In Markov model of the system, I am using minimum repair, when the system is in absorbing state again I applied minimum repair to bring it back to the working condition. But When I tried to find the MTBF of the system it becomes infinity why is this is happening?
You may consider providing the community with your model in case there is an issue with its structure that may be causing the issue.
Mathematically, it is thanks to the heavy tail distribution of the time between failures.
Without the model, it is not really possible to answer to your question.
Anyway:
- If you allow to jump out of the absorbing state, this is no longer an absorbing state.
- If you really have an absorbing state (without repair), this models the occurrence of the first system failure. As it is not repaired the MTTR goes to infinity and the MTBF = MTTF+MTTR goes also to infinity. Therefore you result is "normal" because in this case the concept of MTBF is meaningless.
Beware of the definitions which are often mixed up:
- MTTF: mean time to failure
- MTTR: mean time to restore
- MTBF: mean time between failures = MTTF+MTTR
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