The Maintainability Toolkit does not specifically address MTBO by name.
You may refer to the Department of Defense “Approved Acquisition Objective” document, AAO03: (https://dap.dau.mil/policy/Documents/Policy/AAO03.doc). It says:
“The MTBO is the mean time between scheduled maintenance at the depot (i.e., overhaul, repair and retain (R&R), inspect and repair only as necessary (IROAN), etc.). For new equipment the time factor may be based on the engineering studies, the anticipated life cycle, or historical usage data for similar equipment. Again, an analysis of alternatives needs to be developed to determine the potential impact and associated risk each alternative incurs. For fielded equipment, historical data for that item may be applied to reflect the actual usage experience. The basis used to estimate MTBO must be documented and should be provided with the estimate itself when it is used for computation of the DMFA. Unit of measure needs to be converted to days.”
( DMFA: Depot Maintenance Float Allowance)
Mean time Between Overhaul relates only to the special cases of Scheduled Maintenance, i.e. those related to depot-level overhauls. Overhauls are usually required to circumvent future failures or unacceptable levels of degradation due to wear-out mechanisms or some other form of anticipated degradation mechanism (corrosion, erosion, etc.)
Since MTBO is a form of Mean Time Between Scheduled Maintenance (MTSBM or MTBMS), it can be defined mathematically as:
MTBO = Total Operating Time/Overhaul Events
Depending upon what industry this applies to, the units of measure may differ. Example, for the aircraft industry, the numerator may be “Total Flight Time”.
Mean Time Between Maintenance is covered in the Maintainability Toolkit along with a great deal of other Maintenance-related data. It would be a good reference to have on hand.