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.

1. For a F link, on system failure, system go to somewhere immediately when failure occurs.
2. For a S link, if there is no system failure during this phase, system goes to somewhere by the end of the current phase.

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 100 hours and Phase 2 has duration 500 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 go to Maintenance Phase 3 immediately.

The Block Up/Down plot is as followings:

1. At the first cycle (0-100 for Phase 1 and 200-600 for Phase 2), there is no failure, thus after Phase 2, Phase 1 is executed (back to Phase 1 after this cycle).
2. At 616 (Phase 1 of the second cycle), Block A fails. System doesn't enter Maintenance Phase 3 immediatly because in Phase 1, Block A and Block B are parallel. Only failure of Block A doesn't bring system down. 
3. At 700, after Phase 1, system goes into Phase 2. In Phase 2, failure of Block A (passed from Phase 1) bring the system down because in Phase 2, Block A is in series with Blokc B. Thus system goes into Maintenance Phase 3 immdediately.  Block B is not down, thus it gets PM with duration 20 hours. Block A gets CM with duration 100 hours.
4. At 1669, Block A fails in Phase 2 which bring down the system and system goes into Maintenance Phase 3 immdediately. 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 219, Block A fails in Phase 2. This failure bring the system down. However, Since the link from Phase 2 to Maintenance Phase 3 is a S link, system doesn't go into Maintenance Phase 3 immediately. It would go into Maintenance Phase 3 after the Phase 2. Block A gets CM and Block B gets PM in there.
2. At 1934, Block B fails in Phase 1. This failure doesn't bring system down becasue in Phase 1, system is in parallel structure. After Phase 1, system goes into Phase 2 and the failure of Block B brings system down in Phase 2. However, system doesn't go into Maintenance Phase 3 immediately because the link between them is S link. System goes into Maintenance Phase 3 after Phase 2 and Block B gets CM and Block A gets PM there.