The Math of Reliability
summary
Begins with Guinness and the origin of the student t-test, then shows concrete math: a 15s probe with a 4-fail alert threshold gives 0.4^4 = 2.56% per-try but still a 46% chance of no alert after 30 minutes, 21% after 1 hour, 10% after 90 minutes. MTBF often extrapolates short lab runs across time. Redundancy math shows 10-node clusters can need ~10% overhead (n+1) and larger fleets lower overhead. Demonstrates 5% false positives -> ~2% PPV for a 1/1000 base rate, queueing doubles latency near 70% utilization, and recommends circuit breakers, backoff and avoiding correlated failures.
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chapters (7)
- 0:00Start
- 4:52EXAMPLE: NAGIOS-LIKE ALERTS Nagios service with max check attempts
- 11:12RELIABILITY MEASURES
- 16:35SERIAL RELIABILITY
- 29:07ACTIVE/STANDBY FAILOVER
- 31:33MULTIPLE DEPENDENCIES
- 38:00LITTLE'S LAW
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