 1×10-5 failures/hr and t = 0.1 hr, generate a graph of the state probabilities as a function of time.

Compute the steady state probability vector.

Provide a write-up (in Word or other comparable text editor) of your findings. Include all the plots in your text with correct cross-references to them in the text. Also, include a short discussion for each of the plots and tasks and make sure to include references to any equations or documents that you used.

Continuous to Discrete 22,At 22,At F1 2A,At 3,1 At ,At ,At Overall system failure F2 Discrete Markov Chain Representation Overall system failure!! Dependability.22

Explanation / Answer

ransition_probabilities = [0.1 0.9;0.8 0.2]; starting_value = 1; chain_length = 1000;

chain = zeros(1,chain_length);
chain(1)=starting_value;
for i=2:chain_length
this_step_distribution = transition_probabilities(chain(i-1),:);
cumulative_distribution = cumsum(this_step_distribution);
r = rand();
chain(i) = find(cumulative_distribution>r,1);
end
% provides chain = 1 2 1 2 1 2 1 2 1 1 2 1

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