Summer 2015
Pressure Change
Measurement Leak
Testing Errors
by: Jeff M. Pryor and William C. Walker
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In This Issue...
Pressure Change Measurement
Leak Testing Errors
By: Jeff M. Pryor and
William C. Walker................................ 8
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President’s Message .........................6
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2014/15 Board of Directors
The Enclosure
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Summer 2015www.gloveboxsociety.org
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President’s Message
By: Scott Hinds
“Listen to the record!”
“Come to the Conference!”
Only people who listen to my style of rock and roll from the late ‘70’s
would know where that phrase came from. On the back of the first Boston
album (yes - vinyl), the verbiage that described the members and recording style of the band Boston ended each paragraph with “listen to the
record!” in an enthusiastic request to hear the music. Well, in borrowing
that style from one of my favorite bands, I apply it to my favorite society
and say “Come to the Conference!”
Donna S. Heidel is the Technical Director for Industrial Hygiene for
the Bureau Veritas North America and she is our 2015 AGS Keynote
Speaker. Ms. Heidel leads the development of industrial hygiene services
to support highly effective management of occupational health risks associated with emerging technologies. She will address the society on the
challenges associated with applying glovebox solutions to reduce worker
risks while maintaining quality levels in hazardous drug and nanoparticle
applications.
The American Glovebox Society’s Officers, Board of Directors and
Management team has assembled a comprehensive educational and technical program which is slated to fill three full days of glovebox discussion
focused on our theme of Equipment Integration. Our Fundamentals and
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to complex, across-the-board subject matter discussions to the most experienced glovebox professional. At press time, all of our technical session
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provide topical debate issues to keep us current with our industry.
“Come to the Conference!”
A mainstay for the success of our conferences, our exhibitors and vendors will flood the main exhibition hall with the latest technology available to our industry. From windows and whole scale glovebox designs to
exotic instrumentation and safety applications, our vendors will dazzle,
delight and demonstrate all there is to know about the world of gloveboxes, containments and enclosures.
AGS Sustaining Members
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“Come to the Conference!”
And of course – San Diego!! Our venue could not be a better family
friendly setting. The restaurants, the Zoo, the botanical parks, the beaches, the sunshine, the resort, the shopping, the Gaslamp District, the music,
the amusement parks, did I mention the beaches??
“Come to the Conference!”
Finally, the year has gone by too fast and I do greatly appreciate everyone’s support in helping me be your American Glovebox Society’s president for 2015. A long time ago, I joined the AGS as a standards committee
member with Beth Sliski as the AGS-G001 chairperson. For me, that time
was 1989. G001 was just many words in a computer. The society was
young and we had goals of many more documents to develop. As a societal body, we have accomplished a great deal in the 27 years since I joined
the AGS and the nearly 30 years since the AGS has been in existence. Our
influence in the world of containment science and engineering still grows
with each day. My perspective is that we are a society and membership
that truly enjoys what we do. We are an impassioned and involved group
of like minded individuals that relish the challenge of balancing work,
family, friends and ambitions with our own time constraints. Although we
juggle many balls in the air at one time, please take the occasion to enjoy a
moment with your family, phone your mother, and take a day off to soak it
all in. I look forward to meeting old and new friends this July and passing
the torch to another year.
“Come to the Conference!”
Regards,
Scott Hinds P.E.
AGS President 2014-2015
July 27-29, 2015 Town and Country Resort and Conference Center - San Diego, CA
Keynote Speaker:
Donna S. Heidel
Biosketch
Donna S. Heidel is the Technical Director for Industrial Hygiene for Bureau Veritas North America where
she leads the development of industrial hygiene services to support the effective management of occupational health risks associated with emerging technologies. Prior to her employment with Bureau Veritas she
coordinated the Prevention through Design program at the National Institute for Occupational
Safety and Health, including the occupational health and safety management systems for
safely synthesizing manufactured nanoparticles and commercializing nano-enabled products.
Ms. Heidel also has experience in the pharmaceutical industry, including 15 years at Johnson
& Johnson, as the World Wide Director of Industrial Hygiene. While at J&J, she supported
the development and implementation of engineering containment and control systems for
high-potency drugs. She is certified by the American Board of Industrial Hygiene (CIH), and
is an AIHA fellow. She has received the AIHA President’s Award in 2011 and in 2013. She
also serves on the AIHA Board of Directors. She is the past chair of the AIHA Control Banding
Working Group.
Abstract
The guidelines developed by the American Glovebox Society for design, fabrication and
testing of glovebox isolators have been successfully implemented by the pharmaceutical
industry not only to control worker exposure to hazardous drugs but also to provide contaminant control for sterile products. Innovative designs, including flexible walls, materials
transfer systems, and clean-in place capabilities have supported the need for occupational
exposure control while meeting the specific process requirements for pharmaceutical dosage form manufacture. The successful application of this technology by the pharmaceutical
industry is now being applied to safely synthesize manufactured nanoparticles and nanoenabled products. The occupational health challenges associated with hazardous drugs and
manufactured nanoparticles and the application of glove box solutions to significantly reduce
worker exposure risks will be discussed.
Before or After You become
Critical Path,
LTS has the Resources
to Help You Succeed
Related Recent Publications
Heidel, D; Segrave, A; Baker, J. Occupational Safety and Health Management Systems
for the Safe Commercialization of Nano-enabled Products Nanotechnology 2013: Bio Sensors,
Instruments, Medical, Environment and Energy, Chapter 5: Environmental Health & Safety,
Nanotech 2013 Vol. 3.
Geraci, C; Heidel, D; Sayes, C; Hodson, L.; Schulte, P; Eastlake, A; Brenner, S. Safe Nano
Design: Molecule to Manufacturing to Market; Responsible Practices for Safe Nano Design.
Journal of Nanoparticle Research. 2014.
Heidel, D., Ripple, S. Closing the Exposure Gap, Occupational Exposure Bands, ERAM, and
Prevention through Design. The Synergist (2012), Volume 23, Number 4.
Prevention through Design Plan for the National Initiative; DHHS (NIOSH) Publication No.
2011–121Heidel, D; Murray, K; Gutmann, S. Chapter 9: Identify Impacts. AIHA Value Strategy
Manual. pp. 73-79. American Industrial Hygiene Association, 2010. ❖
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Summer 2015www.gloveboxsociety.org
www.leaktestingspec.com
7
Pressure Change Measurement
Leak Testing Errors
by: Jeff M. Pryor and William C. Walker
Author’s Note
A statement of leakage rate can only be considered complete when it contains a
leakage rate combined with a test temperature and pressure. Typical for the leak
test industry in general, the formula contained in this article is given with an output
of atmospheric cc/sec. (referred to as SCC/S in the article). Additionally, the formulas given are not corrected to standard temperature since the definition of standard
temperature varies widely across the industry. While the principals of the article hold
true for all testing, the math may vary slightly depending on the desired output units.
Reprint Permission
From Materials Evaluation, Vol. 72, No. 5. Reprinted with permission of the American
Society for Nondestructive Testing, Inc.
Introduction
A
pressure change test is a common leak testing
technique used in construction and nondestructive
testing (NDT). The test is known for being fast, simple and
easy to apply. While this technique may be quick to conduct
and require simple instrumentation, the engineering
behind this type of test is more complex than is apparent
on the surface.
A pressure change measurement test (PCMT) is an evaluation
of the leak-tightness of a closed system. A PCMT happens when
a system is driven into a state of pressure differential (by being
placed either under an elevated system pressure or under a
relative vacuum), then closed and monitored over a period of
time for change in pressure. The resulting change in the internal
pressure can then be related to a leakage rate using the ideal
gas law formula. While a PCMT should be a relatively simple test
to physically perform, the calculation of a leakage rate from the
resulting pressure decay data requires careful consideration of
all measurement errors. The American Society of Mechanical
Engineers Boiler and Pressure Vessel Code (BPVC) requires that
the resolution, repeatability and accuracy of the instruments used
be compatible with the specific test system; however, it offers no
guidance on how this requirement is to be met (ASME, 2011).
Uncompensated measurement errors can mask the true leakage
rate, leading to incorrect results. Therefore, they are of the utmost
importance in this type of test. This paper describes the basic
concepts associated with a PCMT, the types of measurement errors
involved with the test, and the governing equations incorporating
the measurement errors into the leakage rate calculation. The
mathematical principles discussed here apply to ideal gases such
as air or other monoatomic or diatomic gasses; however, these
same principals can be applied to polyatomic gasses or liquid
flow rate with altered formula specific to those types of tests using
the same methodology. The methodologies of measurement
discussed here are readily applicable to any specification set and
to all PCMTs, which is particularly valuable since most construction
specifications have equivalent language requiring the test engineer
to evaluate leakage rates consistent with the BPVC.
The leakage rate is typically correlated to standard conditions
(a standard atmosphere at sea level at standard temperature with
a standardized volume and so on) and produces output such as
standard cubic centimeters per second, standard cubic feet per
minute and many more. The determination of a leakage rate is
primarily based on a change in pressure within a closed system.
Accordingly, system pressure must be monitored since this is the
basis for the test. Although a change in system pressure is the
critical measurement for detection of a system leak, there are other
physical attributes beyond leakage in a closed system that impact
the change in system pressure. These attributes include system
temperature, ambient pressure and system volume. A change in
system temperature will result in a proportional change in system
pressure. Ergo, temperature monitoring is necessary during testing
since any observed change in system pressure will need to be
compensated for all observed changes in temperature. Changes
in ambient (that is, barometric) pressure can also influence the
assessed leakage rate. A PCMT depends on a pressure differential
from the inside of the system to the outside of the system in
absolute terms. Consequently, atmospheric pressure changes
affect these types of tests since they change the absolute pressure
differential of the system under test. Finally, system volume must
be known so that the calculation can be performed.
The calculation of a leakage rate from a closed system is derived
from a modified form of the ideal gas law, expressed as follows:
(1)
Q=
where
( P ×V)
( StdAtm × t )
Q = leakage rate (at standard conditions),
rP = relative change in system internal pressure (Pinitial – Pfinal),
StdAtm = ambient (standard) pressure,
V = internal volume,
t = time (duration of the PCMT).
In accordance with the gas law formula, the units are in absolute
Continued on page 10
8
Continued from page 8
Pressure Change Measurement Leak Testing Errors
pressures and absolute temperatures in the units. The selection
of units must be consistent and compatible throughout the entire
computation set from start to finish.
An expanded form of the leakage rate formula, which includes
the effect of barometric pressure, can be expressed as:
(2)
where
B = barometric pressure,
T = temperature.
The subscript i indicates the initial instrument reading, and
subscript f indicates the final instrument reading.
This expanded form of the ideal gas law (Equation 2) allows
for the compensation of pressure changes due to variations in
barometric pressure and temperature. An examination of this
expanded formula highlights the previously discussed need to
monitor system temperature and ambient pressure during the
test. The failure to compensate for barometric pressure when
using gage pressure to express pressure as absolute is a common
error in these tests. The change in barometric pressure on short
duration tests (for example, a few minutes) is generally negligible.
The calculation of a leakage rate from a closed system is
derived from a modified form of the ideal gas law
An assessment of the accuracy of the instrumentation is
critical with respect to quantifying the propagation of uncertainty
associated with the calculated leakage rate. The addition of a
statement of measurement uncertainty to a test result indicates
that not only was the calculated leakage rate acceptable (less
than the maximum allowed leakage rate), but that the calculated
leakage rate is statistically significant (the inherent variability in
the instrumentation measurements did not mask the true value).
The following paragraphs discuss these instrumentation attributes
in detail.
System Resolution
System resolution is the smallest measurement that can be seen
with a specific test and setup. This calculation must be taken in
the context of the test system, not just the individual instrument’s
increment. One must take into account the complete system,
under test conditions, and then use this system information to
find out what a particular instrument’s effects are on the test. It is
only through this process that the system resolution of a particular
instrument can be defined. Resolution must be defined for each
instrument used in the testing system. The test resolution as a
whole cannot be greater, or more sensitive, than the least sensitive
instrument. Using the standard PCMT formula (Equation 3) and
some mathematical manipulation, substitution of each instrument’s
resolution into the actual test conditions produces the following
formulae for evaluating component resolutions:
initial leakage rate formula
(3)
However, on longer duration tests, a change in barometric
pressure can significantly affect test results. The lack of barometric
compensation can mask unacceptable leaks, causing the
acceptance of otherwise rejectable items. By initially choosing to
use an absolute pressure gage, the barometric compensation can
be removed from the equation (this is the preferred technique).
Similarly, a lack of accurate temperature measurement monitoring
over longer test times can result in erroneous calculations and test
outcomes.
An often-overlooked issue regarding the evaluation of a
PCMT leakage rate is accounting for performance attributes of
the instrumentation as used in the test system. These attributes
include:
l Resolution of the test instrumentation (not just the gage resolution),
l Test sensitivity, or repeatability, of the instrumentation,
pressure resolution
(4)
temperature resolution
(5)
time resolution
(6)
l Accuracy of the instrumentation, referred to as measurement errors or uncertainties.
The resolution and repeatability characteristics of the
instrumentation must be compatible with the test conditions.
An assessment of instrumentation resolution and sensitivity
demonstrates that the calculated leakage rate results obtained
are possible under the system configuration by specifying the
minimum detectable leak rate achievable with the instrumentation
used in the test.
where
Q = measured leakage rate,
Gres = pressure gage resolution
(smallest pressure increment measured during test),
Pi = initial absolute pressure,
Pf = final absolute pressure,
Continued on page 14
10
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Pressure Change Measurement Leak Testing Errors
StdAtm = standard atmospheric pressure (used for correlation
to standard conditions),
Ti = initial absolute temperature,
Tf = final absolute temperature,
Tres = temperature gage resolution (smallest temperature
increment measured during test),
t = total time elapsed during test,
tres = time resolution (time increment measured; for example,
0.1 s for stopwatch = 0.0167 min),
tunit = time unit (time increment of output; for example,
1 minfor ft3),
V = volume.
The PCMT resolution is the maximum of the evaluated instrument
resolutions considering pressure, temperature and time (Equations
4, 5 and 6). Using this set of instruments and under these specific
test conditions, this is the smallest leak that could possibly be seen
under the most ideal of conditions (that is, a detectability limit).
Although the system volume must be determined with an
accuracy and precision required for the test, volume resolution
is ignored since the volume is static during the test. As a note of
caution: volume does have a measurement uncertainty associated
with it, which should not be ignored by the test engineer. Volume
measurement uncertainty must be considered in context with the
application involved. The uncertainty in the volume measurement
is included in the total propagated uncertainty for the leakage rate.
As the test volume decreases, the significance of the volume upon
the test and its uncertainty increase.
Resolution Example
In this example, only the pressure resolution will be evaluated.
The system undergoing the test has an acceptance criteria of 6.5
× 10–2 Std L/min (2.3 × 10–3 SCFM). The test volume is determined
to be 1360 L (48 ft3), and test pressure is planned to be established
at +102 mm (4 in.) water column. Finally, the test duration is
planned to be one hour. The pressure gage used for the test had
subdivisions of 704 mm (27.7 in.) water column (6895 Pa [1 psi]).
The evaluated resolution of the pressure instrumentation is as
follows:
= (Gres × V) / (StdAtm × rt)
= (704 mm water column × 1360 L) / (10340 mm water
column × 60 min)
System Repeatability
Although closely related, there is a difference between test
resolution and repeatability. System repeatability or sensitivity
is defined as the smallest test increment that is considered
repeatable. Just because it is theoretically possible to see a leak as
small as the resolution does not mean that it would be expected to
read this every time, which speaks to the repeatability requirement.
A prudent test engineer would require that the test sensitivity be
between two to ten times the maximum test resolution to ensure
repeatability. If the test sensitivity were greater (larger) than the
smallest allowable leak, then the test, as configured, would be
incapable of delivering the desired results. It would therefore be
unacceptable for use. In the case of inadequate sensitivity or
resolution, either different instruments or another test configuration
would be needed. While more accurate gages are often the best
long-term solution, this pricy alternative is not the only solution.
Changes in any of the test variables will affect the test sensitivity.
Repeatability Example
Again, evaluating only at the pressure component, a PCMT test
to be performed on a system where the acceptance criteria is 9
×10–2 Std L/min (3.2 × 10–3 SCFM). The test volume is determined
to be 2832 L (100 ft3) and testing will be conducted at a pressure
of +102 mm (4 in.) water column for one hour using a pressure
gage that had subdivisions of 12.7 mm (0.5 in.) water column. The
following pressure resolution result is obtained:
= (Gres × V) / (StdAtm × rt)
= (12.7 mm water column × 2832 L) / (10340 mm water
column × 60 min)
= 5.8 × 10–2 Std L/min
or
= (0.5 in. water column × 100 ft3) / (407 in. water
column × 60 min)
= 2.0 × 10–3 SCFM
The repeatability (also known as sensitivity) is defined as 2X
minimum resolution. Therefore, this pressure gage has a minimum
sensitivity of 0.12 Std L/min (4 × 10–3 SCFM). This pressure gage
does have the required resolution (less than the acceptance
criteria); however, it is incapable of repeatedly seeing the required
leakage rate in this test system (the sensitivity is greater than the
acceptance criteria). Therefore, this gage is not compatible with
this test. See the PCMT decision tree (Figure 1) for a graphic
example of how system resolution and repeatability affect testing.
= 1.5 Std L/min
System Accuracy
or
Accuracy in the world of metrology (the science of measurement)
is the degree to which a measured value agrees with the actual,
or true, value. There are uncertainties associated with any and
all measurements. An estimate of the magnitude and statistical
confidence of these uncertainties forms a statement of uncertainty
for the original measurement. A measurement without a statement
of uncertainty is incomplete. In order to know what uncertainty is,
one must first understand the definition.
= (27.7 in. water column × 48 ft3) / (407 in. water
column × 60 min)
= 5.4 × 10–2 SCFM
This gage is evaluated to be incapable of evaluating a leakage
rate equal to or less than the acceptance criteria leakage rate.
Therefore, this pressure gage is not compatible with the test as
planned.
Continued on page 16
14
Continued from page 14
Pressure Change Measurement Leak Testing Errors
“The objective of a measurement is to determine the value of the
measurand, that is, the particular quantity to be measured” (ISO,
1995). A measurement depends on the method of measurement
and the measurement procedure. “In general, the result of a
measurement is only an approximation or estimate of the value of
the measurand and thus is complete only when accompanied by a
statement of uncertainty of that estimate” (ISO, 1995).
To fully understand what an uncertainty calculation involves,
an examination of the parts of the measurement system and how
these affect the test outcome is in order. A measurement system is
made of separate components that make up the total system, for
example, pressure, temperature and so on. Each system component
must be evaluated separately. The principal of uncertainty applies
separately to the individual measurement instrument (if more
than one instrument makes up that
component), the system component
and the measurement system as a
total. See the PCMT decision tree
(Figure 1) for a graphic example of
how combining separate pressure
instruments effects the total pressure
uncertainty.
Each instrument component has
a minimum increment to which it
can be read. This is called resolution
uncertainty or simply resolution. Note
that this is the same component
resolution used in the calculation for
system resolution. If using an analog
gage with a reading increment of 5
pressure units (for example, 0, 5,
10…), it would be impossible to read
a 0.1 unit change. An argument could
be made that 2.5 unit increments or
maybe even 1 unit increments could
be read; however, only the 5 pressure
unit increments can be read with true
repeatability and certainty in this case.
Reading between the divisions of an
analog gage is beyond the design of
the instrument and adds additional
un-quantifiable uncertainties. This
minimum measurement resolution
is of extreme importance when
selecting the appropriate gage for a
specific test.
Each
instrument
component
also has some uncertainty involved
Figure 1. Pressure change measurement test (PCMT) decision tree. RSS = root sum square.
with accuracy called measurement
uncertainty. This is different than component resolution;
The three elements that make up a measurement uncertainty measurement uncertainty has to do with just how accurate
are resolution, repeatability and accuracy.
the specific component actually measures the value. Most
The total uncertainty of the system as a total is the most complex manufacturers give a specification on accuracy of instrument
of the three BPVC required elements to calculate. Uncertainty of as percent of full scale. For instance if a 2000 kPa (290 psi)
measurement is often compensated for during the test to ensure gage had an accuracy of ±3% full scale, then the measurement
the most reliable test results. Uncertainty becomes more critical as could be otherwise stated as ±60 kPa (9 psi). This means that a
the test results require more accuracy and precision. Depending reading of 1000 kPa (145 psi) could represent an actual pressure
on the specific objectives of the test, uncertainty could be left of somewhere between 940 and 1060 kPa (136 and 154 psi),
out of the calculation set if the test engineer determined these provided no other uncertainties are entered into the equation.
calculations are insignificant in the particular test, that is, very During the gage selection process, getting a highly accurate gage
small in comparison to the expected results. It is important to note compatible with the leak test is of paramount importance.
that resolution, repeatability and uncertainty calculations must be
Continued on next page
performed for each different testing scenario.
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Continued from previous page
Each measurement component has some uncertainty involved
with how close the instrument has been calibrated to known
standards, called traceability uncertainty. Remembering that
no measurements are perfect, traceability has to do with the
calibration lab and the transfer errors in measuring the calibration
standards. Each time a calibration standard is measured and the
value is transferred to another standard, there is some increase
in uncertainty. This uncertainty value must be supplied by the
calibration lab for each measurement component in the test
system.
Each instrument component also has some uncertainty
involved with accuracy called measurement uncertainty.
Each of the three separate uncertainty elements plays a role
in the total uncertainties of the instrument or component. Total
instrument uncertainty accounts for being able to quantify what
a particular instrument can in truth measure and how accurately,
not just what the instrument displays as a reading. The three
uncertainty elements must be combined to get a total instrument
uncertainty that will be of further use.
Combining the uncertainty elements into a component total
requires a somewhat different approach. For example, measurement
accuracy from the manufacturer is stated as ± percent error. It
is not known if the uncertainty is positive or negative or where
measurement error is within the range stated. If the tolerance is
±10 units, an assumption cannot simply be made to add ten units
to the readings; the measurement could be off only five units. To
further complicate this issue, if there were two components, one
reading could be positive and the other negative, in effect canceling
each other out. Likewise, if both were positive then they would
add error to each other. It would not be correct to simply sum all
the errors or to take any other simplistic approach. It is possible,
however, to base the calculations on what is known as statistical
probabilities. The International Organization for Standardization
has published a text that is most useful for this calculation, the
Guide To The Expression Of Uncertainty In Measurement (GUM)
(ISO, 1995). The GUM states that a valid prediction can be made
based on the standard deviation distribution curve (see Figure
2). Combining the uncertainty elements of components may be
made by the root sum square (RSS) technique to obtain a total
component uncertainty value. Further, the combination of the
total component uncertainties may be performed using the RSS
technique to find the total system uncertainty. With this information,
there is an actual calculation or real number that can be used
for the determination of the uncertainties. One note of caution:
when computing uncertainties, ensure that the units used in the
calculation are consistent with the final leakage rate calculation,
using the technique given here, or there will be a mixing of terms,
giving incorrect results.
Presently, the most common pressure gage used is a handheld
digital gage with a pressure transducer. The principle of uncertainty
applies to both the sending-receiving unit (handheld unit) and to the
pressure transducer itself. To find the measurement uncertainty for
the entire pressure component, each of the separate instrument
uncertainty elements are evaluated. In this example for pressure,
combining the total uncertainties for the sending-receiving unit
with the uncertainties for the transducer will yield the total pressure
component uncertainty. One recommendation on this subject
is to calibrate the receiving unit and the transducer as a single
unit so that there are not two sets of uncertainties to deal with.
Additionally, this gives greater accuracy. See the PCMT decision
tree (Figure 1) for a graphic example of combining uncertainties
(the add as needed box).
Figure 2. Standard deviation distribution curve.
To calculate the total instrument uncertainties, one technique
is to use Table 1 for the total instrument uncertainties calculation.
Note: in this application, for each of the uncertainty components
(accuracy, traceability and resolution), half of the value is used in
the RSS since the units given are assumed to be Kp = 2 (value of
the coverage factor Kp that produces an interval with a confidence
level, p, assuming a normal distribution) to convert to Kp = 1. The
accuracy and traceability terms are gaussian distributions. For the
term of resolution, a bounded
distribution
is
assumed
(also known as uniform or
rectangular), which is further
compensated by dividing by the
square root of three to offset
this bounding before squaring.
Now that an examination
of the individual instrument
component uncertainties has
been made, an examination
of the total instrument system
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Continued from previous page
Pressure Change Measurement Leak Testing Errors
must be performed using the weighting process. For instance, one
unit of pressure change may have more effect on the resulting
leakage rate than of one unit of temperature change. Performing
the weighting of these factors involves a bit of differential calculus,
so it will not be discussed in this paper; however, the formula used
for the most common PCMT is supplied in the following section
without any justification or discussion. The technique used is
fully discussed in the GUM (ISO, 1995). If used, these formulas
should be verified and modified, as needed, to fit the specific test
needs. The formula supplied should serve as a sound basis for
the construction of a specific weighting formula set and help with
establishing the correct technique.
Weighted Uncertainties
Beginning with Equation 3:
(7)
where
(8)
and
LR = Q + UQ
(15)
where
LR = reported leakage rate,
Q = calculated leakage rate,
UQ = total combined uncertainty.
This technique includes the measured leakage rate factoring in
the measurement errors in the instrument system as is required
in PCMT. This technique also shows a quantifiable way of meeting
compliance with the BPVC statement, “The gage(s) used shall
have an accuracy, resolution, and repeatability compatible with the
acceptance criteria” (ASME, 2011).
The reported leakage rate would represent the largest leak
that could be present with a better than a percentage level of
confidence. The percentage level of confidence of calculated
leakage rate would depend on the accuracy associated with the
instrumentation used in the test. Provided standard uncertainty
values are utilized, then the level of confidence for the reported
leakage rate will be 1-sigma (that is, a 68.3% confidence band). If
an expanded level of confidence is required (for example, 2-sigma
or 3-sigma), then the reported leakage rate would be expressed as:
LR = Q + kUQ
(16)
where
k = coverage factor.
(9)
(10
(11)
(12)
Accordingly, for a 2-sigma level of confidence (that is, 95.5%
confidence band), the value of k is 2. For a 3-sigma level of
confidence (that is, 99.7% confidence band), the value of k is 3.
Uncertainty Example
If a system has an acceptance criteria leakage rate of 10 and
a PCMT evaluated leakage rate yields a result of 8 ±1, the test is
acceptable since the variability of the leakage rate does not exceed
the acceptance criteria. In another example, if a calculated leakage
rate of 8 ±3 is obtained, the result is ambiguous because of the
range for the result overlaps the evaluation criteria, that is, the
possibility that the leakage rate is 11 cannot be ignored. When the
uncertainty of the calculated leakage rate overlaps the acceptance
criteria, the result cannot be designated as acceptable.
Conclusion
(13)
(14)
The individually evaluated uncertainty components (Equations
9–14) are determined and substituted into the total combined
uncertainty equation (Equation 8). The total combined uncertainty,
UQ, is added to the measured leakage rate to yield the reported
leakage rate with a high degree or stated degree of certainty using:
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It is essential that calculations be performed to ensure the testing
system in total is capable of the required resolution, repeatability
and accuracy, ensuring results are compatible with the expectations
of the test outcome. As the test results require a higher degree of
accuracy and precision, the more critical it becomes to ensure
all of the measurement variables are properly accounted for. The
resolution and repeatability of the test gages are calculated before
testing commences. The test results, once calculated, in order to
be complete, must be accompanied by a statement of uncertainty
showing the degree of accuracy and precision with which test was
performed.
References
ASME, Boiler and Pressure Vessel Code, Section V, Article 10, Appendix VI,
American Society of Mechanical Engineers, New York, New York, 2011.
ISO, Guide to the Expression of Uncertainty in Measurement, International
Organization for Standardization, Geneva, Switzerland, 1995. v
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