Problem 1 The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .91, and the other has a reliability of .96.
a. What is the reliability of the computer?
b. A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability.
c. If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .97, what is the overall reliability of the system? (Both the switch and the backup computer must function in order for the backup to take over.)
Problem 2 Determine the availability for each of these cases:
a. MTBF = 45 days, average repair time = 4 days.
b. MTBF = 340 hours, average repair time = 6 hours.
Problem 3 A manager must decide between two machines. The manager will take into account each machine's operating costs and initial costs, and its breakdown and repair times. Machine A has a projected average operating time of 130 hours and a projected average repair time of 10 hours. Projected times for machine B are an average operating time of 54 hours and a repair time of 3 hours. What are the projected availabilities of each machine?