Calculating the Mean Time Between Failures?

Blue Booger asks: "I was looking over some fibrechannel hard drives and noticed that the Mean Time Between Failures was rated at 1.2 million hours. I thought that was pretty high, and figured it up to be close to 137 YEARS!! I went to check some regular IDE drives just for comparison, and they were rated at 500,000 hours (57 years). Now, as I understand it, this is supposed to be the average time that you can expect the drive to last before failures. I rarely have an IDE drive last more than 4 years, and my record is 10 years, so what is the deal? BTW, that is 57 years running 24 hours a day...the MTBF is rated as power on time. Here you can find Western Digital's glossary that defines the term MTBF (pdf). Here you can find a spec sheet on one of their 20GB IDE drives. I checked, and Seagate also lists similar MTBFs. How the heck are they coming up with these numbers?"

Comments

You are wrong

[Mensa Babe]

I rarely have an IDE drive last more than 4 years, and my record is 10 years, so what is the deal?

If you have twenty drives with twenty years MTFB (Mean Time Between Failures) each, then you have one failure per year on average. These are basic statistics fighting always against you.

MTBF calculation and estimation

[crmartin]

You know, it's almost a shame to screw up the amusing notions /.ers come up with by adding actual information, but I can't help it, all those years of teaching I guess.

Okay, first of all: "mean time between failures" is obviously a statistical measure -- it is an average over a large number of individual items. In most electronic components (including light bulbs!) the statistical distribution of the time between failures is the exponential distribution, which has the odd property that it's "memory-less" -- it doesn't matter how long since the last failure it's been, the mean time to the next failure will still be the same. A consequence of this is that if the MTBF is 10,000 hours, the probability of failure in any particular hour would be 1/10,000th. So, if you set up 10,000 components, all running simultaneously, you'd expect one of them to fail within the first hour; conversely, if you ran them for 1000 hours, and 998 of them failed, you could be fairly certain that the MTBF would be around 10,000 hours.

Note, by the way, that this is only true when the failure time distribution is exponential -- so it works for electronic components, but not for, say, bicycles and cars and roller skates, which are more likely to fail the older they get.

This has an obvious problem, of course: if the MTBF is high, it can take forever to test. Consider, for example, something I worked on for NASA some years ago: trying to prove that a fly-by-wire system will have a mean time between failures of 1e10 hours. (This is about the same failure rte as the airframe, which is how they came up with the number.) 1e10 hours is about 1.141 million years, by the way.

(Pop quiz: if MTBF is a million years, how do you explain the occasional airframe failure, say, eg TWA 800? Hint: It doesn't require any foul play.)

At that point, you've got a couple of choices: first, you can make a lot of copies and run them simultaneously. Relatively easy for $50 disks, hard for billion dollar 747s.

Second, you can make the estimate by computation and modeling which is what you do for web systems. Conceptually, it's pretty simple to do this, although it can be a kind of pain in the ass.

The third way, which is new and cool, is by Bayesian estimation of failure rates. This method lets you make increasingly accurate estimates of the failure rate based on short experiments. I don't have time to go into it, but there are some good sources available on the web.