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- Question : EX1 - Have each member of the class simulate the TTF example independently until the time of ?rst system failure. Estimate E(Y ), the expected value of the time to ?rst system failure and also a standard error or con?dence interval on this estimate.
- Question : EX2 - Simulate the TTF example to the time of ?rst system failure with three (one active, two spares) components rather than two.
- Question : EX3 - Simulate the TTF example until time T = 30 and compute the average number of functional components and average system availability. Unless you are lucky, time 30 will not correspond to a failure or repair event time, so how can you stop the simulation right at time T = 30? Hint: The system is available if S(t) > 0. Average availability is the fraction of time the system is available from t = 0 to t = T.
- Question : EX4 - For the TTF example, suppose that the repair times are not precisely 2.5 days, but instead are 1 day with probability 1/2, and 3 days with probability 1/2. Use a fair coin to generate repair times. Decide on a sensible tie-breaking rule and simulate until the time of the ?rst system failure.
- Question : EX5 - If in the TTF example the time to component failure and time to repair a com- ponent are exponentially distributed, then the TTF system is a continuous-time Markov chain for which the mean time to ?rst failure and long-run system avail- ability can be derived mathematically. If you know how, do this
- Question : EX6 - Write, in words, the logic for the two system events in the TTF example. Be sure to include updating the value of the state and scheduling any future events.
- Question : EX7 - Add to Table 1.1 a column that updates the area ?ij=1 S(ei?1)
- Question : EX8 - Add to Table 1.1 a column that updates the area ?ij=1 I{S(ei?1) = 2}
- Question : EX9 - Consider a modi?ed TTF system that works as follows. Simulate this system by hand (using dice) until the time of ?rst system failure.
- Question : EX10 - For your simulation in Exercise 9, add a column that updates the area ?j i=1 S(ei?1)

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