There are 36 single-engine aircraft (consists of 6 modules) The failure times ar

Question

There are 36 single-engine aircraft (consists of 6 modules) The failure times are exponentially distributed; failures occur independently. If one of the modules fails the engine is not operational. The estimated operations is to be 40 flight hrs per aircraft per month. Use at least 4 significant digits

Module 1 MTBF 2,000 and cost $700,000.00

Module 2 MTBF 1,500 and cost $500,00.00

Module 3 MTBF 1,000 and cost $300,000.00

Module 4 MTBF 1,200 and cost $500,000.00

Module 5 MTBF 2,500 and cost $300,000.00

Module 6 MTBF 500 and cost $700,000.00

a.. What is the MTBF of the engine?

b. What is the reliability of the engine for a 5 hour mission?

c. In order to improve this engine reliability (during a 5-hr mission) to be 0.980. What should be the target MTBF of the engine?

d. In order to improve the reliability of the module 6 so that the engine reliability (computed in problem (c)) will achieve 0.98. What should be the target MTBF of module 6?

e. When an engine fails, the faulty engine is removed from the aircraft and a spare engine is installed. The faulty engine is sent to away for repair. The average repair turnaround time including transportation is 20 days. The required spare protection level is 90%. (Use the original MTBF values in the table above.)What is the inventory value of the engine spare pool? Each engine costs $3 million.

f. The proposed engine repair policy is to keep the spare modules (instead of engines). When an engine fails, the faulty engine is removed and tested. The faulty module is replaced with a spare module. The faulty module then is sent away for repair. The average module repair turnaround time (includes transportation) is 15 days. Note: For simplicity, assume that the time required for faulty module diagnosis and module replacement is negligible. What is the total dollar value of the module spare pool? The required spare protection level is 90%. (Use the original MTBF values)

Explanation / Answer

a) We can calculate the Failure Rate or Probability of Failure in one Hour for each Module, which is nothing but the reciprocal of MTBF, which is given.

We can then calculate the Failure Rate for the Engine as the sum of the Failure Rates of the 6 Modules, as the Engine is not operational, even if one module fails.

Failure Rate of Module 1 = 1/MTBF = 1/2000 = 0.0005000

Failure Rate of Module 2 = 1/MTBF = 1/1500 = 0.0006667

Failure Rate of Module 3 = 1/MTBF = 1/1000 = 0.0010000

Failure Rate of Module 4 = 1/MTBF = 1/1200 = 0.0008333

Failure Rate of Module 5 = 1/MTBF = 1/2500 = 0.0004000

Failure Rate of Module 6 = 1/MTBF = 1/500 = 0.0020000

Hence Failure Rate for the Engine = sum of Failure Rates of the 6 Modules = 0.0054000

Hence MTBF for the Engine = 1/Failure Rate = 1/0.0054 = 185.2 Hours

b) Reliability of the engine per hour = 1 - probability of failure = 1 - 0.0054 = 0.9946

Hence reliability for a five hour mission = 0.99465 = 0.9733

c) In order to improve the reliability for a five hour mission to 0.980,

the reliability of the engine per hour must be (0.980)(1/5) = 0.9960

Hence probability of failure in 1 hour must be 0.0040 and Target MTBF must be 1/0.0040 = 250 Hours

d) In order to achieve engine reliability of 0.98, the failure rate of the engine has to come down

from 0.0054 to 0.0040 per hour. For this the failure rate of module 6 has to come down from 0.0020000 to 0.0006000.

Hence target MTBF for Module 6 = 1/target failure rate per hour = 1/0.0006 = 1667 Hours.

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