Information for questions 1 and 2: consider a system with two machines - one is an active machine and the other is an inactive spare. The spare machine becomes active when the (currently) active machine fails, while the failed machine immediately starts repair. The failed machine becomes the spare when its repair is completed. Only one component at a time can be repaired, so the system as a whole fails if both components have failed, and it is operational as long as at least one of the components is working.

The time to failure of a machine can with equal probability be 2, 4, 6, 8 or 10 days, while repair takes exactly 10.5 days. A repaired machine is as good as new.

1. (5 marks) Modify the TTF simulation such that it works with any number of machines (integer > 1). Find the average time to failure with 5 machines (100 replications). Plot the graph of average time to failure against number of machines when the number of machines ranges from 2 to 7. The graph must be properly plotted, with axes clearly labeled.

2. (2 marks) Modify the system in Problem 1 such that time to repair is 10.5 days with probability 0.4 and 12.5 days otherwise. Generate the same plot as in problem 1 for this problem as well.