# Systems Engineering or Statics for MTBF and probability of failure

Please review these attached Systems Engineering problems and provide assistance. The problems are related to Mean Time Between Failure and failure rates for systems.

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10. The failure rate (λ) of a device is 22 failures per million hours. Two standby units are added to the system. Determine the MTBF of the system.

11. Calculate the reliability of a system consisting of one operating unit and one identical standby unit operating for a period of 200 hours. The failure rate (λ) of each unit is 0.003 failure/hour and the failure sensing switch reliability is 1.0.

12. A system consist of five subsystems with the following MTBF's:

? Subsystem A: MTBF = 10,540 hours

? Subsystem B: MTBF = 16,220 hours

? Subsystem C: MTBF = 9,500 hours

? Subsystem D: MTBF = 12,100 hours

? Subsystem E: MTBF = 3,600 hours

The five subsystems are connected in series. Determine the probability of survival for an operating period of 1,000 hrs.

13. Ten components were tested for 500 hours, each within prescribed operating conditions. Component 1 failed after 30 hours; Component 2 failed after 85 hours; Component 3 failed after 220 hours; And component 4 failed after 435 hours. Determine the overall composite failure rate (λ) for the system.

14. Suppose that you have the following design data on an equipment item and that, based on this data, you may wish to accomplish a reliability prediction. What is the predicted MTBF?

Component Quantity of Parts Used Failure Rate (% 1,000hrs)

A 16 0.135

B 75 0.121

C 32 0.225

D 44 0.323

E 60 0.120

F 15 0.118

G 28 0.092

#### Solution Preview

10. The failure rate (λ) of a device is 22 failures per million hours. Two standby units are added to the system. Determine the MTBF of the system.

This question is little tricky, here I assume that the device can fail when idle also (i.e. all three systems work in parallel). However if the standby device works only if the first one fails we may have to use the method I used in next question.

MTBF of the device is 1000000/22=45454.6 hours

MTBF of systems in parallel (redundant units) = MTBF*(1+1/2+1/3)=83333.3 hours

11. Calculate the reliability of a system consisting of one operating unit and one identical standby unit operating for a period of 200 hours. The failure rate (λ) of each unit is 0.003 failure/hour and the ...

#### Solution Summary

The systems engineering of statics for MTBF and probability failure is examined.