BlockSim Example: Phase with Failure or Success Paths

Phase with F/S links

Purposes

The purposes of this example is to illustrate how to apply F/S links in Phase simulation.

RBDs for Phase and settings

The RBDs for Phase 1 and Phase 2 are as followings:

In Phase 1, Block A follows Weibull distribution with Beta = 1.5 and Eta = 1000 hours. Block B follows Weibull distribution with Beta = 1.5 and Eta = 1200 hours. No maintenance.

In Phase 2, Block A follows Weibull distribution with Beta = 1.5 and Eta = 900 hours. Block B follows Weibull distribution with Beta = 1.5 and Eta = 1150 hours. No maintenance.

Example 1

The Phase diagram is as followings:

Maintenance phase has a CM with duration 80 hours and PM with duration 20 hours for both Block A and B.

Phase 1 has duration 500 hours and Phase 2 has duration 100 hours.

If there is no failure in Phase 1, upon finish, it goes to Phase 2. If there is a failure in Phase 1, it would go to Maintenance Phase 3 immediately. If there is no failure in Phase 2, upon finish, it goes back to Phase 1. If there is a failure in Phase 2, it would to go Maintenance Phase 3 immediately.

The Block Up/Down plot is as followings:

1. At the first cycle (0-500 for Phase 1 and 500-600 for Phase 2), there is no failure, thus after Phase 2, Phase 1 is executed (back to Phase 1 after this cycle).
2. At 1135 (Phase 2 at second cycle), Block A fails. System doesn't enter Maintenance Phase 3 immediatly because in Phase 2, Block A and Block B are parallel. Only failure of Block A doesn't bring system down. 
3. At 1200, system finishes Phase 2 and goes back to Phase 1. There is not system failure in Phase 2 (only failure is Block A). In Phase 1, Block A and Block B are in series. Failure of Block A passed from Phase 2 will bring system down in Phase 1. Thus there is a system failure in Phase 1 and system goes to Maintenance Phase 3 immediatly. Block B is not down, thus it gets PM with duration 20 hours. Block A gets CM with duration 100 hours. 
4. At 2738, Block A fails in Phase 1 and bring system down immediatly. System goes into Maintenance Phase 3 immediatly. Block A gets CM and Block B gets PM.

Example 2

The Phase diagram is as followings:

Everything is the same as that in Example 1 except that the link from Phase 2 to Maintenance Phase 3 changes from F link to S link. This means that whether or not there is a failure in Phase 2, the system would go to Maintenance Phase 3 after Phase 2. But if there is a  failure in Phase 2, system would go to Maintennace Phase 3 after Phase 2, not immediately. 

The Block Up/Down plot is as followings:

1. At the first cycle (0-500 for Phase 1 and 500-600 for Phase 2), there is no failure, thus after Phase 2, the system go to Maintennace Phase 3 for PM for both Block A and B with duration 20 hours.
2. At 1171, Block A fails in Phase 2. Due to the parallel system structure in this phase, this failure doesn't bring system down. However, after Phase 2, system still go to Maintenance Phase 3.
3. At 2835, Block A fails in Phase 1. Due to the series system structure in this phase, this failure bring the system down and thus system go to Maintenance Phase 3 immediately. 

The Phase diagram is as followings: