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I am modeling the reliability of a system with four units, numbered 1 through 4. The system needs at least two of the four units to be operational. Initially units 1 and 2 are active and units 3 and 4 are in warm standby. If either unit 1 or unit 2 fails, unit 3 becomes active (unless it has already failed while in standby). If a second active unit fails, unit 4 becomes active (again unless it has already failed while in standby). When a unit fails it remains failed.

Unit 1 has reliability distribution d1, unit 2 has reliability distribution d2, unit 3 has reliability distribution d3a when active and d3s when in standby, and similarly for unit 4.

StandbyDistribution handles cases where initially there is only one active unit. However, in StandbyDistribution[dist1, {..., {distxstandby, distxactive}, ...}, ...], it is not at all obvious to me what the expression dist1 should be for the case I am looking at.

At the same time, BooleanCountingFunction is well suited for an M of N system where all of the units are active, but there doesn't seem to be any way of specifying that N - M units are initially in warm standby.

Has anyone successfully dealt with the case I am looking at?

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