Mean Time Between Failures

Availability is set by how often a plant fails and how long each repair takes; MTBF and MTTR together, not a single number, decide whether the burner is firm.

Two clocks behind one number

Availability is MTBF / (MTBF + MTTR): the mean time between failures divided by that plus the mean time to repair. A plant can be available either by failing rarely or by recovering fast. Early hardware tends to be weak on both — more faults, and longer repairs while procedures and spares mature.

# Availability from MTBF and MTTR
def availability(mtbf_h, mttr_h):
    return mtbf_h / (mtbf_h + mttr_h)

# Illustrative early-life burner numbers (design study, not measured):
print(round(availability(2000, 100), 4))  # 0.9524  frequent, slow repair
print(round(availability(8000, 40),  4))  # 0.9950  matured
# Tier III (0.99982) needs, e.g. one 8h outage per ~44,000 h:
print(round(availability(44000, 8), 5))   # 0.99982

The arithmetic makes the availability gate concrete. To reach the burner's modelled high end of 0.995 alone, a unit must run thousands of hours between faults and repair in tens of hours. To reach Tier III's 0.99982 as a single machine would require tens of thousands of hours between failures with same-day repair — a maturity no first-of-a-kind fusion device can claim.

This is why the honest path to Tier III is redundancy rather than a heroic single-unit MTBF. It is also why the program builds the breeder first and treats the burner as a design study through ~2032: MTBF and MTTR only improve with operating hours, and there are none yet.

The design levers are clear: raise MTBF by de-rating the hardest-run components and adding condition monitoring, lower MTTR with modular replacement and staged spares, and cover the residual with the hybrid.

• Availability = MTBF/(MTBF+MTTR)
• Improve by failing less or repairing faster
• Single-unit Tier III needs maturity fusion lacks today
• Redundancy substitutes for the MTBF the machine has not earned