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Unformatted text preview: CS112 - Homework #7 1. Consider a system containing 5 components that fail and can be repaired. The time to failure of each component is exponential with mean 5 hours. The repairman comes at 5:00 PM each day and instan- taneously repairs up to two failed components (e.g., he only carries two replacement parts). So if, for example, there are 4 failed components when the repairman arrives then immediately 2 are fixed and the others must wait at least until the repairman returns the next day. You are to construct a discrete-time Markov model for this system, where the states describe the system at the instants just as the repairman arrives, i.e., before fixing any machines. (a) What is the probability that a given component, operational when the repairman visits one day, is still operational the next day when the repairman visits again? (b) Draw the state transition diagram for the model. Be sure to define the meaning of the state labels. (c) In terms of the model parameters and state probabilities, what fraction of days does the repairman arrive to find all components operational?...
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- Spring '08