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SD p101: MTBF

Not considering that there is quite a lot of discussion about the usage of the acronyms MTBF, MTTF, MTRS and so on, this is simply wrong (or at least inconsistant):

MTBSI = Available time in hours / Number of breaks
MTBF = (Available time in hours - Total downtime in hours) / Number of breaks

Available time to my understanding is the time the service is up and running properly. Some people call it "uptime", though that is easily confused with the moment in time the service comes up. So it should be:

Available time in hours = uptime = Total time - downtime

Hence:

MTBSI = Total time / Number of breaks
MTBF = (Total time - Total downtime) / Number of breaks

I wonder why the term "downtime" is used without hesitation, the term "uptime" not. Would simplify things. One could then decide whether to compare to agreed service time (AST) or the total time passed (T). It could be:

MTBSI = AST/n

Though the figures would look worse, as the AST is most certainly always smaller then T.

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MTBSI and MTBF formulas not well stated in ITIL book

I agree. Good observation!

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