The Availability Math

Combined availability is computed from each layer's uptime and independence; the arithmetic shows how a 0.995 burner contributes to a 0.99982 system.

How the nines combine

For independent redundant layers, the system is down only when all layers are down at once, so unavailabilities multiply. If two independent sources each have unavailability 0.02 (availability 0.98), the chance both are down together is 0.02 x 0.02 = 0.0004, giving combined availability 0.9996 — better than either alone. Add a third and the product shrinks further.

# Combined availability of independent redundant layers
burner = 0.995      # modelled high end of the burner
battery = 0.999     # UPS/battery layer
grid    = 0.999     # utility import path

def combined(*avails):
    unavail = 1.0
    for a in avails:
        unavail *= (1 - a)   # all must be down together
    return 1 - unavail

print(round(combined(burner, battery, grid), 6))  # -> 0.999999995 (ideal, independent)
# Real numbers are lower: outages are not fully independent,
# and switching/transfer adds its own failure modes.

The code shows the principle and its trap. In the idealized independent case, even a 0.995 burner plus a battery and a grid tie clears Tier III comfortably. In reality the layers are not perfectly independent — a regional grid event, a shared switchgear fault, or a transfer-switch failure can take more than one layer at once — so the true combined number is lower than the naive product.

This is why the availability gate is stated as a floor to design against, not a number to explain away. The burner's 0.86-0.995 is the input; Tier III is the target output; the engineering is in choosing enough independent layers, and reducing common-mode failures, so the real combined availability reaches 0.99982.

The honest reading: the math permits Tier III from an imperfect burner, but only with genuine independence between layers and careful attention to the switching that ties them together.

• Independent unavailabilities multiply
• A 0.995 burner + battery + grid can clear Tier III on paper
• Common-mode failures and transfer switches lower the real number
• The gate is a design floor, not a rounding error