## Message Posted: Mon, 19 Jan 2004 @ 12:28:06 GMT

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 Subj: Re: Fallback vs. RAID1 vs. Journaling From: OHara, Daniel

Hi Sanjaya,

Mean Time Between Failure (MTBF) is the reciprocal of the probability of failure ie. the chance of failure is 1/MTBF.

The chance of not failing is 1-1/MTBF.

The chance all of the n similar components in a system not failing is (1-1/MTBF)^n.

The chance of this system failing is 1-(1-1/MTBF)^n).

The MTBF of this system is 1 /(1-(1-1/MTBF)^n))

Thus for out 100 disk with MTBF of 4 years

1/(1-(1-1/(365.25*4))^100) = 15 days

If you set up the system so that it will only fail both of a pair of component fail you need to calculate the chances of one of the components failing and the other failing before it is repaired. At this point the Mean Time to Repair (MTR) comes into play. Without going through the derivation the MTBF for the pair is MTBF^2/MTR/2. Thus for the same disks with a MTR of 1 day

MTBF for pair = 4^2/(1/365.25)/2 = 2,992 years

MTBF for system with 100 pairs = 1/(1-(1-1/(2992))^100) = 30 years

Hope this helps.

Daniel O'Hara
Project Manager
NCR

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