June 2, 2015
Suggestion for Analysis of Inspection Results for RMFD Meters
Submitted by Henry Oppermann, Weights and Measures Consulting
I think that the most effective justifications for weights and measures programs are to use the
actual inspection results for the jurisdiction. The first step is to analyze the meter accuracy test
results for over delivery versus under delivery (i.e., meter underregistration versus
overregistration). Second, the rejection rate for inaccuracy can be compared to the rejection rates
obtained by other jurisdictions. Third, if sales figures are available and the errors for rejected
meters are in a database or can be estimated in a reasonable way, then the economic impact of
the meter errors for the inaccurate meters can be estimated (calculated). One suggested method
of analysis is provided below.
Nebraska Weights and Measures recorded all meter errors for their inspections of RMFDs in a
database. Below is a histogram of their inspection results for 2008.
NE 2008 All Dispensers: 21,616 meters
Tolerance
Zero
4486
5000
4500
4000
2000
2270
1584
2500
178 meters or 0.82%
were out of tolerance
for over delivery
2951
3103
2542
3000
147 meters or 0.68%
were out of tolerance
for under delivery
1545
Number of Meters
3500
463
237
679
39
36
17
15
8
4
4
5
7
2
4
5
1
3
1
1
3
1
1
2
1
2
1
7
6
9
6
4
17
15
25
45
151
368
1000
500
912
1500
0
Fast Flow Delivery Errors (in3)
1. The first assessment is the rejection rate for inaccuracy, which is 1.5%. This rejection rate
for inaccuracy is very low and can serve as a benchmark against which to compare
results from other jurisdictions. It is unrealistic to expect 100% compliance. The law of
diminishing returns applies in that above a certain compliance rate, it takes a considerable
increase in inspection effort to reduce the number of inaccurate meters in the jurisdiction. I
think that the Nebraska results illustrate about the highest level of accuracy compliance for
RMFD meters that can realistically be achieved.
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June 2, 2015
2. Next, the rejection rate for meters out-of-tolerance for under delivery (meter overregistration)
should be compared to the rejection rate for over delivery (meter underregistration). The
Nebraska data shows that a slightly larger percentage of meters were rejected for over
delivery than for under delivery; however, the values are nearly equal. This is an excellent
result. If a much larger percentage of meters was rejected for under delivery than for
over delivery, then this would indicate a need to increase inspection and enforcement
efforts for RMFDs.
3. Now an estimate of economic impact assessment can be made for the meters that were found
to be out of tolerance. Sales figures for gasoline stations are needed to identify that dollar
value of product sold by service stations. Various sources may be available to obtain the sales
figures. In this example, the Economic Census data for 2007 are used, which are the latest
currently available for Nebraska. Data from the 2012 Economic Census should be available
later this year. Estimated average errors for the meters that were out of tolerance both plus
and minus deliveries are also needed. A spreadsheet has been created for these calculations.
Total sales for Nebraska gasoline stations in 2007 were $4,275,079,000.
The total number of RMFD meters tested by Nebraska in 2008 was 21,616.
Excluding extreme outliers, the percentage of meters that under delivered beyond the
tolerance limit was 0.6708%.
The average error for these meters was -10.7 in3 on a 5-gal test draft. This represents an error
of -0.9279%.
Based on the total sales in 2007 and assuming that the meters delivered the average
amount of gasoline for one year, the total dollar amount of the measurement errors for
the meters that were out of tolerance for under delivery in 2008 was $266,096. The
consequences of these sales were against the consumer.
The same calculation can be performed for the meters that were out of tolerance for over
delivery.
Excluding extreme outliers, the percent of meters out of tolerance for over delivery:
0.7032%
Average error for these meters: 10.3 in3 or 0.8937% on a 5-gal test draft.
Based on the total sales in 2007 and assuming that the meters delivered the average
amount of gasoline for one year, the total dollar amount of the measurement errors the
meters that were out of tolerance for over delivery in 2008 was $268,664. The
consequences of these sales were against the owner of the service station.
The total economic impact for the measurement errors for the out-of-tolerance meters
was $534,760.
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June 2, 2015
Below is the spreadsheet layout for these calculations.
Enter data below
Amount of sales for the
station ($)
4,275,079,000
Total Number of meters
21,616
Number of meters minus
and out of tolerance
Average of minus errors
for meters out of
tolerance for under
delivery (in3 )
Number of meters plus
and out of tolerance
Average of plus errors for
meters out of tolerance
for over delivery (in3 )
145
Percent of meters minus and
out of tolerance
0.6708
-10.7172
Percent of under delivery on
5-gal test
-0.9279
152
10.3224
3
Percent of meters plus and
out of tolerance
Total % of meters out of
tolerance
Percent of over delivery on 5gal test
0.7032
1.3740
0.8937
$ amount of transactions for
under delivery errors for
meters out of tolerance
$28,677,205
$ amount of transactions for
over delivery errors for
meters out of tolerance
$30,061,621
Total $ for transactions for
meters out of tolerance
$58,738,826
$ amount of under delivery
errors for meters out of
tolerance
$266,096
$ amount of over delivery
errors for meters out of
tolerance
$268,664
Total $ amount of errors for
deliveries out of tolerance
$534,760
June 2, 2015
Now calculations can be done to look at hypothetical situations (i.e., “what if” scenarios) to
estimate the economic impact or benefits of the Nebraska program. What if Nebraska had a
rejection rate for RMFD meters that was about 5% instead of 1.5%? A rejection rate of 5%
for inaccuracy is relatively common for RMFD meters. Assume that half of the rejections are
for under delivery and half are for over delivery. The normal distribution of meter errors will
be spread out more for a 5% rejection rate than for the 1.5% rejection rate. This means that
the average error for meters outside of tolerance will be larger than for the 1.5% rejection
rate. We need some basis for an estimate of how much these average error values can change.
Based on data that I have for a jurisdiction, the average meter error for under deliveries for
the out-of-tolerance meters is -12.9053 in3 on a 5-gal test. The average meter error for over
deliveries for the out-of-tolerance meters was 15.8477 in3. I suspect that this jurisdiction has
a rather high rejection rate for RMFD meters, so the range of the average values for Nebraska
and this jurisdiction provide a reasonable initial estimate of how much the average meter
errors can vary for the out-of-tolerance meters.
Nebraska
Other Jurisdiction
Average Error for Under
Delivery for Out-OfTolerance Meters (in3)
-10.7
-12.9
Average Error for Over
Delivery for Out-OfTolerance Meters (in3)
10.3
15.8
Suppose that (1) for a hypothetical higher rejection rate of 5% for Nebraska and (2) suppose
that the average errors for meters out of tolerance increased by 1 in3 for both the under and
over delivery errors for the meters. Then, using the same spreadsheet as above, we can
calculate (estimate) the economic impact of the measurement errors for the out-of-tolerance
meters, which would now be $2,130,373. The spreadsheet layout for this calculation is
shown on the last page.
The difference in the dollar amounts in the calculations for the 1.5% rejection rate ($534,760)
and the 5% rejection rate ($2,130,373) represents the economic impact if Nebraska were to
allow its compliance rate to decrease by 3.5%. This difference is $1,595,613.
On the other hand, if the unnamed jurisdiction mentioned above had to goal to improve its
compliance rate by 5%, then the jurisdiction could estimate the economic impact of the
improved compliance rate by using the sales figures for gasoline stations in its jurisdiction.
This could be used as justification for modifying its inspection and enforcement practices and
increasing staff to improve its inspection and enforcement.
This calculation approach (and spreadsheet) to estimate economic impact can be used for
each type of meter, such as, RMFD meters, high-speed diesel fuel dispensers, VTMs, loading
rack meters and LPG meters. The rejection rates vary among these types of meters, but these
estimates can help with management decisions to identify where programs can obtain the
most benefit for their enforcement efforts.
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June 2, 2015
This calculation approach can probably be used to estimate the economic impact for price
verification inspections. The error distributions and the values of the pricing errors must be
known for each type of retail segment (e.g., supermarkets, department stores, sporting goods
stores, auto parts stores, etc.). Jurisdictions that perform price verification inspections should
have this information available. However, each type of retail segment must be analyzed
separately, because the cost of items offered for sale, the percentage of pricing errors found
and the values of pricing errors may vary significantly from one type of retail segment to
another.
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June 2, 2015
Enter data below
Amount of sales for the
station ($)
4,275,079,000
Total Number of meters
21,616
Number of meters minus
and out of tolerance
Average of minus errors
for meters out of
tolerance for under
delivery (in3 )
Number of meters plus
and out of tolerance
Average of plus errors for
meters out of tolerance
for over delivery (in3 )
540
Percent of meters minus and
out of tolerance
2.4981
-11.7172
Percent of under delivery on
5-gal test
-1.0145
540
11.3224
Percent of meters plus and
out of tolerance
Total % of meters out of
tolerance
Percent of over delivery on 5gal test
2.4981
4.9963
0.9803
$ amount of transactions for
under delivery errors for
meters out of tolerance
$106,797,865
$ amount of transactions for
over delivery errors for
meters out of tolerance
$106,797,865
6
Total $ for transactions for
meters out of tolerance
$213,595,731
$ amount of under delivery
errors for meters out of
tolerance
$1,083,443
$ amount of over delivery
errors for meters out of
tolerance
$1,046,931
Total $ amount of errors for
deliveries out of tolerance
$2,130,373