ENTROPY LIMITED .
EPA 510-S-92-80&
ANALYSIS OF MANUAL INVENTORY RECONCILIATION
EXECUTIVE SUMMARY
Report for
Office of Underground, Storage Tanks
Environmental Protection Agency
Submitted to
Midwest Research Institute
Falls Church, YA
Under EPA Contract No. 68-01-7383
Richard F. Eilbert
Entropy Limited
Lincoln, MA
March 18, 1988
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ENTROPY LIMITED
ANALYSIS OF MANUAL INVENTORY RECONCILIATION
Richard F. Eilbert
Entropy Limited
Lincoln, MA
EXECUTIVE SUMMARY
Objectives
This report documents the findings on manual Inventory reconciliation as
practiced at gasoline service stations. The objectives are 1) to identify
factors affecting daily recordkeeping accuracy, and 2) to evaluate the leak
detection capability of proposed regulatory standards. Leak detection
capability is assessed by numerically modifying actual inventory data through
computerized simulations of various leak rates.
Data Base Selection
The study is based on 586 underground storage tanks at 188 facilities
nationwide. Data are comprised of 20,036 measurements of daily inventory.
Geographic coverage spans 34 states. This is, to our knowledge, the largest
data base on manual inventory assembled to date.
Entropy Limited has performed statistical inventory analysis for many
thousands of underground storage tanks. A sampling of these has been selected
to form this project's data base. Statistical inventory analysis greatly
improves the leak detection capability of Inventory recordkeeping, but
requires advanced computerized methods available from firms providing such
services. This project focuses on manual inventory reconciliation as
practiced by dealers in the retail gasoline trade.
Facilities and recordkeeping periods were selected on the basis of geographi-
cal and seasonal representativeness. It is not known which, if any, of the
tank/piping systems might have actually been leaking. Industry estimates
suggest that most of the systems, perhaps 98 to 992, were tight.
When the sample was drawn, recordkeeping accuracy was not considered and, in
fact, was not yet known. The recordkeeping in the sample is expected to be of
somewhat higher caliber than that maintained in the retail gasoline trade at
large. Reasons for this include: 1) clients submitting records are ususally
trying to meet regulatory or insurance requirements and thus are motivated to
perform recordkeeping more conscienciously, 2) obviously deficient inventory
records are returned without analysis under Entropy Limited's Quality
Assurance protocols, and 3) arithmetical blunders have been eliminated by
computerizing the bookkeeping procedure. Entropy Limited's Quality Assurance
protocols also include checks to reject artificially contrived inventory data.
Data Base Characteristics
Within the data base, 95% of the tanks are used to store gasoline or diesel
products. Geographical coverage of the nation's major regions is consistent
with general motor fuel consumption patterns with the exception that the Rocky
Mountain region is under-represented.
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Inventory record length for the tanks consists on average of 34 reconcili-
ations covering a 43 day period. This reflects the fact that statistical
inventory analysis normally is based on 30 submitted measurements, not
including days on which the station is closed. The averaged tank size Is
7,277 gallons and monthly throughput averages 16,258 gallons/month. As a
whole, the net loss of product exhibited in the data base is quite small,
averaging 0.40 gal/day or 0.10% of throughput. Individual tanks, on the other
hand, are characterized by much larger gains or losses of product.
Factors Affecting Daily Inventory Reconciliation
The accuracy with which inventory is reconciled on a particular day is
quantified as the "daily discrepancy." This discrepancy is defined as the
measured change in stored volume plus dispensed sales minus delivery receipts.
Overages exceeding 90 gallons occur 5% of the time. Similarly, underages of
90 gallons or more occur with 5% frequency. Daily losses and gains exceeding
220 gallons each occur only 1% of the time. Daily discrepancies in the range
of -20 to +20 gallons are more typical, and account for 50% of the
observations.
The capabilities of manual inventory reconciliation as a leak detection method
are, to an extent, limited by the tank operator's ability to obtain accurate
daily reconciliation. In the retail trade, it is widely recognized that some
of the day-to-day variability cancels out when looking at reconciliations over
a longer time frame, such as a month. The reason for this cancellation is
that bookkeeping inaccuracies on one day will be compensated on subsequent
days, assuming no physical loss of product occurs. In assessing manual
inventory reconciliation, it is important to look at performance on daily,
monthly and even longer time scales.
A number of factors impact the accuracy of daily inventory reconciliation.
These are studied by examining the standard deviation in the daily
discrepancy. This standard deviation is 39 gallons for the entire data set,
excluding outliers beyond 125 gallons (less than 6% of the data). Factors
impacting the dally reconciliation accuracy include throughput, delivery, tank
size, stick reading accuracy, product and season or month.
STRONG DEPENDENCIES
o Product throughput. A strong dependency of daily discrepancies on
throughput exists. This occurs because discrepancies caused by
dispensing meter error, thermal changes in product volume, vapor loss and
conversion chart inaccuracy are proportional to the volume of throughput.
Also, high throughput stations receive more frequent product deliveries,
introducing additional cause for discrepancy.
o Occurrence of product delivery. Higher discrepancies are exhibited on
delivery days than on non-delivery days. When analyzed with outlier
rejection, the standard deviation is only moderately higher for delivery
days than non-delivery days (44 versus 37 gallons). However, the
percentage of outliers on delivery days is unusually high, 10%, versus 5%
on non-delivery days. Delivery days comprise 22% of the data base.
o Tank size. The strong dependence of daily discrepancies on tank size 1s
partially due to its significant Intercorrelation with throughput
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(r=0.62). This occurs because tank pihers tend to use large tanks for
products with high activity. Tank size directly affects discrepancies
through scale error, that 1s, a 1/4" error 1n dipstick reading causes a
proprotionally larger Inventory discrepancy for larger sized tanks.
MODERATE DEPENDENCIES
o Stick reading accuracy. Stick reading accuracy 1s 1/8", 1/4", 1/2" or
1". The accuracy of the stick readings Is known for 87% of the tank data.
Dally discrepancies are reduced with finer stick reading accuracy, down
to and Including 1/8". However, the reduction in discrepancies 1n going
from 1/4" to 1/8" is only partially attributable to the finer measurement
accuracy.. A major portion of the reduction is due to other factors such
as a more consdencious attitude of operators seeking high measurement
accuracy and their reliance on conversion charts precalibrated in 1/8"
increments.
WEAK DEPENDENCIES
o Product. Daily discrepancies have only minor dependency on the type of
product contained in the tank, with slightly higher discrepancies
exhibited for unleaded than for leaded gasoline. This increased
discrepancy is a result of the generally higher throughput of the
unleaded product.
o Month of year. There is no clearcut trend or annual cycle in the
magnitude of daily discrepancies. This contrasts with the generally held
belief that accurate inventory reconciliation is more difficult during
the winter months.
The accuracy of daily reconciliation discussed above characterizes the size of
typical daily overages or shortages. On average, positive and negative
discrepancies will tend to cancel so that the expected daily reconciliation is
close to zero. In fact, the data base exhibits an expected discrepancy of
-0.50 gallons for daily reconciliations, which is but a small fraction of the
39 gallon standard deviation characterizing daily reconciliation accuracy.
Factors affecting daily discrepancies were assessed for biases that would*
shift the expected reconciliation away from its -0.50 gallon average.
A detectable bias exists for high throughput tanks, namely, those with over
20,000 gallons of monthly throughput. This bias is well explained by vapor
loss. A bias is also evidenced within the annual cycle. This becomes more
apparent when the data are restricted to the northern states, which experience
larger seasonal temperature swings. Loss of product occurs in May through
August, while the rest of the year experiences gains which peak in
November/December. This annual cycle is well recognized within the retail
trade, summer losses being known as thermal shrinkage. Within a specific
season, thermally induced biases in inventory reconciliation are expected to
vary proportionally with product throughput.
Evaluation of Proposed Regulatory Standards
A number of regulatory standards have been suggested to enable inventory
reconciliation to function as a leak detection method. Two of the most
familiar are the "0.5% of monthly throughput" rule recommended by the API and
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the "action number" approach developed by the EPA. We evaluated the
performance of these rules applied on a monthly basis. Through computerized
calculations, constant, artificial leak rates from 2 to 50 gal/day were
Imposed on the Inventory data base to simulate tank leakage. In this way, the
sensitivity of the above rules 1n detecting leakage can be estimated.
Findings are expressed in terms of the false alarm (FA) rate (I.e., the
frequency with which a standard indicates a leak when none exists) and the
leak rate, Rg5, at which a standard would detect the leak 95% of the time.
The findings presume, in accord with industry and insurance company estimates,
that only a very small fraction of the data-base tanks are actually leaking.
This assumption is born out by the high degree of symmetry between positive
and negative dally discrepancies within the data base. If a significant
fraction of the data base tanks were leaking, an asymmetry toward negative
discrepancies would occur. The analysis concludes the following:
o 0.5% of monthly throughput rule. The false alarm rate for,product loss
occurs with frequency FA = 302. Product gains exceeding 0.52 of
throughtput occur 27% of the time. The high FA rate makes this rule
unworkable without modification.
o Action number approach. For 30 days of measurement, action is triggered
if losses exist on 20 or more days. This occurs with false alarm rate
FA = 4.6%. A 95% chance of detection occurs at a leak rate of Rgs =2.0
gal/hr. This rate is considered to be rather high for leak detection
purposes.
A class of standards expressable as a percentage of monthly throughput plus a
constant term was examined for their leak detection performance. Significant
Improvement in leak detection capability is demonstrated with such rules.
Leak detection efficiency at a fixed 5% FA rate is optimized by selecting the
criterion to be 150 gallons plus 0.8% of throughput. Specifically:
o 150 gallons + 0.8% of monthly throughput rule. A 5% FA rate is expected
and 95% chance of leak detection occurs at leak rate, Rg5 = 0.9 gal/hr.
According to our data, this rule has more than twice the sensitivity of
the action number approach.
This standard 1s somewhat more efficient than the "123 gallons plus 1.23% of
monthly throughput" rule reported in a preliminary study, for which Rqs =1.5
gal/hr at a 5% FA rate. A convenient standard that is nearly optimal Ts "130
gallons plus 1.0% of monthly throughput," for which Rqc = 1.1 gal/hr at a 5%
FA rate.
The validity of such rules is governed by the data upon which they are based.
In particular, the rules are applicable to underground tanks In the retail
gasoline sector of capacities in the range 500 to 50,000 gallons with
throughputs in the range of 1,000 to 100,000 gallons per month.
Daily Inventory Reconciliation Standards
Imposing daily inventory standards for leak detection would be a futile
exercise. Employing, for example, a 90 gallon loss rule to achieve FA = 5%
results in a sensitivity of Rgs = 5.9 gal/hr. Of course, an FA of 5% on a
daily basis creates an 80% chance for one or more false alarms per month.
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Some standard governing dally reconciliation is worthwhile to prevent
procedural and arithmetical blunders 1n bookkeeping. For tanks of capacity
below 20,000 gallons, 50 gallons plus 1% of tank size defines a reasonable
maximum allowable daily discrepancy. About 95% compliance rate with this rule
is exhibited in the data base. Conscienciously practiced inventory
reconciliation should be routinely capable of meeting this upper limit on
daily product discrepancy.
Improving Leak Detection Capabilities of Inventory Reconciliation
Higher leak detection sensitivities result by extending the baseline period
for the inventory reconciliation beyond one month. Since the data base
contains few Instances of periods exceeding 45 days, the performance of longer
time-period rules has to be extrapolated based on theoretical models.
Analysis shows the following to be achievable for a 3-month rule:
o 300 gallons plus 0.5% of 3-month throughput rule. The false alarm rate
is expected to be FA = 1%. This is one-fifth of the previous FA rates
and low enough to be practicable. The leak rate detectable with 95%
confidence is expected to be Rqt. = 0.4 gal/hr. If the extrapolation is
valid, the sensitivity of the optimal one-month rule can be more than
doubled.
In theory, leak detection capability continues to Improve with increasing
baseline period of inventory observation. In practice, factors such as meter
error, vapor loss, thermal shrinkage of product and other systematic errors
ultimately limit the leak detection capability of manual inventory reconcili-
ation. Statistical inventory analysis programs account for such factors and
make more intensive use of the daily inventory records. They can achieve
sensitivities of about 0.1 gal/hr on 30-day analyses, representing the
state-of-the-art capability for leak detection through inventory
reconciliation.
Conclusion
Analysis of manual Inventory reconciliation data as practiced in the retail
gasoline trade indicates that leak rates of 0.9 gal/hr are detectable with
high confidence over a one month time period. The major factors impacting the
operator's ability to achieve accurate daily inventory balance are product
throughput, tank size, product delivery, and the precision of dipstick
reading. Bias In inventory reconciliation can be induced by vapor loss,
thermal product shrinkage, meter error and other causes. Improved leak
detection capability is possible by using longer baseline periods for
reconciliation and by using computerized statistical inventory analysis.
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