I think it depends on your requirements. To be honest I have never dealt w/ FCR specifically but certainly have dealt w/ a lot of customer support processes.
After pondering this more, rather than a custom field I might simply add a Resolution code called "FCR". So if the agent resolves on the call they will have created the ticket during the call and transitioned it immediately to In Progress and if resolved on the call they would transition to Done w/ Resolution of FCR. I can then create charts, e.g. a pie chart, that would illustrate resolution type:
10% = FCR
80% = Done
2% = Invalid
However, maybe you would want a custom drop down "FCR TTR" that had options of "<10min", "w/in 30min", "w/in 1h", ">1hr". In this way if the agent resolves the issue during the initial call they would be required to select the FCR TTR value. This would allow you to show things like: 30% of issues are resolved during the initial call and then of that 30% here is the breakdown of the TTR.
hope that helps
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