Data-center availability (Tier III power, cooling, network, storage)
A four-stage reliability block diagram for a Tier III data center — dual-source power (utility in parallel with a generator-plus-ATS chain), N+1 (2-of-3) CRAC cooling, dual core switches, and mirrored storage. The engine reduces the whole nested structure to one availability figure.
For the data-center architect proving an availability target
What this shows
A realistic Tier III topology where the whole facility is a series of four subsystems, each internally redundant. The power stage is the interesting one: the utility feed runs in parallel with a backup chain — a generator that only helps if its transfer switch also works (a nested series). Cooling is N+1 (2-of-3 CRAC units), and both the network and storage tiers are mirrored pairs.
The engine reduces the nesting to one number. It rolls the generator chain (0.98 · 0.995) into the power parallel, evaluates the 2-of-3 cooling exactly, and multiplies the four series stages to a facility availability of ≈ 0.9972. No single point of failure survives — every stage has redundancy — and the Birnbaum importance ranks which subsystem to harden first. This is the kind of nested success logic a generic diagram tool draws but never computes.