Title: The Mathematics of Reliability

Description:

We often hear talks of "scale" and "reliability", mostly based on personal experience and lessons learned. What can Mathematics tell us about reliability and scale? Can math help us scale our systems and companies? It turns out that failure models, probability, statistics and other domains can help our analysis and provide insights.
This talk presents various mathematical models that support our understanding of reliability and failure. There are many nuances and pitfalls associated with reliability and mathematical modelling helps to reveal and avoid them.
This talk will present basic models of failure and reliability and discuss their implications:

• Statistically independent failures (redundancy theory)
• Statistically dependent failures
• Active/standby failover and the base rate fallacy
• Queue theory applications to reliability