# [rc5] Re: OS/2 ramdisk and spindown

James Mastros root at jennifer-unix.dyn.ml.org
Mon Oct 13 17:49:15 EDT 1997

```On Mon, 13 Oct 1997, Skip Huffman wrote:
> On Sun, 12 Oct 1997 01:17:25 -0400 (EDT), James Mastros wrote:
> >> MTBF means that if all the drives of that model were running at the same
> >> time, and the total time they were running were added to each other they
> >> would run for X hours combined!!!  before one of them failed.
> >If you want to be techinical, MTBF meens Mean Time Between Failures or Mean
> >Time Before Falure (one or more of those "Me[ae]n"s are misspelled, I
> >know...).  That is to say, if you ran a infinite number of hard drives for
> >that amount of time, exactly half of them should have failed.
>
> This is extremely basic statistics.  There are three primary types of
> averages.  Mean, Median, and Mode.  A Mean average is derived by adding the
> measurements of all items in a sample and then dividing the total by the
> number of items in the sample.  A Median average is the point where half of
> the items in a sample measure below that point and half measure above.  A
> mode average is that measurement where the largest number of items have that
> measurement.

Umm... I specified an infinite sample size, so the median is nonsensical.
With an infinate number of drives (if you want to be technical, a set of
drives having the same cardnality as the non-negitive reals (we consider a
drive that dosn't work when first spined up as having a failure time of
zero, not as failing before it was started, since we have no way of
assigning a value in the later case).  It has been proven that you can't
prove or disprove if that is Aleph-1, however.), the mean should be
equivilent to the median.  In any case, you cannot compute the limit as n
approaches infinity of the median of a set of n, but you can compute the
limit as n approaches infinity of the sum of a set of n members over n (I
think.  I can't describe the median of an infinite set, wheras I can
describe the mean).  So the median is undifined, whereas the mean is a
limit.  In any case, I'm fairly certian that as the sample size increases,
the mean and median tend to converge.  I could be completly wrong here.  In
fact, I wouldn't be at all surprised.

-=- James Mastros

(PS - You should probably turn word wrap on in your mail client.)
---
"I'm not saying you should flash your hooters... but it would help"
-=- Howard Stern

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