Yes, a failure is a failure. If something keeps having early life failures, it's MTBF will be low, no point hiding the early life failures, as ultimately, they are a failure that has an impact on the plant / business.
MTBF and any other metric for that matter must be used in context of something. MTBF is usually used on the context of a reliability program to help prioritize where attention should be paid to solve problems, so a low MTBF = problem = do something to stop the startup failures.
If MTBF is being used on contractual / performance guarantee context, then you would need to refer to whatever the contract says, but it'd be surprised if it sadi to ignore commissioing / early life failures.
Andrew O'Neill
Specialist Mechanical Engineer
Australia