[rescue] Fun With Statistics

[Joshua D Boyd]

On Sat, Jun 01, 2002 at 10:40:17AM -0500, Leslie Connally wrote:

> He was telling me the new 5 series (?) now had 6 coils in them.. one for
> each cylinder. We discussed how an old 2002 just needed one, and they never
> ever failed anyway.
> But then he said, they (the new coils) were shit coils nad went out all the
> time. I said, "Good to have extras then I suppose", and he replied: "No, if
> one goes out, the computer wont let the engine start, so the other five
> dont matter".

Dodge does that on some (if not all) of their trucks now.  I heard a
reason for it that sounded good, but now I forget.  It might have had
something to do with performance tuning.
 
> So then I was thinking.. Do 6 coils  make the care MORE reliable? And he
> said, NO. More Coils, More Chance of One Failing. It would be better to
> have one shit coil than six.
> 
> Is he right?

Yes.  

If you have events A and B, where P(A) and P(B) are the probabilities
of that event happening, then
P(A and B)=P(A)*P(B)
P(A or B)=P(A)+P(B)

So, in this case, we have 6 events (the failure of one of the six
coils), so we are looking at
P(A or B or C or D or E or F)=P(A)+P(B)+P(C)+P(D)+P(E)+P(F),
which obviously greater than just P(A) (where P(A) is the probability
of failure in a single coil system).

Of course, this ignores things like each coil now probably gets less
wear than the single coil from older cars did, etc, etc, etc.
 
> Is one disk "more reliable"  than striping six RAID 0.

With RAID 0, one disk is more reliable.  It is that OR relationship
again.  If disk A or disk B fails you are screwed.

On the other hand, with RAID 1, you need disk A AND disk B to fail for
that same screwed state, and P(A)*P(B)<=P(A) (note, typically
probabilities are expressed as a number between 0 and 1.
 
> Is a 4 processor machine more likely to crap out than one with only one.

Presumably, but processors just don't fail all that often.
 
> If one of four processors crap out, wont you get a kernal failure.. making
> the other three unuseable ?  (yes I do know 4 processors are *not* for
> *reliability*)

Depends on the system.  IBMs mainframes can handle CPU failures
without causing kernel failures, linux can't.

-- 
Joshua D. Boyd