I, for one, appreciate Doug McKean's analysis. Even though I do not draw the
same conclusions, his presentation stimulated thinking. Applying a sanity check
leads me to suspect that there is something wrong with the results of
mathematical manipulation. I'll use the 10 dB margin as the example. He states:
"Now, let's pick the -10dB below standard and assume 50dB is the standard.
Our limit is now 40dB. Assuming 8 samples 3dB below and 2 samples 3db again
we have the following:
Samples 1 - 8 = 37dB, Samples 9 and 10 = 43dB.
Average = 38.2
Variance = 6.4
% Confidence Variance Lower limit Upper limit
80% Confidence +/- 2.59 35.61 40.79
95% Confidence +/- 3.97 34.23 42.17
99% Confidence +/- 5.21 32.99 43.41
Here, even at 99% confidence (1% unaccounted for)
we have less than 6dB 'headroom' where before we had less than 3dB. "
My comments:
The results of the analysis shows that we can be confident that 99% of
production units will fall between the levels of 32.99 and 43.41. Yet we
started with units which at best, met at 40 dB level during testing. I have
never seen production units get better than what was tested at the site. The
calculations come up with units which could have gotten better by 7.1 dB.
That's a 17 dB margin to the limit, and I just can't buy those figures.
I also cannot place any trust in figures that conclude that the units get even
worse than the actual units tested from production. i.e. the worse production
unit was 43 dB and the calculations come up with 43.41 dB.
While I admire the mathematics, personally I think that the results do not pass
the logic test.
Gabriel Roy
Hughes network Systems
Md
----------------------------- snip ---------------------------------
Doug McKean wrote:
At the risk of being solidly flamed, I'd ask to raise the
dB Margin discussion one more time and if need be off-line.
See my email address below. If you're going to flame me, do it quick
to the bone and I'll be done with it.
My discussion is going to:
1. Assume an awful lot and may be unacceptable to some,
2. Stay somewhat nonrigorous statistically.
I'll readily admit to these flaws up front for the sake of discussion
and not so much for actual fact. The facts are dependent upon your
own experience, the designers you work with, and your equipment, etc...
It has been my own experience that the difference between a -6dB
margin and a -10dB margin for a product 'could be' the difference between
100's of dollars of 'fixes' and 1000's of dollars of 'redesign' respectively
in manufacturing quantities. (Remember I say 'could be'.)
Somewhere in the back of everyone's mind with whatever margin
you should pick should be a thing called statistical 'variance' of data.
And dependent upon variance is another thing called 'confidence' margin.
Let's say also that the 80% of the products made works out to be 10 samples to
be
tested (just for ease of discussion). 80% of the samples passing means 8
pass/2 fail.
Let me assume that someone picks -6dB as the goal below the standard.
Let's say the limit of the standard is 50dB.
For demonstration purposes, 8 samples test 3dB below the limit (now 44dB)
and 2 test 3dB above the limit.
Samples 1 - 8 = 41dB, Samples 9 and 10 = 47dB.
Average = 42.2
Variance = 6.4
The following confidence levels are:
% Confidence Variance Lower limit Upper limit
80% Confidence +/- 2.59 39.61 44.79
95% Confidence +/- 3.97 38.23 46.17
99% Confidence +/- 5.21 36.99 47.41
In other words, even at 99% confidence (1% unaccounted for)
we have less than 3dB 'headroom'.
Now, let's pick the -10dB below standard and assume 50dB is the standard.
Our limit is now 40dB. Assuming 8 samples 3dB below and 2 samples 3db again
we have the following:
Samples 1 - 8 = 37dB, Samples 9 and 10 = 43dB.
Average = 38.2
Variance = 6.4
% Confidence Variance Lower limit Upper limit
80% Confidence +/- 2.59 35.61 40.79
95% Confidence +/- 3.97 34.23 42.17
99% Confidence +/- 5.21 32.99 43.41
Here, even at 99% confidence (1% unaccounted for)
we have less than 6dB 'headroom' where before we had less than 3dB.
For those of us not familiar with all this, first notice how the
variances didn't change (as long as I was assuming the same type of data
spread around the limit) and how the upper/lower limits fit
around the 'average' with respect to the variances.
Now, I won't conclude which is the better. It could be argued that
-6dB is neccessary and -10dB is sufficient. As I said before,
this could result in a small amount of money or alot of money
being used to comply. That's for you to decide.
This example has been crudely done I admit, but I thought to
start somewhere. There's a high possibility someone out there
is much smarter than me to shoot holes in this entire discourse.
I'm open for any suggestions.
*******************************************************
Doug McKean
[email protected]
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The comments and opinions stated herein are mine alone,
and do not reflect those of my employer.
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*******************************************************
