On Sun, 23 Jul 2017 10:04:30 -0500, dpb wrote:

On 07/22/2017 9:40 PM, Mad Roger wrote:
On Sat, 22 Jul 2017 19:44:26 -0500,
dpb wrote:

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:

[2 quoted lines suppressed]
s =
min: -50
max: 146
mean: -0.0788
std: 3.7681
median: 0
mode: 0
...

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.

...

But your numbers confuse me because they seem to be in cubic inches.

Well, yes, as said before the NIST standard for compliance testing is a
metering error of 6 cu in in 5 gal so the reported data are the
observed errors in a 5 gal test...

For the mathematically and engineering challenged, that is 3.325
fluid ounces - or less than half a cup - or 3.25 in 640 - or an error
of less than 0.5%
You also mentioned that metric pumps are more accurate, ...

_I_ said nothing about metric anywhere during the thread. Another
respondent pointed out that a liter, being smaller than a gallon, when
metered to the same tenth of a unit as the gallon will be a smaller
absolute error than in gallons. Seems fairly obvious...

Anyways, can you just summarize what the error is for a typical USA pump in
gallons?

The above data showed that the most probable error was 0 (actually less
than +/-1 ci since data are reported to nearest whole number). I
mentioned multiple times already and its in the table the distribution
was symmetrical and the mode and median were both 0. The mean is just
under 0.1 ci (-0.08) so there'd be a good place to start for just a
random pump taken from the population of pumps.

For a typical 20-gallon fill, how many gallons off can reality be, plus or
minus from the indicated reading on the pumpmeter?

Take your choice of how conservative you want to be or how likely it is
to be of that magnitude--that's why I gave the ecdf data--you can choose
the appropriate number for the particular use.

20*0.018 -- 0.36 gal would encompass 99.9% of all observed pumps on
either the over- or under-dispensing side; the likelihood finding an
operational pump of that drastic a metering error would be only 0.1%
though, so not likely.

OTOH the most probable pump taken from random would be 1 and so using
that as a bound, 1 ci-- 0.004329 US gal * 20 -- 0.0866 gal. Or, iow,
about what the 0.1 gal pump readout would indicate.

Of course, like any probability, what a particular realization will be
is totally dependent upon the actual pump used but the (sizable)
sampling of operating pumps taken during routine weights and measures
compliance checks shows that in general they work pretty well with a few
that have issues.

An interesting sidelight on that was the summary table of percentage
failures (exceeding the 6 cu in threshold) by pump manufacturer. There
were 4 with 100% compliance, another for in the high 80-90% range,
another 4/5 in the low 80% and then one laggard at 73%. I'd not have
guessed there were so many manufacturers but it appears there's a
price/performance element there as is so often the case...

(The manufacturers were anonymous so no way to use the data to go find a
station with one of the compliant pumps, unfortunately ). It did
note that W&M compliance checks could be much more effective at a given
cost/manpower level if used stratified sampling by vendor...