BlockSim Example: Aircraft Phases with Forced Landing

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This example also appears in the System analysis reference.

Consider simulating a flight mission for a four-engine aircraft. The configuration of the aircraft changes at different time. During the taxiing phase, the navigation system, one out of the four engines and all three landing gears are needed. During the take-off phase, all four engines, the navigation system and all three landing gears are needed. During the cruising phase, the navigation system and three of the four engines are required. During the landing phase, the navigation system, two of the four engines and all three landing gears are required. After finishing a journey with these four phases, the aircraft goes into a maintenance phase for maintenance. However, in addition to the four operational phases discussed, there is a special operational phase called the forced landing phase. This phase is used for modeling the case when there is a failure during take-off, cruising or landing phase, forcing the aircraft to land. If the forced landing succeeds, the aircraft goes into the maintenance phase. However, if the forced landing fails, the aircraft crashes and the simulation ends.

The purpose of this example is to illustrate how to create a nonlinear system with Failure/Success links in phase simulation.

RBDs and Phase Diagram

The RBDs for the Taxiing phase and the Take-Off phase are:

The RBDs for other three phases are:

The Phase diagram is:

The reliability of the navigation system follows a Weibull distribution with Beta=1.5 and Eta=30 hours. The reliability of the engines follows a Weibull distribution with Beta = 1.5 and Eta = 20 hours. The reliability of the landing gears follows a Weibull distribution with Beta = 1.5 and Eta = 15 hours.

In the maintenance phase, all blocks have CM with duration = 3 hours. CM is performed upon item failure. All blocks also are subjected to PM with duration = 0.5 hours and the PM is performed when the maintenance phase starts. Both CM and PM restore the blocks to as good as new.

Block Up/Down plot

1. At time 5.506 hours, in the Cruising phase, Engine 2 fails. However, this failure doesn't bring the system down because in the Cruising phase, only three of the four engines are required. 
2. At time 6.41 hours, in the Cruising phase, Engine 1 fails too. This failure brings the system down and the system goes into the Forced Landing phase immediately. 
3. At time 7.91 hours, the Forced Landing phase is done. No failure happened in this phase, which means the forced landing is successful. The system goes into the Maintenance phase. All blocks except Engine 1 and Engine 2 get PM in the Maintenance phase.
4. At time 10.91 hours, Engine 1 and Engine 2 are done with their CM and the system goes back to the Taxiing phase.
5. At time 20.721 hours, in the Cruising phase, Engine 1 fails again. Of course, this failure doesn't bring the system down.
6. At time 23.25 hours, in the Cruising phase, Engine 3 fails and this failure brings the system down. The system goes into the Forced Landing phase. After the Forced Landing phase, the system goes into the Maintenance phase.
7. At time 33.706 hours, in the Cruising phase, Engine 1 fails again. This failure doesn't bring the system down.
8. At time 34.25 hours, the system goes into the Landing phase.
9. At time 34.576 hours, in the Landing phase, Landing Gear 3 fails and this failure brings the system down. The system goes into the Forced Landing phase immediately. 
10. At time 45.953 hours, in the Landing phase, the navigation system fails. This failure brings the system down and the system goes into the Forced Landing phase immediately. In the Forced Landing phase, the navigation system is in series with other blocks, the failure of the navigation system brings the system down. Thus there is a system failure in the Forced Landing phase, which means the forced landing fails and the system goes into the Stop node. Simulation stops.