1. A space shuttle carries 5 computers onboard. Each computer has been designed with the reliability target of 90% for a 30 day-mission (24 hrs/day operation). (You may use Model 3 in the reliability worksheet of the Spreadsheet Models for Logistics Engineering.)

1. What should be the target MTBF (in hours) of a computer assuming exponential failure times?

2. In the worst case scenario, if at least one computer functions, the shuttle can return to the earth. What is the probability that the shuttle can return to the ground control station after a 30-day mission?

2. Six F/A-18s have been assigned to destroy six different targets (one aircraft for each target). Each aircraft carries three missiles, and each missile has 80% chance of destroying the target. What is the probability of destroying allsix targets?

3. The AF has 500 F-XX fighter aircraft. The Standard Depot Level Maintenance (SDLM) must be done every 3 years. The turn-around-time (TAT) for SDLM is 6 months. The company has allocated $100 million to improve their operation. Which of the following two options is preferred? Justify your answer.

Option 1: buy 10 more aircraft at $10 million each

Option 2: invest $100 million to improve information systems so that the SDLM TAT will be reduced by 50% (i.e., 3 months instead of 6).

4. The Navy has 550 F/A-YY fighter/attack aircraft. The Mean Down Time (MDT) of an F/A-YY is 73 days per year. The Navy has determined that in order to meet the more demanding operational tempo it will require on average 500 fully mission capable (FMC) aircraft.
   1. Assuming MDT remains the same, how many additional F/A-YY should be acquired to meet the Navys requirement of 500 FMC aircraft?

2. Assuming that the Navy will not acquire new aircraft, what should be the target MDT to meet the Navys requirement of 500 FMC aircraft?

5. 5 EA-18G Growlers have been sent to support a 5-hour strike mission. Each Growler has two F414 engines. An engine consists of 6 modules. The MTBFs of the modules are listed in the table below. Assume that the failure times are exponentially distributed; failures occur independently. If one of the modules fails the engine is not operational. If at least one engine functions, the aircraft can fly. Find the probability that all 5 Growlers will return to the home base.

module	MTBF
Compressor	1,000
Fan	1,000
HPT (high pressure turbine)	1,000
LPT (low pressure turbine)	2,000
Combustor	2,000
Afterburner	2,000

6. You operate an unmanned aerial vehicle (UAV) in Afghanistan from a laboratory at NPS. The commands from the NPS control station are sent to the UAV via satellite to a relay station in Afghanistan. There are two control stations at NPS (one main and another backup). You only need one control station at NPS to operate the UAV. A UAV consists of an engine, a propeller and a navigation computer. An engine or propeller failure will cause a loss of a UAV. In case of a loss communication between the UAV and the NPS control station, the UAV will return using the preprogrammed navigation computer. In case of a failure of a UAV navigation computer, the operator at NPS can manually bring the UAV back to the ground station. Loss of both communications between NPS and the UAV, and the navigation computer at the same time will cause a loss of a UAV. The MTBF of each subsystem is specified below, and the failure time for each component is assumed to follow an exponential distribution. Also assume that each component operates independently.

1. Draw a Reliability Block Diagram (RBD).

2. Calculate the probability of loss of a UAV during a 24-hr mission.

Component	MTBF (op hrs)
1.NPS main control station	2,000
2. NPS backup control station	1,000
3.Satellite	2,000
4. Relay station in Afghanistan	1,000
5.UAV engine	1,000
6.UAV propeller	1,000
7.UAV Navigation computer	2,000