failure rate

The spares number falls out of the failure rate times the repair turnaround, and the cheap items are the ones people forget. The arithmetic for GPUs, the very different arithmetic for transceivers, and the rule that decides whether to hold a part at all.

Modules do not fail randomly at three times a published rate, so the excess has a cause and it is usually thermal or a batch. The cohort cuts that localize it, the counters that separate a dying module from a dirty connector, and the environmental cause that looks like a hardware defect.

Meta's Llama 3 report counted 419 unexpected interruptions in 54 days on 16,384 GPUs, one every three hours. The failure-rate arithmetic, the loss as a function of the interval, the square-root formula that minimizes it, and why the write must be sharded and asynchronous first.

A published run gives the numbers directly: 419 unexpected interruptions in 54 days on 16,384 GPUs, and about three quarters of them hardware. What that implies per GPU-hour, which components dominate, and why a fleet above a few thousand GPUs must treat failure as routine rather than exceptional.

Published data gives an interruption rate, and replacements are a fraction of interruptions, so the comparison needs care before it means anything. The derivation that turns one into the other, the answer for a healthy fleet, and the four cuts through the data that turn an anomalous number into a cause.