Undergrad version: the lifespan of a single drive should be exponentially distributed with some rate lambda. The time to first failure from among k drives would

Undergrad version: the lifespan of a single drive should be exponentially distributed with some rate lambda. The time to first failure from among k drives would then have an exponential distribution with rate k * lambda. The confidence interval for lambda is: http://en.wikipedia.org/wiki/Exponential_distribution#Confidence_intervals http://en.wikipedia.org/wiki/Exponential_distribution#Confid... Grad-level version: drive lifetime is exponential with an inhomogeneous (increasing, presumably) rate function lambda(t). Inferring lambda(t) is difficult without additional assumptions on the functional form. But potentially do-able. Real-life version: None of the classical distribution fit that well. (https://www.usenix.org/legacy/event/fast07/tech/schroeder/schroeder_html/ https://www.usenix.org/legacy/event/fast07/tech/schroeder/sc...) (This is survival analysis: http://en.wikipedia.org/wiki/Survival_analysis http://en.wikipedia.org/wiki/Survival_analysis)