On 07/21/2017 8:30 PM, dpb wrote:
On 07/21/2017 7:02 PM, dpb wrote:
...

+ How accurate& precise is a reading of 20.25 gallons on a gas pump?

NIST tolerance is 6 in^3 in a 5 gal measure. AFAIK that's what all state
W&M departments use for their tolerance. A NIST document of 20,000
tested meters showed 0-mean normally distributed discrepancies at about
90% bounds on the +/-6 number. The 6/5gal -- ~0.5%

....

And remember that is the "shut 'er down" tolerance, not the average...as
noted, the most probable based on the NIST sample was in the +/-0 bin (1).

I didn't quite recognize what the figure was yet when first looked at it
and had closed the link when I realized the significance so don't have
the actual numbers at hand...but the +/-6 number was quite a way out on
the tails of the distribution altho I don't know just precisely the
tails percentages.

And, actually while the report used "normal" in discussing the
distribution, it really wasn't normal as in bell-shaped, it was
symmetric and zero-mean, but the tail in each direction dropped off more
as hyperbolic than a normal--hence the tail percentages would actually
by somewhat lower than a real normal of same mean, standard deviation.


I got curious myself on what the numbers revealed and looked at the NIST
numbers again.

I computed an empirical cdf and compared it to normal...statistics from
the 20,036 observations are below:

[h,s]=cdfplot(x);
s
s =
min: -50
max: 146
mean: -0.0788
std: 3.7681
median: 0
mode: 0


I then compared to normal on the same plot and as outlined above
N(mean,std) is too long-tailed on both ends in comparison. It turns out
that N(mean,std/1.5) is pretty close on both tails to about the +/- 6 point.


Anyway, from the above it's simple enough to get some pretty good
estimates of what pump volume errors one might expect...the table below
is from the empirical cdf NIST data...

P error(in^3)/5Gal error(%)
0.001 -22 -1.82
0.005 -9 -0.78
0.010 -8 -0.69
0.025 -6 -0.52
0.050 -5 -0.43
0.250 -2 -0.17
0.500 0 0
0.750 2 0.17
0.900 4 0.34
0.950 5 0.43
0.975 6 0.52
0.990 7 0.60
0.995 10 0.86
0.999 22 1.82

From the above, one can conclude the pump metering error small for all
except the extreme outlier pumps.

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