Cost-Benefit Analysis of Switching from Cesium-Chloride Blood Irradiators to X-ray Blood
Irradiators
Erik Bakken
Katie Cary
Allison Derrick
Ellen Hildebrand
Kyle Schroeckenthaler
Malika Taalbi
Prepared for:
Global Threat Reduction Initiative
National Nuclear Security Administration
_____________________________________
TABLE OF CONTENTS
Executive Summary ........................................................................................................................ ii
Abbreviations ................................................................................................................................. vi
Introduction ..................................................................................................................................... 1
Our Task.......................................................................................................................................... 5
Costs................................................................................................................................................ 6
Assumptions.................................................................................................................................. 18
Methodology ................................................................................................................................. 21
Results ........................................................................................................................................... 26
Limitations .................................................................................................................................... 37
Recommendations ......................................................................................................................... 38
Conclusion .................................................................................................................................... 40
Appendix A: Irradiator Types and Configurations ....................................................................... 47
Appendix B: Lifecycle of Sealed Sources, According to the EPA ............................................... 48
Appendix C: OSRP Total Sealed Sourced Backlog ..................................................................... 49
Appendix D: Gammacell 1000 Elite/3000 Elan ........................................................................... 50
Appendix E: Rad Source 3400 Revolution ................................................................................... 52
Appendix F: Technological Change ............................................................................................. 55
Appendix G: Cost Estimates ......................................................................................................... 57
Appendix H: Monte Carlo Instruction Sheet ................................................................................ 60
Appendix I: Output Tables............................................................................................................ 67
Appendix J: Stata Code................................................................................................................. 77
i
EXECUTIVE SUMMARY
At the request of The Global Threat Reduction Initiative (GTRI), a division of the
National Nuclear Security Administration (NNSA), our team completed a cost-benefit analysis
of replacing cesium-chloride (CsCl) blood irradiators with X-ray blood irradiators to reduce the
threat of CsCl being diverted to a radiological dispersal device (RDD). An RDD combines
conventional explosives with radioactive material to contaminate people and the environment.
Although it would not cause mass casualties, an RDD is a potential terrorist weapon because it
can deny use of a large area, causing economic losses. CsCl irradiators have been identified as
presenting a significant risk as a domestic source of radiological material for use in RDDs. This
designation resulted in recent regulatory and policy changes regarding the use of CsCl
irradiators. Nevertheless, the risk still remains. We provide a cost-benefit analysis of switching
from CsCl irradiators to a less risky alternative: X-ray irradiators. We find positive net benefits
for switching from CsCl to X-ray irradiators in almost every case; however, since the net benefits
are much larger and more certain for older devices, we recommend planning the replacement of
CsCl devices in phases in order to replace the oldest irradiators first.
Our analysis examines the lifecycle costs of both devices, including costs measured in
installation, operation, and termination. We examine these costs at three output levels of blood
units irradiated per year: 5,000 (low), 10,000 (medium), and 15,000 (high). To analyze the
benefits of replacing an irradiator, we compare the costs of continuing to operate a cesium
irradiator to the costs of replacing the irradiator with an X-ray and operating the X-ray for the
same period.
In addition to the private costs of operating each irradiator, we also consider the social
costs associated with the devices. Currently, the social costs of using the riskier CsCl irradiators
ii
are not being incurred by the private users of these devices. Instead, they are borne by various
governmental regulatory agencies. Our goal is to uncover the costs of switching to X-ray
irradiators from both the private and social perspective so that the NNSA can fully evaluate
potential policies to mitigate risk. In addition, we aim to identify the irradiator age at which the
benefits of replacing a CsCl device would be the highest. We then use this age to recommend
the appropriate process for phasing out the CsCl irradiators.
Our analysis finds that in most cases replacing a CsCl irradiator with an X-ray irradiator
has positive net benefits from both a private and social perspective. The main reasons for this
are the costs of securing a CsCl irradiator and the costs of disposing of a CsCl irradiator. In
addition, the variable costs of operating a CsCl irradiator are much larger due to its limited
operating capacity in comparison with the X-ray irradiator. We also find that the results are
strongest for the oldest CsCl irradiators, as the private operators will have to internalize the costs
of disposal sooner than they would with a new device. In addition, we find that the results are
stronger for high throughput devices. This is because variable costs are higher for CsCl
irradiators, so with a larger throughput, the cost difference becomes even greater.
However, our findings must be tempered because of a lack of appropriate data. After
conducting an extensive literature review and receiving results from a recent American
Association of Physicists in Medicine (AAPM) survey, we were able to estimate ranges for
relevant costs, but these ranges are statistically uncertain. We recommend that the GTRI
compile more comprehensive data so that the parameters used in calculating results are clearer.
Despite the statistical uncertainty, we recommend that the NNSA adopt policies that incentivize
switching from CsCl irradiators to X-ray irradiators. We also recommend phasing out CsCl
irradiators and replacing them with X-ray irradiators, starting with the oldest CsCl devices.
iii
ACKNOWLEDGEMENTS
We would like to thank Dr. Whit Creer, of the Pacific Northwest National Laboratory and
consultant with the Global Threat Reduction Initiative, who was our contact for this project. We
also appreciate the technical experts from the Global Threat Reduction Initiative (GTRI) Rad
Replacements Project for their assistance in gathering information and data for our analysis. Its
members include:
 Dr. Leonard Connell, a Senior Scientist with the Systems Analysis Group at Sandia
National Laboratories;
 Dr. Arden Dougan, Physical Scientist in the Office of Nonproliferation and
Verification Research and Development
 Lynne Fairobent, the Legislative and Regulatory Affairs Manager for the American
Association of Physicists in Medicine
 Dr. Charles D. Ferguson, President of the Federation Of American Scientists
 William (Rusty) Lorenzen, the Radiation Safety Officer at Boston Children’s Hospital
and Manager of the Research Laboratory Support Office
 Ken Love, the Blood Bank Manager at Christiana Care in Delaware
 Ruth McBurney, Executive Director of the Conference of Radiation Control Program
Directors
 Patrick McDermott, Board Certified Health Physicist and member of the ABHP Part I
Panel of Examiners
 Blair Menna, engineering consultant for Northern Nuclear Services
iv
 David L. Weimer, professor of political economy at University of Wisconsin –
Madison.
We would also like to thank certain members of the University of Wisconsin-Madison
community for their expertise and guidance during this project. Dr. David Weimer, who is also a
technical expert for the GRTI, instructed the team about how to conduct cost-benefit analysis.
Dr. Victor Goretsky, the Radiation Safety Officer at University of Wisconsin-Madison, granted
us an interview and described how the university’s CsCl irradiator was managed and operated.
He also referred us to Dr. Bruce Thompson, professor at the Wisconsin Institute for Medical
Research and Dr. Keith M. Hoerth, Clinical Labs Manager, Transfusion Services, for University
of Wisconsin-Madison Hospital. They both made time to answer questions about their
experience with irradiators. Dr. Greg Nemet, professor at University of Wisconsin-Madison,
contributed his expertise for our section on technological change.
v
ABBREVIATIONS
AAPM: American Association of Physicists in Medicine
CsCl: Cesium-Chloride
DoE: Department of Energy
GTCC: Greater than Class C
GTRI: Global Threat Reduction Initiative
GVH: Graft-versus-host disease
NNSA; National Nuclear Security Administration
NRC: Nuclear Regulatory Commission
OSRP: Offsite Recovery Source Project
RDD: Radiological dispersal device
RED: Radiation exposure device
RSO: Radiation security officer
TA-GVH: Transfusion-associated graft-versus-host disease
vi
INTRODUCTION
Sealed source machines enclose radioactive material in metal containers and shielding
devices in order to perform industrial, research, and medical tasks in several sectors.1 Examples
of sealed source usage include sterilization of equipment or measurement of material density.
Users must demonstrate minimum levels of adherence to security and protection regulations, so
sealed sources do not pose an overt risk to health from radiation exposure.2 Nevertheless, there
are always security concerns when dealing with radioactive material. One type of radionuclide,
cesium-137 chloride (CsCl), poses an especially large security risk when used in blood
irradiators. This risk predominantly derives from the physical nature of the matter itself, the
geographic locations of the device users, and the limited options for long-term or permanent
disposal pathways.3 Using an X-ray blood irradiator does mitigate most of these risks; however,
our research indicates that users consider X-ray irradiators to be more expensive and less
reliable.4 Thus far, there has been little analysis of the choice of irradiator technology using a
cost-benefit or lifecycle analysis framework. Our report conducts private and social lifecycle
analyses for the Global Threat Reduction Initiative (GTRI) of the National Nuclear Security
Administration (NNSA).
Sealed source radioactive material poses a risk because of the potential diversion to a
radiological dispersion device (RDD), or “dirty bomb.” An RDD combines “conventional
explosives with radioactive material,” but does not include a nuclear detonation.5 Radiation
exposure from an RDD would likely be limited to a few blocks or square miles. RDDs are
considered a weapon of mass “disruption”—not “destruction”—because expected losses occur
from area denial and resulting economic shocks. Any fatalities would likely be caused by the
conventional explosive blast, not from radiation exposure. Radiation levels would be high
1
enough to require evacuation of an area and render it temporarily inhospitable for residents and
businesses. The objective of an RDD attack is not mass casualties; instead, it aims at causing
psychological trauma, long-term health and environmental concerns, and economic disruption.
An RDD attack in a densely populated area, for example, could cost billions of dollars in
economic losses and cleanup costs.6
In the aftermath of 9/11, United States intelligence reports and activity overseas revealed
that individuals associated with Al-Qaeda planned to acquire materials for an RDD.7
Consequently, there was a renewed focus on strengthening U.S. policy regarding the protection,
conversion, and replacement of at-risk radiological material. Most sealed sources would not be
appropriate for use in an RDD, but CsCl blood irradiators present one of the highest risk levels
for diversion.8 In order to use the radionuclide cesium-137 in a blood irradiator, it is
manufactured as CsCl powder (or salt) that is compressed and double encapsulated in steel.9 The
compressed powder form of CsCl is readily dispersible and water-soluble, which means that if
used in an RDD, it has the capability to be spread via air-ventilation or water supply systems.
Obviously, this greatly increases the area denial capacity of the RDD.
There are approximately 327 licensees of 575 CsCl blood irradiators in the United
States.10 In 2004, CsCl devices irradiated over 2.25 million (over 90%) of all blood components
in the United States.11 Licensees are typically located in populous city centers at hospitals, blood
centers, and universities. It would therefore be likely that an RDD made from CsCl would be
detonated in a densely-populated area, which would inflict the most economic and psychological
damage. Border controls and homeland security policies help to prevent unauthorized
radioactive material from entering or leaving the United States, but it is more difficult to control
domestic sources.
2
CsCl security breaches may occur at four points in the lifecycle: (1) in transit to
installation; (2) during service-life; (3) in transit after service-life; and, (4) in disposal or longterm storage.12 Domestic policies have recently tightened regarding security of CsCl irradiators,
upon the recommendation of the 2008 report by the National Research Council.13 Users must
upgrade to a minimum level of security, including retina or fingerprint scanners, specialized
training, and background checks. In addition, CsCl device users must follow various protocols,
such as GPS tracking, to ensure security during transit, although the protocols differ greatly
based on the city and state. In a highly concentrated urban area, such as New York City, the
entire street may have to be blockaded by law enforcement while the device is being removed
from the building. In more rural areas, though, law enforcement may just escort the device from
the building to the truck. Variation in security procedures could exacerbate security threats and
may be a subject for future policy analysis. Prior to the CsCl security upgrades, researchers
identified the highest risk occurring during device usage.
In 2003, researchers at Los Alamos National Laboratory conducted an analysis of the risk
levels occurring at different life-cycle phases of a sealed-source device. They determined that the
highest risk occurred during the phase of “device usage.” Researchers applied a hypothetical set
of policy recommendations that increased security regulations during that specific high-risk
phase, but then found that risk levels during the next two phases, disposal and storage, actually
increased from the status quo. Security regulations have since been increased for CsCl
irradiators, many changes specifically applied to the “device usage” phase. If the findings of the
report hold, we anticipate that the risk levels during the disposal and the storage phases have
increased after those policy changes. Consistent with this analysis, we also expect that the lack of
3
a permanent, secure disposal pathway most directly contributes to the risk of RDD diversion
overall.14
Blood irradiators provide a necessary medical service. Irradiation of blood components
occurs prior to transfusion for patients, especially those with compromised immune systems,
such as transplant recipients or HIV positive patients.15 This procedure is necessary to prevent
transfusion-associated graft-versus-host disease (TA-GVH). TA-GVH occurs when newly
transplanted blood cells attack a recipient’s body; in contrast, graft-versus host (GVH) occurs
after a tissue transplant (typically bone marrow). TA-GVH has a faster onset and higher
mortality rate than GVH, but its symptoms are clinically very similar. While rare, TA-GVH is
fatal in more than 90 percent of cases.16 Additionally, TA-GVH has been observed in both
immune competent and immune-suppressed individuals, increasing the range of possible blood
components recommended for irradiation.
CsCl irradiators use gamma rays emitted during radioactive decay to irradiate blood. As
a compressed powder, CsCl is useful for irradiation because of its strong radioactive decay, high
specific activity, and relative ease in manufacturing.17 A variety of factors—including perceived
cost-effectiveness, reliability, longevity, and low maintenance costs—make CsCl irradiators the
preferred technology for irradiation of blood components.
X-ray irradiators are the most promising replacement for CsCl irradiators. Cobalt
irradiators, the only other option, are generally not feasible for hospitals or other blood
processing facilities, as the extreme weight of the shielding device necessitates costly facility
upgrades.18 Because X-ray technology does not pose the same RDD-related security threat as
CsCl irradiators, it has the primary advantage of decreased security costs.19 In addition, the
disposal costs are almost negligible in comparison with a CsCl irradiator, as an X-ray irradiator
4
can be disposed of in a regular landfill after being disassembled. Although X-ray irradiators
have similar initial purchase prices as CsCl irradiators, they require more frequent and costlier
repairs.20 In addition, they do not last as long (approximately 10 to 15 years versus 30 years) and
would therefore require at least one full device replacement to cover the same lifetime as the
CsCl irradiator.21 Despite this, the decreased costs of using an X-ray irradiator—specifically
from the RDD attack losses—may be enough to justify choosing it over a CsCl irradiator.
OUR TASK
The Global Threat Reduction Initiative, a division within the National Nuclear Security
Administration (NNSA), requested an assessment comparing the costs of replacing CsCl
irradiators with X-ray irradiators. Our analysis excludes CsCl irradiators used primarily for
research or calibration purposes and focuses on the blood irradiators used by hospitals and blood
banks. It may be beneficial to replace CsCl blood irradiators because of the risk that cesium-137
compounds will be diverted into RDDs.
Our analysis determines the costs of continuing to operate a CsCl irradiator and compares
them to the costs of replacing that irradiator with an X-ray unit. If the costs of converting to and
operating an X-ray irradiator are less than continuing to use a cesium irradiator, then there are
benefits of replacement even without considering RDD risk. If the costs of replacement are
greater than maintaining the status quo, the difference in costs indicates the value that would
need to be assigned to RDD risk in order to justify replacing that irradiator. RDD risks are not
directly included in our model because of the difficulty in calculating different threat levels
based on device, location, and user characteristics.
5
We consider the perspectives of both the device user and society in our analysis. An
analysis of the private costs of operating an irradiator help to determine the circumstances in
which it may be in the financial interest of an irradiation user to switch from CsCl irradiation to
X-ray technology. To assess the costs to society, we perform our analysis a second time
including social costs that a private operator may not consider, but which the general public
bears indirectly.
COSTS
In order to compare the costs of operating CsCl and X-ray irradiators and assess the value
of replacing the former with the later, we collected a significant amount of data primarily related
to four types of costs. Important costs include resources invested into the installation of a new
device, annual fixed costs that occur regularly regardless of how much an irradiator is used,
annual variable costs that are affected by how frequently an irradiator is used, and termination
costs that are incurred at the end of the lifetime of an irradiator.
Data was collected from a variety of sources. We used data gathered in a GTRI survey of
American Association of Physicists in Medicine (AAPM) member institutions that use CsCl or
X-ray devices for blood irradiation. The survey had a limited sample size, but the information
gathered was useful in forming parameters for use in our Monte Carlo analysis. We gathered
additional data directly from the expert panel of the GTRI project. Our research team also
conducted interviews with various staff members at UW-Madison to collect additional
information and cost estimates. When the data provided by these sources was not sufficient to
estimate parameters, we used data gathered from the literature on blood irradiation.
6
Installation Costs
A major installation cost is the purchase price of the X-ray or CsCl device. The purchase
price can vary for several reasons. First, both CsCl and X-ray devices vary in size. Large
hospitals and blood banks require larger devices that are capable of handling a larger throughput.
The literature suggests that institutions may not pay the listed price for large capital purchases
because of their relationship with the vendor, the size of the hospital, and the services included in
the purchase price.22 The purchase price is roughly comparable between the two technologies.
Before either device is installed, there are costs to prepare the physical space for device
use. Rooms containing X-ray devices must be able to accommodate the high electricity demand
of the machine and may need structural reinforcements to support their weight. Older models of
X-ray may need a connection to a water line in order to cool the machine. Because some
hospitals may install X-ray machines in rooms that already contain these requirements, and
others may have to pay for all upgrades, there is a high degree of uncertainty to this estimate.
Rooms containing CsCl irradiators may also need structural reinforcements to bear the
weight of the device, but do not require a large amount of electricity or a water line. CsCl
irradiators also differ from X-ray machines in that they require security updates to secure the
room up to standards set by the Nuclear Regulatory Commission (NRC). Institutions have some
latitude in choosing how to secure their CsCl irradiators. The regulations governing security
allow for the fact that institutional circumstances vary, making a one-size-fits-all approach to
security impossible.23 Security upgrades may include iris readers, card readers, alarm systems,
and surveillance cameras, depending on the security decisions made by the institution. We
decided to exclude the opportunity costs of space occupied by the devices for two reasons: it is
difficult to quantify, and the two devices take up similar amounts of physical space.
7
Both alternatives incur a delivery cost, but this cost is much higher in the case of the CsCl
irradiator because of the security required as the controlled substance is transported, and the
import fee required when controlled substances cross the border into the United States.
Transportation costs of CsCl irradiators depend on the location of the institution in relation to the
vendor and the security required by the state or municipality. Institutions generally pay security
firms or law enforcement to escort the device, although some costs may be included in the
purchase price. In some municipalities, such as Boston and New York, streets must be closed
down when the device is moved, greatly increasing transportation costs. The transportation costs
of X-rays are much lower, estimated at approximately $2,000, as security is not required.24
Personnel are required to perform the initial legal and licensing work, as well as assess
the impact of the irradiator on the operation of the hospital or blood bank. These costs are larger
for the CsCl blood irradiator because a radiation security officer (RSO) must ensure initial
compliance with NRC regulations, in addition to increased licensing fees and additional legal
work (a further discussion of the RSO position is included in the Annual Fixed Costs section).
When using CsCl irradiators, any person who could come in contact with the irradiator must be
instructed in the security and safety measures to use when around the device. According to Best
Theratronics, the manufacturer of the most popular X-ray blood irradiator, the installation of the
device should take one to three days, including the physical installation and the training of staff
in the operation of the new machine. Assuming an 8-hour workday, this means costs of between
8 and 24 hours of paid, but unproductive, work time for the staff being trained. The relevant
employees who require training are the technicians and some managerial and administrative
staff. However, unlike the federal regulations guiding the use of CsCl irradiators, the X-ray
machine has fewer rules regulating who must be trained in the risks associated with the device.
8
Table 1: Installation Costs
Component
(Unit)
Cesium Irradiator Purchase Price:
(Total Dollars)
X-Ray Purchase Price:
(Total Dollars)
Cesium Site Preparation:
(Total Dollars)
X-Ray Site Preparation:
(Total Dollars)
Cesium Initial Legal/Licensing/RSO/Public
Health Costs:
(Total Dollars)
X-Ray Initial Legal/Licensing/RSO/Public
Health Time Costs:
(Total Dollars)
Cesium Initial Fingerprinting/Background
Check Costs:
(Total Dollars)
Cesium Installation/ /Shielding Design
Considerations:
(Total Dollars)
Cesium Transportation of Device:
(Total Dollars)
X-Ray Transportation of Device:
(Total Dollars)
Cesium Import Permit- Cesium Only
(Total Dollars)
Cesium Global Threat Reduction Initiative
Security Equipment/Installation:
(Total Dollars)
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
160,000
325,000
242,500
160,000
240,000
220,000
5,000
10,000
7,500
0
50,000
18,600
4,000
20,000
15,400
2,000
3,000
2,500
2,000
5,000
3,800
30,000
38,000
34,000
3,000
50,000
28,800
0
2,600
2,000
7,000
7,000
7,000
317,800
500,000
404,800
The NNSA recently began the GTRI Voluntary Radiological Enhancement program.
This program is a federally funded voluntary program that seeks to reduce the threat posed by
domestic radiological sources by securing nuclear and radiological materials while in use across
the United States. The focus of the program is currently on securing high risk CsCl irradiators at
9
an estimated total cost of $105 million.25 Dividing this cost estimate by the number of irradiators
that NNSA plans to secure, the upgrades are expected to cost the program roughly $404,800 per
high risk CsCl irradiator.26 Under the GTRI program policy, security upgrades beyond what is
required by security regulations are provided to institutions using a CsCl irradiator at no cost.
Hospitals must pay the costs of maintaining the security upgrades after a three to five year
warranty period.27 We evaluate the initial cost of the program only in the social cost analysis; we
include the cost to hospitals of maintaining the upgrades after the warranty period in the financial
analysis. A summary of the installation costs can be found in Table 1.
Annual Fixed Costs
The largest fixed operating expense for many users of CsCl blood irradiators is the cost
of licensing. The cost of a license and annual licensing fees can be very large, especially for
small-scale users, whose costs are approximately $8,700.28 In contrast, large-scale users such as
hospitals usually own other radioactive medical equipment in a higher license category.
Hospitals only have to pay the federal licensing costs of the most expensive device, so the blood
irradiator is added to the existing license without additional cost. The official license costs for
different devices can be found on the Nuclear Regulatory Commission’s website, under
regulations 10 CFR 171.16 Annual Fees. X-ray irradiators are not subject to the NRC’s license
costs.
Besides licensing, there are other costs associated with government regulation of CsCl
devices. According to federal regulations, the use of CsCl blood irradiators requires the
supervision of an RSO who is trained in handling radioactive material, the safety and security
requirements of the device, and the federal regulations concerning its operation.29 While the
Bureau of Labor Statistics does not have specific compensation data for this position, we
10
estimate that the salary would be comparable to a “Compliance Officer,” whose job it is to
“examine, evaluate, and investigate eligibility for or conformity with laws and regulations
governing contract compliance of licenses and permits, and perform other compliance and
enforcement inspection and analysis activities not classified elsewhere.”30 X-ray machines
require similar supervision, but by a “medical physicist advanced”, who manages their operation.
As the job responsibilities related to irradiator supervision are similar for both an RSO and a
“medical physicist advanced,” this analysis assumes no significant difference in staff pay.
An X-ray irradiator will generally have lower security costs than a CsCl irradiator. RSOs
will not have to put extra time into enhancing or maintaining security measures. This cost is
measured in terms of the salary paid to the employee during the lost time. Moreover, fewer
security guards may be necessary; this would produce an avoided cost equivalent to the average
salary: $31,800.31 CsCl irradiators’ security systems are often linked directly into police
stations’ grids, which costs local police some time for monitoring, a social cost which would not
appear in a business’s decision about the type of blood irradiator to purchase.
Federal regulations also require that staff with access to the CsCl irradiator undergo
background checks, which can be expensive and time-consuming. Fingerprinting and
background checks cost about $125 per employee. According to a survey conducted of
American Blood Center members, the average costs per center were $2,300 per year. Outside
the direct cost of the background checks and fingerprinting, there were additional costs of delays
in receiving background checks, confusion over the exact requirements, and the inability to
recover these added expenses.32 If an institution has participated in the GTRI Voluntary
Radiological Enhancement program and received security upgrades, it bears costs in maintaining
the new security infrastructure after the warranty period.
11
The largest fixed expense associated with X-ray devices is maintenance of quality and
replacement parts. The RS 3400 Revolution, which is our preferred X-ray device, requires a
power source upgrade at years seven and ten; the upgrades have a total cost of $15,000.
Calibration costs for X-ray units vary per year, depending on the device and frequency of use.
Calibration is important for quality control; users need to ensure that the device maintains the
required level of radiation exposure per unit of blood. The highest estimates for this cost are
$1,000 per year.33
Many manufacturers’ service contracts for X-ray irradiators cover replacement parts and
calibration; they are attractive to users because the uncertainty of these expenses is decreased.
According to blood bank surveys, these can cost $6,000 to $20,000 per year, depending on the
type of contract.34 The RS 3400 has a service contract which does not include all of the
calibration and maintenance costs; the price of this contract is $10,000 per year.
We assume that the contracts for X-rays include calibration costs, but not the costs of the
power upgrade and replacement parts. This is consistent with the information we received about
the RS 3400, though it will not apply to every contract. In addition, the service contracts vary
widely in the amount of maintenance costs they cover. Many only cover bulb replacements after
a certain period of time; high-throughput facilities would then need to replace the bulbs more
frequently than the service contract allowed. In addition, there was little information about the
differences in service contracts and how inclusive they were. Since part replacement can be a
large cost for X-ray machines, we chose to evaluate it separately. Fixed power upgrades are
included with fixed costs, and bulb replacement is included in variable costs.
CsCl irradiator operators also carry service contracts, though they tend to be less
expensive because the machines require fewer replacement parts. Estimates for these costs range
12
from $1,000 to $14,000 per year.35 Therefore, the service contract cost is highly uncertain and
greatly influences the ranges of net benefits in the Monte Carlo sensitivity analysis. We have no
estimates for the costs of CsCl unit calibration, so they are assumed to be negligible. No relevant
difference in the total cost of insurance between X-ray units and CsCl units was discovered. A
summary of the annual fixed costs can be found in Table 2.
Table 2: Annual Fixed Costs
Component
(Unit)
Cesium Security Infrastructure Maintenance:
(Annual Total Dollars)
Cesium Security Background Check:
(Annual Total Dollars)
Cesium Anticipated Security Ongoing Costs:
(Annual Total Dollars)
Cesium Service Contract/ Warranty:
(Annual Total Dollars)
X-Ray Service Contract/ Warranty:
(Annual Total Dollars)
X-Ray Year 7 Power Supply Upgrade:
(Total Dollars)
X-Ray Year 10 Power Supply Upgrade:
(Total Dollars)
Cesium Regulation Personnel:
(Annual Salaries in Dollars)
Cesium Regulation Licensing:
(Annual Total Dollars)
X-Ray Regulation Licensing:
(Annual Total Dollars)
Nuclear Regulatory Commission Costs Not
Covered by Licensing:
(Annual Total Dollars)
13
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
1,000
8,600
4,900
2,400
2,400
2,400
4,000
7,500
5,800
1,000
14,000
6,000
2,000
17,000
8,500
5,000
5,000
5,000
10,000
10,000
10,000
57,500
57,500
57,500
650
8,700
4,700
3,000
8,700
5,900
4,600
4,600
4,600
Annual Variable Costs
Variable costs change based on increases in output, and they are borne by the operator of
the irradiator. These costs can be broken into four categories: labor, utilities, maintenance, and
failure. Each irradiator requires labor in order to operate and irradiate blood units. Labor costs
are calculated by multiplying the wage of a technician by the time it takes to operate the
irradiator. Wages for the technicians do not vary based on the type of device; for either, the
wage ranges between $27 and $37 per hour.36 Differences in labor costs for the two irradiators
can therefore be attributed to changes in operation time. While both types of irradiator average
five minutes per batch, they differ in the number of blood units that can be irradiated in each
batch.37 CsCl irradiators average 2.5 units in a batch, while the X-ray irradiator can process 5
units at one time.38 Therefore, X-ray irradiators will typically take half the time to irradiate the
same number of blood units as a CsCl machine, so the labor costs for X-ray machines will be
half those of CsCl machines.
Both CsCl and X-ray irradiators also require some utility use, though the utility
requirements are typically much higher for X-rays. CsCl irradiators have low utility costs; the
machines only require electricity to operate, not to irradiate blood. Therefore, they can operate at
about 0.3 kW of electricity per minute and do not require water.39 X-ray irradiators, however,
require electricity to irradiate blood. The RS 3400 Revolution operates at 2 kW of electricity per
minute, which is nearly seven times the energy required for CsCl irradiators.40 Most X-ray
machines require an external water line and large amounts of water for tube cooling. However,
the RS 3400 Revolution is a self-contained unit with no external water requirement.41 Because
we recommend this model, we assumed that water costs are zero for X-rays and for cesium for
the purposes of our analysis.
14
X-ray machines require a higher level of maintenance than CsCl irradiators. CsCl
irradiators have very few parts and the active agent is the CsCl, which simply needs to decay in
order to produce radiation. X-ray machines, however, require bulbs in order to produce
radiation, and these bulbs wear down as they are used. The RS 3400 Revolution has only one
bulb, which costs $10,000 to replace and should be replaced every 10,000 irradiation cycles.42
Table 3: Annual Variable Costs
Component
(Unit)
Cesium Blood Units Per Site Per Day:
(Average Daily Blood Units Irradiated)
X-Ray Blood Units Per Site Per Day:
(Average Daily Blood Units Irradiated)
Cesium Blood Units Per Batch:
(Average Blood Units Irradiated Per Run)
X-Ray Blood Units Per Batch:
(Average Blood Units Irradiated Per Run)
Cesium Wage of Technician/Operator:
(Hourly Wage in Dollars)
X-Ray Wage of Technician/Operator:
(Hourly Wage in Dollars)
Cesium Irradiation Time Per Batch:
(Run Time in Minutes Per Batch)
X-Ray Irradiation Time Per Batch:
(Run Time in Minutes Per Batch)
Price of Electricity:
(Dollars Per Kilowatt Hours)
Cesium Kilowatts of Electricity Consumed:
(Kilowatts Consumed Per Minute of Run-Time)
X-Ray Kilowatts of Electricity Consumed:
(Kilowatts Consumed Per Minute of Run-Time)
X-Ray Parts Replacement:
(Average Annual Dollars)
Cesium Costs of Downtime:
(Average Annual Dollars)
X-Ray Costs of Downtime:
(Average Annual Dollars)
15
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
0
50
25
0
50
25
1
4
2.5
5
5
5
27
37
29
27
37
29
1.7
8.6
5
5
5
5
0.076
0.1647
.1081
0.3
0.3
0.3
2
2
2
10,000
10,000
10,000
2,300
2,300
2,300
4,000
4,000
4,000
Each machine also has the potential to fail or break, which would render the device
useless until repaired. Operators would then have to use an alternative method to irradiate blood
or purchase irradiated blood from another facility while the malfunctioning device is repaired.
The GTRI survey found that the cost associated with this downtime was about $2,300 per year
for CsCl irradiators and about $4,000 per year for X-ray irradiators. Because the costs associated
with one day of down time are equivalent between the two devices, this indicates that X-ray
irradiators are expected to be down nearly twice as often as CsCl irradiators. A summary of the
variable costs is provided in Table 3.
Termination Costs
At the point of replacement, users have two options for disposal of their CsCl blood
irradiator: the manufacturer’s program or the National Nuclear Security Administration’s
program, the Offsite Recovery Source Project (OSRP). Since cesium-137 is classified as Greater
than Class C (GTCC) low-level radioactive waste, users are not able to utilize other low-level
radioactive waste sites.43 Instead, they are obligated to store the sealed source device at their
own site until other disposal options can be pursued. Some users are able to go through the
device manufacturer for return and sealed source recycling or disposal. This is a limited pathway
because vendors typically only accept their own devices for return. Furthermore, some devices
have been discontinued and are no longer accepted by the manufacturer. Users are still obligated
to pay return fees to the vendor, although the vendor usually covers the cost of the shipping
container. Return fees can vary from $15,000 to $40,000 and may depend on the user
relationship with the vendor and their likelihood of purchasing a new CsCl machine.44
Users can also contact OSRP to request pickup of their unwanted or defunct CsCl blood
irradiator. As part of the GTRI, OSRP removes “excess, unwanted, abandoned, or orphan
16
radioactive sealed sources that pose a potential risk to health, safety, and national security.”
OSRP has recovered 54 blood irradiators from users since 2006. This is a promising number;
however, there are currently 67 backlogged blood irradiators whose users have requested OSRP
pickup. Of these, 34 of these are disused and unwanted and 33 are still in use. Furthermore,
there are multiple reports from the last few years that claim that the DOE is “not yet in the
position to accept GTCC sources” except under “special circumstance.”45 Users can expedite the
process and pay for transport themselves, or they can wait up to a year for the OSRP’s transport
and disposal process. If it is not expedited, then the costs fall almost exclusively on OSRP; the
user would just be responsible for the continuing cost of maintaining security standards (i.e.
surveillance and possession-only licenses) at the device’s location.
Our analysis accounted for both the private costs (fees from the user to the manufacturer
and fees from the user to OSRP) and the public costs of termination (OSRP’s transport and
disassembly costs and OSRP’s long-term storage cost). The largest disposal cost results from
transporting the device because there is only one shipping container (10160 B) in the United
States available to the OSRP.46 According to sources affiliated with the NNSA, there is one
other company with one shipping container for general use. The costs to rent this container
range from $75,000 to $150,000 per use. Two other containers are expected to be certified over
the next decade and could lower the transport costs if available on time. Finally, we consider the
scrap value cost factors to be negligible for the X-ray irradiators (approximately $160). It is
difficult to monetize this cost for the CsCl irradiators because manufacturers have the option to
take a decommissioned device and refurbish the machine for resale. As such, this analysis omits
scrap value as a cost factor. A summary of the termination costs can be seen in Table 4.
17
Table 4: Termination Costs
Component
(Unit)
Cesium Physical Costs of Disposal:
(Total Dollars)
X-Ray Physical Costs of Disposal:
(Total Dollars)
Cesium Site to Vendor Disposal Fee:
(Total Dollars)
Cesium Site to Off-Site Recovery Project
Disposal Fee:
(Total Dollars)
Off-Site Recovery Project Costs Not Covered by
Fees:
(Total Dollars)
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
75,000
150,000
---------------
0
2,600
1,300
15,000
40,000
---------------
0
190,000
---------------
75,000
920,000
---------------
Summary of Cost Categories
We use the four cost categories to produce a lifecycle analysis for each device. We add
up the costs for each device, then we compare across the two devices. Our analysis only deals
with costs; there is no calculation of benefits. Any benefit to the user comes in the form of
avoided costs of operating a more expensive device; any social benefit comes in the form of
avoided costs of the recovery programs.
ASSUMPTIONS
It was necessary to make various assumptions about irradiators and how they are
operated in the design of our analysis.
We assume that the X-ray device is the RS 3400 Revolution, a relatively new X-ray
blood irradiator model produced by RadSource. This model appears to be the most effective Xray device on the market and has multiple advantages over other models that make it a strong
18
alternative for the technology to replace CsCl irradiators (see Appendix E). We used this model
assuming that the user would be purchasing a new X-ray device, and would therefore choose the
model with the largest benefits. We used the RS 3400 as the base for estimating X-ray costs, and
then used additional survey data and research to complement our information.
We assume the CsCl irradiators are similar to the Gammacell 1000 Elite/3000 Elan
model (see Appendix D). The Gammacell 1000 Elite/3000 Elan is one of the most popular CsCl
model, and it had readily available data. We used data describing the throughput and other
requirements for this device to estimate parameters for our analysis, along with existing
information on cesium chloride irradiators and information obtained from the GTRI survey. We
assume that both CsCl and X-ray blood irradiators are used at full batch capacity, meaning that
the maximum number of blood units is irradiated each time that the machine is used. If this isn’t
the case, users could easily change their operational practices to irradiate all blood units at one
time.
Though the lifetime of both types of blood irradiator can vary, we assume that X-ray
machines have a lifetime of 12 years and CsCl machines have a lifetime of 30 years, which
appear to be industry averages. Institutions may choose to use their CsCl irradiator longer, but as
the source material decays and becomes less effective, the time it takes to irradiate blood will get
longer. We assume that end-of-lifetime disposal costs are uniformly distributed and do not vary
across facility size or throughput of blood units.
We assume that 45 percent of facilities containing a CsCl device have more than one
sealed-source device. These larger users benefit from some administrative and operations
efficiencies that reduce their total costs. For example, the NRC issues licenses based on the
highest activity device a facility possess and does not require fees for additional devices. We do
19
not assume a correlation between the number of sealed-source devices and the amount of
throughput for these facilities, because not all of the sealed-source devices are blood irradiators.
Because of difficulties in predicting future changes we assume no significant changes,
such as technological change or changes in the real prices of variables, during the period of
analysis. Recent innovations in X-ray technology have led to newer X-ray irradiators, such as
the RS 3400, that have eliminated the need for water and water filters and decreased the number
of x-ray tubes. In the near future, technological change may cause additional decrease in the
operating costs of x-ray irradiators. For example, service contracts and replacement parts are
major costs of operating X-ray devices. These costs could fall considerably if the lifespan of xray bulbs and power sources increase. Accurately estimating improvements requires more
information than currently available. For further explanation of how to include technological
change in future analyses, see Appendix G.
Because costs occur in different time periods, a discount rate must be used to account for
the present value of future costs.47 Our results were calculated using both a 3 percent and 7
percent discount rate in accordance with Office of Management and Budget guidelines.48 In
order to simplify our analysis, we assume that annual costs accrue mid-year in accordance with
standard cost-benefit analysis procedure. Installation costs occur preceding the first year and
termination costs are assessed at the end of the final year of a device’s expected life.
We did not include benefits in our calculation of labor costs. Instead, we calculated the
costs with pure salary figures from the Bureau of Labor and Statistics. We did this for two
reasons. First, we assumed that much of the labor cost was an opportunity cost of that labor
being used elsewhere. For example, many RSOs are also employed by the hospitals in other
capacities. Therefore, the costs associated with the position are not that of a separate individual,
20
but are opportunity costs of the RSO spending time on his other position. The RSO would
receive benefits whether his time was used on the RSO position or the other position. Second,
we found that calculations of benefits varied greatly from state to state, and it was difficult to
find accurate data. Contrastingly, salary data was easier to find and verify. Given that our model
had a great deal of uncertainty in other variables, we were hesitant to introduce additional
uncertainty in our model without good reason to include it.
Given these assumptions, we were able to collect enough data in our cost categories to
complete a lifecycle analysis of CsCl and X-ray irradiators.
METHODOLOGY
Analysis of the difference in costs is carried out using a Monte Carlo analysis. Monte
Carlo analysis is a modeling technique which accounts for the uncertainty of the data collected as
well as the variability between users of irradiators. In short, Monte Carlo analysis is able to
account for uncertainty and variability by performing many randomized simulations or trials.
We implemented our analysis using Stata, a statistical software package frequently used in the
social sciences. An excel tool was also developed in order to assist with case-by-case irradiator
replacement decisions.
Monte Carlo Analysis
The Monte Carlo analysis can be divided into two sections. The first section evaluates
the decision to purchase a new blood irradiator assuming a site does not currently own an
irradiator and could choose either CsCl or X-ray technology. The second section is significantly
larger and assesses the costs of replacing a CsCl irradiator with an X-ray irradiator. The costs of
continuing to operate a CsCl irradiator are compared with the costs of replacing the irradiator
21
with an X-ray unit and then operating X-ray machines for the number of years the CsCl unit had
remaining in its expected life. Analysis is carried out twice to test both three percent and seven
percent discount rates.
In order to test the importance of sites irradiating different annual volumes of blood,
1,000 trials are simulated at throughputs of 5,000 units, 10,000 units, and 15,000 units. Actual
throughput varies significantly across sites but results provided at these three levels provide
understanding of important trends. This range is representative of small, medium and large
irradiation users. It is expected to influence net benefits because the impacts of some cost
categories, especially annual fixed and variable costs, depend greatly on throughput.
The model design simulates 3,000 trials for each age of an irradiator for a period of 30
years, which is the expected life of a CsCl irradiator. We include variation in the age of the
irradiators at year zero to accurately reflect the current variation in irradiator age. This variation
is also important because termination costs are a large portion of expected CsCl costs. Devices
that start at different ages will have a different value for the termination costs because they occur
in the future, and therefore the costs are discounted for the number of operable years remaining
on the device. In addition, the relative influence of annual costs and one-time costs change based
Figure 1: Accounting for Different Device Lifespans
22
on the number of operable years considered. In total, Stata simulates the costs of 93,000
hypothetical users operating CsCl irradiators and X-ray irradiators.
The first 3000 trials assume that there is no current device, so they are a simple
comparison of the annualized lifecycle costs of installing, operating and disposing of either a
CsCl or X-ray irradiator. Lifecycle costs are discounted back to the current year and then
annualized to account for the fact that the two technologies have different expected lifetimes.
The annualized cost of operating an X-ray will be used again in the second section of the
analysis.
The second simulation assumes that a CsCl device was replaced with an X-ray irradiator
and then operated for the remaining expected life of the original CsCl device. 3000 trials were
performed for each remaining year in expected life. The second analysis section requires several
additional cost considerations. Continuing to operate a CsCl device requires no installation costs.
The remaining cost categories are annual fixed costs, annual variable costs, and termination
costs. Replacing a CsCl device with X-ray technology involves CsCl termination costs and Xray installation, annual fixed, annual variable, and termination costs. Additionally, a single X-ray
irradiator may be insufficient to cover the remaining years of lifetime that the retired CsCl
irradiator was expected to operate, requiring additional X-ray units to meet the user’s future
needs.
The second section considers the potential need to purchase additional X-ray devices in
the future including the costs of their operation and termination. As shown in Figure 1, this is
accomplished by adding the future costs of an entire X-ray machine lifecycle if the remain years
are greater than or equal to twelve and, when fewer than twelve years remain, adding on the
annualized costs one year at a time (these were calculated in analysis section 1). This method
23
allows us to use the same time frame for each device, so costs can be discounted back to the
current year and the net present values can be directly compared to assess which technology has
lower total cost.
The year zero purchase analysis and the 30 years of replacement analysis are also
conducted a second time to include social costs. GTRI security updates, NRC administrative
costs not covered by licensing fees, and termination costs associated with the Off-Site Source
Recovery Project (OSRP) are the major social costs considered by the analysis. If sites continue
to operate CsCl irradiators the model assumes that GTRI will provide security updates to their
facilities within the next eight years. The model does not account for users electing not to have
GTRI provide security improvements. NRC administration is included ten percent of those costs
are not covered by fees and licenses; instead, it is covered by taxes. The largest social cost
consideration in the model is the cost of OSRP transporting, storing and disposing of sealed
sources.
RDD Risk
The value of the RDD risk determines what monetized risk level would be necessary to
justify removing irradiators. There are several ways to think about how the value of RDD risk
can be determined from the model. We suggest using either the mean net present value for each
year or the lower bound method. Using the mean net present value, the RDD risk would be
sufficient to justify replacement if one half of users in that year have positive net benefits and
one half have negative net benefits. Using the lower bound method, the RDD risk would be
sufficient to justify replacement if 95 percent of users in that year have positive net benefits and
five percent have negative net benefits. Because of the expected variation based on the number
of remaining years, we expect that a variable policy based on the age of an irradiator would
24
probably be more sensitive to user costs; we conduct the analysis from this point of view. It
would also be possible to average costs across ages so that the impact on older and newer users
were unequal, or to again set a policy under which 95 percent of users benefited after considering
the cost of RDD diversion risk. These dollar amounts are calculated for both private and social
costs.
Excel Tool
Included as a supplemental document, we produced an excel tool which estimates costs
for individual facilities and allows users to input their own data. The excel tool can be used to
calculate preliminary cost estimates of switching technologies for a facility. Unlike the Stata
analysis, the excel tool is intended to be used on a facility by facility basis. The tool provides
estimated values of costs for comparison purposes. It conducts 5000 random trials of switching
from CsCl to X-ray technologies. This tool uses average annualized costs based on an assumed
lifespan of 30 years for a CsCl irradiator and 12 years for an X-ray irradiator, to calculate the
annual average costs for calculation for any lifespan. All costs in the excel tool are assumed to
have uniform distributions. However, we acknowledge that some variables’ distribution could
be non-uniform. We did not have enough information about facility-wide variations in our
variables to be confident about the distributions of each variable, so uniform distributions were
used for extra randomness.
25
RESULTS
New Purchase Analysis
Analysis of the year zero scenario for a user purchasing their first irradiator finds that in
almost all cases X-ray devices are expected be cheaper to purchase, operate, and dispose of over
their lifetimes. Table 5 provides a summary, by throughput and for each discount rate, of the
percent of model trials which found X-ray machines to have lower lifetime costs. Considering
only private costs, 98 percent of trials suggest lower lifetime costs; after including social costs,
all simulation trials show that X-ray irradiators are less expensive.
Table 5: New Purchase Analysis
Trials with Lower Private Costs of Purchasing and
Operating X-Ray Irradiator
(Percentage)
Throughput
Discount Rate 5,000 10,000 15,000 Total
3%
98
98
99
98
7%
98
98
98
98
Trials with Lower Social Costs of Purchasing
and Operating X-Ray Irradiator
(Percentage)
Throughput
5,000
10,000 15,000
Total
100
100
100
100
100
100
100
100
Figure 2 is a histogram of the distribution of the difference in annualized lifetime
operating costs between CsCl irradiators and X-ray irradiators using the three percent discount
rate. The histogram shows that from the 3,000 trials, there is a mean annual benefit of roughly
$20,000 dollars from choosing to use an X-ray irradiator. Only two percent of the trials fall to
the left of the red line, which marks no difference in costs. Similar distributions exist for the
social costs and seven percent discount rate trials.
These results confirm that the relevant analysis period is the remaining years of life for a
CsCl irradiator being considered for replacement. If private users consider the total lifecycle
costs, our results suggest that almost all users will make the decision to switch to X-ray
26
technology at the end of the current CsCl irradiator’s lifetime, instead of replacing with a new
CsCl device. There is no consideration of the RDD risk necessary to encourage the average
blood irradiator user to begin using X-ray technology. We also did not include any social cost
considerations, other than providing accessible information about total lifecycle private costs.
Figure 2: Private Benefits for X-ray over CsCl Irradiator Purchase
Private Costs Analysis of Replacement
Having determined that new purchase decisions should favor X-ray irradiators, the model
shows that private actors are also likely to benefit from replacing a CsCl irradiator with an X-ray
irradiator in the majority of cases. However, the likelihood of reductions in cost from
replacement is sensitive to the age of the irradiator. Table 6 and
27
Table 7 show that if a business currently uses a CsCl blood irradiator less than 10 years
of age, they are on average likely to be as cheap to continue to operate as they are to replace,
especially for low throughputs. At medium and high throughputs, a slight majority of users
would benefit from replacing the device with an X-ray irradiator even in the first year that the
CsCl irradiator is operated. The ambiguity in cost savings across users decreases for older
Table 6: Percentage of Trials with Positive Savings from Replacement, 3 percent
discount rate
devices. See Appendix I for full the values of the information in Table 6 and
Table 7 from every year and a comparison of social and private costs.
Private Cost Analysis
(Percentage)
Throughput
Age
1
5
10
15
20
25
30
5,000
53
52
50
55
57
68
98
10,000
52
54
58
60
65
78
100
15,000
51
59
61
78
78
88
100
Social Cost Analysis
(Percentage
Throughput
Total
52
55
56
67
67
78
99
5,000
56
61
70
86
98
100
100
10,000
56
62
75
88
97
100
100
15,000
57
67
76
90
99
100
100
Total
56
63
74
88
98
100
100
Table 7: Percentage of Trials with Positive Savings from Replacement, 7 percent discount
rate
Age
1
5
10
15
20
25
30
Private Cost Analysis
(Percentage)
Throughput
5,000 10,000 15,000
14
15
15
18
19
24
15
21
25
18
22
31
16
25
38
28
43
55
98
99
100
Total
15
20
20
24
27
42
99
Social Cost Analysis
(Percentage)
Throughput
5,000 10,000
15,000 Total
11
13
12
12
18
18
16
17
17
19
21
19
26
29
28
27
43
46
51
47
86
88
91
88
100
100
100
100
28
For low throughput, the percentage of trials showing cost savings from replacement
increases more slowly than for medium and high throughput. This suggests that high volume
users benefit more from replacement. By years 28 and 29, more than 90 percent of users,
regardless of throughput, would benefit from immediately switching to X-ray technology. If
every blood irradiator user replaced cesium chloride technology with X-ray technology, total
benefits would be significantly positive after averaging across age groups.
Figure 3: Private NPV of Switching from Cesium to X-ray
29
The benefits of replacing a cesium irradiator increase for older devices for several
reasons. One reason is that there is no longer such a large cost difference for moving up the
termination date of the irradiator. For a device that is only one year old, termination costs can be
discounted to a large degree because they do not occur for 29 years. The present value of this
amount at a three percent discount rate is only 42 percent of its nominal future cost. Replacing
this device with an X-ray irradiator means that 100 percent of this cost must be paid this year. As
termination costs are a major portion of the devices’ total lifecycle costs, this is a significant
impediment.
A second reason is that X-ray devices continue to operate at a constant cycle time over
their entire lifetime, whereas the cycle time of a cesium irradiator nearly doubles by the end of its
expected life due to radioactive decay. The model captures this operation time increase by
adjusting CsCl cycle time; the effects of this change are clear in Figure 3. Looking at the green
curve, which represents high throughput users, we can see that X-ray irradiators have
significantly lower costs in middle years. In these years, annual costs make up a significant
Figure 4: Private NPV of Switching from Cesium to X-ray
30
portion of total costs and CsCl cycle times have started to increase. For CsCl irradiators near the
end of their expected lifetime, the relative weight of annual costs diminishes, and the difference
between various throughput levels decreases as termination costs become the main component of
total costs.
Whereas Figure 3 depicts the average cost savings from choosing to replace a CsCl
irradiator, Figure 4 shows the range of estimate cost savings for each irradiator age. Every one
of the 1,000 trials conducted for each year of a CsCl irradiator’s expected life is plotted for one
level of throughput. This figure is representative of the results for 10,000 and 15,000 blood units
per year as well. Uncertainty falls considerably with age, largely because a much of the
uncertainty in the model is captured in fixed and variable costs, which lose relative weight in
later years.
Figure 5: Private Benefits for X-Ray over Irradiator Purchase, year 15
31
It’s important to consider the range of costs, as they show that an individual user’s
benefits could stray dramatically for the mean. The mean for a newer CsCl irradiator is less than
$20,000, but the range of cost savings is greater than positive or negative $500,000. Some of
these observations of cost change are considerably reasonably extreme. Figure 5 shows a
histogram of the year 15 distribution of trials; the majority of trials in this year are much closer to
the mean. The large variation in our results reflect the diversity of the users and devices we
considered, as well as the uncertainty about the values of variables. The analysis of the
percentage of devices simulated to have positive net benefits should allow observations to be
made about the United States as a whole.
Figure 6: Private NPV of Switching from Cesium to X-ray
32
As can be seen from
Table 7, using a seven percent discount rate as opposed to a three percent discount rate
significantly decreases the benefits of replacing a CsCl irradiator. This is because the higher
discount rate makes future costs have an even smaller net present value. This greatly decreases
the impact of future savings in annual costs. In addition, it incentivizes pushing CsCl disposal
into the future, as the costs borne in the present day from accelerating disposal have a much
higher present value than the costs borne in the future if delayed. Figure 6 presents the mean
difference in costs from replacements. At the much higher discount rate, replacement is only
attractive to a private actor in the final few years of a CsCl irradiator’s lifetime. While we treat a
three percent discount rate as a much more accurate number from a cost-benefit analysis
perspective, many private actors may consider a higher discount rate in their decisions, which
makes this change in output very relevant to the project.
Social Costs Analysis of Replacement
The social costs of operating CsCl irradiators provide further justification for policies to
limit their use and suggest their phased replacement. The security updates funded by the GTRI
and the disposal costs absorbed by OSRP are very large. These one-time costs decrease the
relative impact of annual costs in the replacement decision and lead to a mean benefit which
confidently increases with age. Because termination costs are a much greater concern when
social costs are included, the benefits of replacement increase more quickly as the device
approaches the end of its expected life. Figure 7 displays the rising social cost savings of
replacement.
33
Figure 8: Social NPV of Switching from Cesium to X-ray, 3 percent discount rate
Figure 7: Social NPV of Switching from Cesium to X-ray, 7 percent discount rate
34
Figure 8 shows the mean values of the simulation using the seven percent discount rate.
With this discount rate, the impact of annual costs is further reduced, while the impact of
accelerating the disposal of the CsCl irradiator is also exacerbated. Unlike the three percent
scenario for social costs, average cost savings with a seven percent discount rate do not exceed
zero until around a CsCl irradiator exceeds age 20. However, given that several of the major
costs of this analysis are born by the government (especially in the social cost analysis), a lower
discount rate is recommended.
As seen in
Table 7, the percent of trials showing social benefits of replacement increase with age in
a similar manner to the private case, although at an accelerated rate. The benefits again increase
faster for high throughput operators and slower for low throughput operators. Around year 17,
more than 90 percent of users benefit from replacement – ten years sooner than when accounting
Figure 9: Social NPV of Switching from Cesium to X-ray, range
35
only for private costs.
Figure 9 plots the 1,000 trials conducted each year using a throughput of 5,000 units per
year and can be compared to the distribution of private costs estimates in Figure 4. The range of
values for social costs is even wider in the beginning year’s operation for a CsCl irradiator.
Notably, from at least age 24 onwards, 100 percent of the trials simulated for that age have a net
present value of the benefits of replacement that is greater than zero. If it is considered
acceptable to allow 5 percent of extreme cases to have negative benefits, the year at which
replacement is fully justified is shifted even farther forward to around age 17 or 18.
RDD Risk Value
The preceding sections have largely addressed the cases in which there is a justification
for replacement of CsCl irradiators with X-ray technology regardless of the risk of RDD
diversion. Results show that there are a significant number of situations in which replacement
can be justified, including on the sole basis of user costs. An additional social consideration that
is not explicitly included in the model is the cost of a potential diversion of CsCl to use as an
RDD. However, the potential risk threshold that the model suggests would be necessary to
provide positive benefits for replacement could be compared with an estimated risk value
calculated by GTRI. Table 8 contains information that can be used for analysis at the two
thresholds mentioned in the methodology. In all cases with positive cost differences, an RDD
risk valuation is unnecessary to justify replacement. When the cost difference is less than zero,
however, an RDD risk valuation could be included to justify replacement. Our analysis
examines both the mean cost difference and lower 5 percent bound of trials as potential
thresholds GTRI may consider.
36
Private Cost Difference
(Dollars)
3 percent
7 percent
Age
1
5
10
15
20
25
30
Social Cost Difference
(Dollars)
3 percent
7 percent
Average
Lower 5%
Average
Lower 5%
Average
Lower 5%
Average
Lower 5%
15,000
23,000
27,800
35,900
39,000
36,500
27,700
(277,400)
(245,500)
(187,100)
(145,000)
(80,200)
(33,900)
7,800
(116,400)
(94,500)
(83,200)
(61,600)
(37,400)
(7,200)
25,500
(307,100)
(277,100)
(248,400)
(208,600)
(140,400)
(72,900)
6,000
42,300
77,400
120,600
183,300
238,300
297,200
363,600
(350,000)
(283,300)
(175,500)
(69,200)
41,600
152,300
254,700
(196,500) (687,000)
(238,600) (610,400)
(198,400) (544,300)
(116,800) (428,400)
(10,500) (259,400)
127,500
(38,300)
315,800
206,900
Table 8: Possible RDD Valuations Necessary for Replacement
Values from Table 8 are averaged across the tested throughputs. In general, these values
show that a three percent discount rate makes RDD risk valuation unnecessary if the desire is to
have a majority of locations benefit on average. The “Lower 5%” columns show the RDD risk
valuation necessary to ensure that at least 95 percent of all users benefitted from irradiator
replacement. These columns suggest possible year by year evaluations of sites and could be
developed into pricing mechanisms to encourage replacing irradiators. If a policy were to be
developed regardless of irradiator age, an RDD risk valuation of around $150,000 may be
necessary to ensure the majority of irradiators of any age benefit, though operators with newer
irradiators would still suffer. The seven percent discount rate presents a larger challenge. Results
from this discount rate suggest that relatively large RDD risk valuations would be necessary in
order to meet even the average costs difference across years. Lower five percent bounds were
not calculated for all irradiator ages but Appendix I provides addition information on mean,
minimum and maximum values of the cost difference.
37
LIMITATIONS
While cost-benefit analysis is a useful tool in evaluating potential policies, it has
limitations. Accurate cost-benefit analysis depends upon the quality of data used to estimate
parameters.49 In the case of our model, the quality and availability of data may have
compromised the accuracy of our estimates, and therefore, our predictions of net benefits. In
some cases, our parameters are based upon a single cost estimate provided by an operator of an
irradiator. Other assumptions are based on a GTRI survey with a small sample size. Despite
these limitations, our model may still be used as a baseline in the case that additional data is
gathered.
Second, our analysis is limited to CsCl blood irradiators used in hospitals or blood banks
to irradiate blood. We did not consider replacement of research CsCl irradiators in our analysis.
Research irradiators are used to expose different types of material to irradiation for research
purposes.50 The length of exposure times varies, differing from the exact batch time required of
blood irradiators, and the machine may not be operated as consistently as blood irradiators. The
size of the machine may also be different, depending on its research application. It is less certain
whether X-ray research irradiators are a suitable replacement for CsCl research irradiators. This
will likely require continued study as new X-ray technology becomes available.
Finally, cost-benefit analyses are inherently limited in that they only consider monetized
costs and benefits, and leave out factors such as political and technological feasibility and social
considerations. Our cost-benefit does not monetize RDD risk, which could affect the distribution
of net benefits.
38
RECOMMENDATIONS
Our results indicate that if the NNSA aims to incentivize users to replace CsCl irradiators
with X-ray irradiators, it should focus on lessening the disposal costs of CsCl irradiators. In
doing so, users would not face a large cost barrier in replacing the CsCl device with an X-ray
device. Once incentivized to switch, users would that find purchasing and operating a new X-ray
device can be cheaper in the long-run than purchasing and operating a CsCl device. Moreover,
society would experience positive net benefits if CsCl irradiators are phased out of use, as
taxpayers currently bear disposal costs. Additionally, because X-ray devices do not require
security, the social costs of the GTRI Voluntary Radiological Enhancement program could be
avoided.
Admittedly, our results are based on uncertain data, but in order to facilitate further
analysis, we recommend that GTRI compile more comprehensive statistics on the different
disposal procedures and costs to the device users. We were able to compile an overall range from
our data collection, but our research revealed a large variance in estimates with few complete
descriptions of what those costs actually entail. In addition, many users either do not know what
their actual costs are, or they fail to account for all potential costs of disposal (i.e. long-term
storage in a facility prior to disposal). GTRI recently undertook a survey of AAPM members
about irradiator usage; unfortunately, the survey respondents provided little to no information
about their disposal costs.
We also recommend that the NNSA consider the following areas for policy analysis and
exploration. First, a comprehensive review should be conducted to determine the current
security protocols among contractors, vendors, and device users for transporting CsCl devices in
39
different cities and states. This research could identify policy discrepancies and opportunities to
increase the minimum regulations. Second, the NNSA should continue to encourage the
development and certification of new shipping containers, as shipping is a major component of
disposal cost. As more shipping containers become available, the costs of shipping will
decrease, and overall CsCl disposal costs will become less prohibitive. Finally, the NNSA
should conduct additional analysis on the potential costs of subsidy or grant program alternatives
to incentivize users further to retire their CsCl device and transition to an X-ray device. The
excel tool we provide can be used to assess the likely replacement costs to specific institutions.
CONCLUSION
Upon request from GTRI, our team conducted a lifecycle analysis of the private and
social costs of replacing a CsCl blood irradiator with an X-ray blood irradiator. In order to
assess the value of replacement, we collected data on cost factors involved in the installation,
annual usage, and termination phases of the devices. Our extensive literature review and data
analysis allowed us to estimate ranges for these costs. After conducting a statistical analysis, our
findings indicate that the replacement of CsCl irradiators with X-ray blood irradiators have
positive net benefits from both a private and social perspective. The larger purchase price of a
CsCl device and its even larger disposal cost drive this result. We also find that this result is
stronger for both CsCl devices that operate with a high throughput of blood units and those
devices that are the oldest in their usage life. Our analysis does not directly analyze the risk level
of potential sealed-source material diversion to an RDD; however, it provides estimates for the
risk level necessary to justify replacement. We recommend that the NNSA pursue policies that
incentivize replacement. These policies should focus on mitigating the large termination costs
40
associated with cesium devices. However, we also feel that users should switch to X-rays
without additional incentives from the NNSA. We believe that users haven’t switched to X-rays
because they haven’t performed a full lifecycle analysis for their devices, and are therefore
ignoring the large termination costs that they will need to pay in the future. It is important that
the NNSA inform users of the lifecycle costs of their machines. With full information, users
should have a strong incentive to switch to X-rays. Incentivizing this switch is incredibly
important; even with heightened security measures, the threat of RDD diversion remains. The
NNSA must stop attempting to mitigate the risk of CsCl use; instead, they should focus on
decreasing the CsCl available for diversion. By using the results of our analysis, we believe the
NNSA will be well-equipped for that challenge.
41
ENDNOTES
1
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press.
2
Ferguson Charles, Kazi Tahseen, Perera Judith. “Commercial Radioactive Sources: Surveying
the Security Risks.” Center for Nonproliferation Studies at the Monterey Institute of
International Studies. January, 2003. Monetary, CA.
3
Ibid
4
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press.
5
United States Nuclear Regulatory Commission. “Fact Sheet on Dirty Bombs.” December 2012.
Accessed via http://www.nrc.gov/reading-rm/doc-collections/fact-sheets/fs-dirty-bombs.html
6
Cuthbertson, Abigail, Meaghan Jennison, David Martin. “Status of Global Threat Reduction
Initiative’s Activities Underway to Address Major Domestic Radiological Security
Challenges.” National Nuclear Security Administration: WM2012 Conference. February 26 –
March 1, 2012. Phoenix, AZ. Accessed via:
http://www.wmsym.org/archives/2012/papers/12105.pdf &
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press.
Ferguson Charles, Kazi Tahseen, Perera Judith. “Commercial Radioactive Sources: Surveying
the Security Risks.” Center for Nonproliferation Studies at the Monterey Institute of
International Studies. January, 2003. Monetary, CA.
7
8
United States Environmental Protection Agency. “Sealed Radioactive Sources.” Last updated
on June 12, 2013. Accessed via: http://www.epa.gov/radiation/source-reductionmanagement/sources.html
9
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press. &
John P. Jankovich. “Overview of the U.S. Nuclear Regulatory Commission’s Initiatives on the
Use of Cesium-137 Chloride Sources.” U.S. Nuclear Regulatory Commission. March 2011.
42
Accessed via: http://www.nrc.gov/public-involve/conferencesymposia/ric/past/2011/docs/abstracts/jankovichj-h.pdf
10
Borchardt, R.W. “Strategy for the Security and Use of Cesium-137 Chloride Sources.”
ACMUI CsCl Irradiator Subcommittee. November 24, 2008. Accessed via:
http://hps.org/govtrelations/documents/nrc_cscl-options_secy08-0184.pdf
11
Ibid.
12
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press.
13
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press
Van Tule, Gregory J.; Strub, Tiffany L.; O’Brien, Harold A.; Mason, Caroline F.V.; and
Gitomer, Steven J. Reducing RDD Concerns Related to Large Radiological Source Applications
(September 2003). Accessed via : http://www.hsdl.org/?view&did=441986
14
15
Mintz Paul. “Cesium Cessation? An Advantage of Pathogen Reduction Treatment”.
Transfusion. 2011;51;p.1369-1376.
16
The Royal Children’ Hospital Melbourne. “Irradiation of Blood Products.” Last updated
December 12, 2012. Accessed via:
http://www.rch.org.au/bloodtrans/about_blood_products/Irradiation_of_blood_products/
17
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press
18
Ibid.
19
Ferguson Charles, Kazi Tahseen, Perera Judith. “Commercial Radioactive Sources:
Surveying the Security Risks.” Center for Nonproliferation Studies at the Monterey Institute of
International Studies. January, 2003. Monetary, CA.
20
Ibid.
21
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press.
43
22
Yong PL, Saunders RS, Olsen LA. Prices That Are Too High. The Healthcare Imperative:
Lowering Costs and Improving Outcomes: Workshop Series Summary. Institute of Medicine
(US) Roundtable on Evidence-Based Medicine. Washington (DC): National Academies Press
(US); 2010. 5, Accessed via: http://www.ncbi.nlm.nih.gov/books/NBK53933/
23
U.S. Government Accountability Office. 2012. Nuclear Nonproliferation: Additional Actions
Needed to Improve Security of Radiological Sources at U.S. Medical Facilities. Accessed via:
http://www.gao.gov/assets/650/647931.pdf
24
Kirk, Randal. Interview with Connell, Leonard. Personal Interview. November 26, 2013.
25
U.S. Government Accountability Office. 2012. Nuclear Nonproliferation: Additional Actions
Needed to Improve Security of Radiological Sources at U.S. Medical Facilities. Accessed via:
http://www.gao.gov/assets/650/647931.pdf
26
Ibid
27
Ibid
28
10 CFR Part 170. 2013 ed. & 10 CFR Part 171. 2013 ed.
29
Ibid
30
Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2012
Edition. Accessed via: http://www.bls.gov/oes/current/naics4_622100.htm
31
Ibid
32
Bianco, Celso, Ruth Sylvester. 2008. Presentation on Blood Irradiators in ABC Member
Centers. Washington, DC: America’s Blood Centers. Accessed via:
http://pbadupws.nrc.gov/docs/ML0827/ML082770671.pdf
33
“Nuclear Regulatory Commission Public Meeting on Cesium Chloride Uses, Including Blood
Irradiators” AABB. Accessed via:
http://www.aabb.org/events/government/public/Pages/nrcmeeting092908.aspx
34
Ibid &
Bianco, Celso, Ruth Sylvester. 2008. Presentation on Blood Irradiators in ABC Member Centers.
Washington, DC: America’s Blood Centers. Accessed via:
http://pbadupws.nrc.gov/docs/ML0827/ML082770671.pdf &
ICF Incorporated, LLC. 2009. Cost-Benefit Analysis for Potential Alternative Technologies for
Category 1 and 2 Radiation Sources. Rockville, MD: U.S. NRC.
44
35
ICF Incorporated, LLC. 2009. Cost-Benefit Analysis for Potential Alternative Technologies
for Category 1 and 2 Radiation Sources. Rockville, MD: U.S. NRC. &
“Nuclear Regulatory Commission Public Meeting on Cesium Chloride Uses, Including Blood
Irradiators” AABB. Accessed via:
http://www.aabb.org/events/government/public/Pages/nrcmeeting092908.aspx
36
Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2012
Edition. Accessed via: http://www.bls.gov/oes/current/naics4_622100.htm
37
Best Theratronics. 2013. Gammacell 1000 Elite / 3000 Elan. Accessed via:
http://www.theratronics.ca/PDFs/BT_MBTS_8005_GC1000E_3000E_3_V112013_webSECUR
E.pdf &
Kirk, Randal. Interview with Connell, Leonard. Personal Interview. November 26, 2013.
38
Ibid
39
Best Theratronics. 2013. Gammacell 1000 Elite / 3000 Elan. Accessed via:
http://www.theratronics.ca/PDFs/BT_MBTS_8005_GC1000E_3000E_3_V112013_webSECUR
E.pdf
40
Kirk, Randal. Interview with Connell, Leonard. Personal Interview. November 26, 2013.
41
“FAQ’s – Blood Irradiation,” Rad Source, accessed November 29, 2013.
http://www.radsource.com/library/blood_irradiation/4/
42
Kirk, Randal. Interview with Connell, Leonard. Personal Interview. November 26, 2013.
43
In terms of hazard, Class A LLW is intended to be safe after 100 years, Class B after 300
years, and Class C after 500 years. These LLWs are typically disposed of in shallow land burial
sites; however, because of its high hazard, GTCC waste is not typically disposed of in shallow
land burial sites or commingled with Class A, B, and C LLW.
(http://www.state.nv.us/nucwaste/gtcc/gtcc.htm)
44
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press.
45
(Policy Statement of the U.S. Nuclear Regulatory Commission on the Protection of Cesium137 Chloride Sources, July 2011). And News report - winter of 2012 by the Office of Federal
and State Materials and Environmental Management Programs,
46
The packages previously used for disposal and decommissioning had certificates that expired
in 2008. Specific manufacturers, i.e. Best Theratronics, may have their own packages to use for
45
transport, but they do not have any incentive to create a general-purpose package usable by noncustomers.
47
Boardman, Anthony E., David H. Greenberg, Aidan R. Vining, and David L. Weimer. 2010.
Cost-Benefit Analysis. 4th ed. Boston, MA: Prentice Hall.
48
“Circular A-4.” Office of Management and Budget. September 17, 2003. Accessed via:
http://www.whitehouse.gov/omb/circulars_a004_a-4
49
Boardman, Anthony E., David H. Greenberg, Aidan R. Vining, and David L. Weimer. 2010. &
Cost-Benefit Analysis. 4th ed. Boston, MA: Prentice Hall.
50
National Research Council, Committee on Radiation Source Use and Replacement. 2008.
Radiation Source Use and Replacement: Abbreviated Version. Washington, DC: National
Academies Press.
46
Appendices
APPENDIX A: IRRADIATOR TYPES AND CONFIGURATIONS
Diagrams (A) a configuration of a gamma irradiator using cesium-137 and (B) a configuration of
a linac irradiator. The plastic bolus is a container that enhances the dose uniformity in the
irradiation configuration shown.
Source:
Committee on Radiation Source Use and Replacement, National Research Council, Radiation
Source Use and Replacement (2008). Accessed via: http://www.nap.edu/catalog/11976.html
47
APPENDIX B: LIFECYCLE OF SEALED SOURCES, ACCORDING TO THE EPA
Source:
Sealed Radioactive Sources, United States Environmental Protection Agency, accessed October
16, 2013, http://www.epa.gov/radiation/source-reduction-management/
48
APPENDIX C: OSRP T OTAL SEALED SOURCED BACKLOG
GTRI/OSRP Registered Sealed Sources – Percent of Total Backlog and Number of Sources by
Curies
This chart does not differentiate between cesium-chloride blood irradiators and other sources;
however, analysis indicates that the backlogged CsCl irradiators are within the 1000 – 10000 Ci
distribution. There are currently 67 CsCl irradiators on OSRP’s backlog.
Source:
STATUS of GTRI’s Activities underway to address major domestic Radiological Security
challenges (Mar 2012). Accessed via: https://www.wmsym.org/archives/2012/papers/12105.pdf
49
APPENDIX D: GAMMACELL 1000 ELITE/3000 ELAN
50
Source:
Best Theratronics. 2013. Gammacell 1000 Elite / 3000 Elan. Accessed via:
http://www.theratronics.ca/PDFs/BT_MBTS_8005_GC1000E_3000E_3_V112013_webSECUR
E.pdf
51
APPENDIX E: RAD SOURCE 3400 REVOLUTION
Technical Specifications and Costs:
52
Product Description:
53
Sources:
Kirk, Randal. Interview with Connell, Leonard. Personal Interview. November 26, 2013.
“Blood Irradiation,” Rad Source, accessed November 29, 2013.
http://www.radsource.com/applications/blood_irradiation
54
APPENDIX F: TECHNOLOGICAL CHANGE
If a future study decides to include technological change, the change in cost can be
estimated with equations provided. In the first equation, KS is knowledge stock, CUM is
cumulative experience, C0 is initial cost, CCUM is cumulative cost, and m and n are functions of
the progress ratios:
(1) CCUM = C0 CUMm KSn
The values m and n are estimated by the learning-by-doing and learning-by-searching progress
ratios. The progress ratios take on a percentage value and measure the rate of improvement in a
certain technology. Most technologies have a progress ratio distributed around 80 percent. The
learning-by-searching progress ratio represents the unitary cost decrease if research and
development from knowledge stock doubles.
(2) PRLBD = 2m
(3) PRLBS = 2n
Current knowledge stock (KSt) can be calculated using knowledge stock from the previous year
(KSt-1), current research and development expenditures (RDt-x) where t is current year and x is
time lag of adding RD to current knowledge stock, and the annual depreciation rate ().
(4) KSt = (1-)KSt-1 + RDt-x
This outlines the four equations needed to account for the technological change that could
improve x-ray blood irradiators (Van Stark et al). If nuclear-source irradiators are phased out, the
incentives for better x-ray irradiators could increase the investment in research and development
and speed the pace of technological change.
55
Sources:
Van Stark et al. “Chapter 2: General aspects and caveats of experience curve analysis.” In
Technological Improvement. 2009.
“FAQ’s – Blood Irradiation,” Rad Source, accessed November 29, 2013.
http://www.radsource.com/library/blood_irradiation/4/
56
APPENDIX G: COST ESTIMATES
Please refer to the Methodology section for information on how this data was obtained.
Installation Costs
Component
(Unit)
Cesium Irradiator Purchase Price:
(Total Dollars)
X-Ray Purchase Price:
(Total Dollars)
Cesium Site Preparation:
(Total Dollars)
X-Ray Site Preparation:
(Total Dollars)
Cesium Initial Legal/Licensing/RSO/Public
Health Costs:
(Total Dollars)
X-Ray Initial Legal/Licensing/RSO/Public
Health Time Costs:
(Total Dollars)
Cesium Initial Fingerprinting/Background
Check Costs:
(Total Dollars)
Cesium
Installation/Setup/Commissioning/Shielding
Design Considerations:
(Total Dollars)
Cesium Transportation of Device:
(Total Dollars)
X-Ray Transportation of Device:
(Total Dollars)
Cesium Import Permit- Cesium Only
(Total Dollars)
Cesium Global Threat Reduction Initiative
Security Equipment/Installation:
(Total Dollars)
57
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
160,000
325,000
242,500
160,000
240,000
220,000
5,000
10,000
75,000
0
50,000
18,600
4,000
20,000
15,400
2,000
3,000
2,500
2,000
5,000
3,800
30,000
38,000
34,000
3,000
50,000
28,800
0
2,600
2,000
7,000
7,000
7,000
317,800
500,000
404,800
Fixed Costs
Component
(Unit)
Cesium Security Infrastructure Maintenance:
(Annual Total Dollars)
Cesium Security Background Check:
(Annual Total Dollars)
Cesium Anticipated Security Ongoing Costs:
(Annual Total Dollars)
Cesium Service Contract/ Warranty:
(Annual Total Dollars)
X-Ray Service Contract/ Warranty:
(Annual Total Dollars)
X-Ray Year 7 Power Supply Upgrade:
(Total Dollars)
X-Ray Year 10 Power Supply Upgrade:
(Total Dollars)
Cesium Regulation Personnel:
(Annual Salaries in Dollars)
Cesium Regulation Licensing:
(Annual Total Dollars)
X-Ray Regulation Licensing:
(Annual Total Dollars)
Nuclear Regulatory Commission Costs Not
Covered by Licensing:
(Annual Total Dollars)
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
1,000
8,600
4,900
2,400
2,400
2,400
4,000
7,500
5,800
1,000
14,000
6,000
2,000
17,000
8,500
5,000
5,000
5,000
10,000
10,000
10,000
57,500
57,500
57,500
650
8,700
4,700
3,000
8,700
5,900
4,600
4,600
4,600
Variable Costs
Component
(Unit)
Cesium Blood Units Per Site Per Day:
(Average Daily Blood Units Irradiated)
X-Ray Blood Units Per Site Per Day:
(Average Daily Blood Units Irradiated)
Cesium Blood Units Per Batch:
(Average Blood Units Irradiated Per Run)
X-Ray Blood Units Per Batch:
(Average Blood Units Irradiated Per Run)
(Continued on Next Page)
58
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
0
50
25
0
50
25
1
4
2.5
5
5
5
----------------
---------------
--------------
Cesium Wage of Technician/Operator:
(Hourly Wage in Dollars)
X-Ray Wage of Technician/Operator:
(Hourly Wage in Dollars)
Cesium Irradiation Time Per Batch:
(Run Time in Minutes Per Batch)
X-Ray Irradiation Time Per Batch:
(Run Time in Minutes Per Batch)
Price of Electricity:
(Dollars Per Kilowatt Hours)
Cesium Kilowatts of Electricity Consumed:
(Kilowatts Consumed Per Minute of Run-Time)
X-Ray Kilowatts of Electricity Consumed:
(Kilowatts Consumed Per Minute of Run-Time)
X-Ray Parts Replacement:
(Average Annual Dollars)
Cesium Costs of Downtime:
(Average Annual Dollars)
X-Ray Costs of Downtime:
(Average Annual Dollars)
27
37
29
27
37
29
1.7
8.6
5
5
5
5
0.076
0.1647
.1081
0.3
0.3
0.3
2
2
2
10,000
10,000
10,000
2,300
2,300
2,300
4,000
4,000
4,000
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
75,000
150,000
---------------
0
2,600
1,300
15,000
40,000
---------------
0
190,000
---------------
75,000
920,000
---------------
Termination Costs
Component
(Unit)
Cesium Physical Costs of Disposal:
(Total Dollars)
X-Ray Physical Costs of Disposal:
(Total Dollars)
Cesium Site to Vendor Disposal Fee:
(Total Dollars)
Cesium Site to Off-Site Recovery Project
Disposal Fee:
(Total Dollars)
Off-Site Recovery Project Costs Not Covered by
Fees:
(Total Dollars)
Source: Author
59
APPENDIX H: MONTE CARLO I NSTRUCTION S HEET
Monte Carlo Instructions Sheet
The attached spreadsheet (which is publicly accessible at
https://dl.dropboxusercontent.com/u/4188829/Excel%20Monte%20Carlo%20Tool.xlsx) is a
financial tool for preliminary analysis of switching from a CsCl to X-Ray irradiator for a single
facility. The tool provides estimated values of costs for comparison purposes. It will execute
5000 random trials of the cost estimates for switching from CsCl to X-Ray technologies. This
tool uses average annual costs based on an assumed lifespan of 30 years for a CsCl irradiator and
12 years for an X-Ray irradiator to calculate the annual average costs for any current CsCl
lifespan. Although we acknowledge that some variables’ distribution could be non-uniform, all
randomly generated variables are calculated using uniform distribution due to lack of reliable
data estimates.
Instructions
1. Enable Manual Calculation Settings in Excel: For the tool to function properly, Excel
must be in the “manual calculations” setting. This prevents the random number variables
from constantly generating new numbers when anything is changed in the document. The
excel sheet should be set to this when opened. However, if other excel documents were
open prior to opening the tool that were set to automatic (the default excel setting), the
tool will also be set to automatic. The following are steps in setting the calculation method
to manual. This will become important after entering your cost estimates.
60
o Windows: Left click the “tools” tab for Excel 2007 or “file” tab for Excel 2013.
Under “tools or file”, left click the “options” tab. This will open a new menu of
options. Left click the “calculation” tab in the “options” menu. Left click and
select “manual calculations”.
o Mac: Left click the “Excel” tab. Under “Excel” tab, left click “preferences” tab.
This will open the “preferences” menu. Left click the “calculations” icon under the
“preferences” menu. Select “manual calculation”.
2. Enter cost estimations under the fixed and variable inputs cells. Detailed explanations of
the cost categories are included as an appendix to this document.
3. To generate a new set of estimated random trials once all inputs are entered, press:
o Windows- F9 key
o Mac- “Command” + “=” keys
4. The results are displayed automatically in the results section. Results include the mean
value, median value, standard deviation, maximum value, and minimum value of the
random trials for each technology.
o Because the technologies have different timespans, a conversion method is
employed for comparison purposes. The mean estimates are converted into a
yearly annual average costs that is equivalent to the net present value of total costs
for the selected lifespan. Thus, the annual values shown allow for comparison of
the two technologies.
61
Input Category Definitions
Monte Carlo models are used to deal with uncertainty. If exact data is unknown for some inputs,
use your best estimates.
Fixed Inputs

X-Ray/CsCl Irradiator Purchase Price- Total purchase price.

Value of Grant(s)/Awards- The value of any grants or award for purchasing a device or
upgrading facilities, this is for single year grants only.

Discount Rate- The rate at which the value of capital diminishes annually.

Staff Salary Costs- The annual total salary of all staff that directly draw their salary from
the operation of an irradiator.

Cost of Blood Purchase of Contracting Out- The price paid for blood from outside
sources or from contracting out irradiation services, when the irradiator is inoperable. If
your facility has capacity to handle irradiation with another device, put the value as 0.

Operator or Technician Hourly Wage- The hourly wage rate of irradiator operators or
technician, used to calculate the opportunity cost of staff time.
Variable Inputs

Estimated Costs of Device Installation- This includes all transportation, construction,
calibration, installation, importation fees, and any other costs associated with installing a
device.

Number of Blood Units Irradiated Annually- The total output of blood units irradiated
annually.
62

Estimated Irradiation Time- Average time taken to irradiate a single load.

Price of Water- Price per gallon of water in dollars.

Price of Electricity- Price per kilowatt-hour in dollars.

Annual Electric Usage- Total number of kilowatt-hours consumed by device.

Annual Water Usage- Total number of gallons consumed by device.

Estimated Cost of NRC security compliance- Annual costs of complying with Nuclear
Regulatory Commission’s increased security policies regarding CsCl irradiator security.

Maintenance Costs- Annual Costs for labor and parts for maintenance and repair of
irradiators.

Annual Days Inoperable- Annual number of days an irradiator was inoperable for any
reason (disrepair, calibration, etc.).

Permitting and Licensing- Annual average costs of obtaining permits, licenses, and
regulatory fees necessary to operate an irradiator.

Removal and Disposal- This includes all transportation, construction, calibration,
installation, importation fee, and any other costs associated with removing and disposing
of a device.

Miscellaneous expenses- All other expenses not included in the above categories or can
be used to adjust total cost estimates.

Global Threat Reduction Initiative Security and Equipment per Device - Costs to Global
Threat Reduction Initiative Security and Equipment in providing security and equipment
for Cesium use.
63

Nuclear Regulatory Commission Costs Not Covered by Licensing per Device - Costs to
the Nuclear Regulatory Commission Costs not covered by the operators’ permits and
licensing.

Off-Site Source Recovery Project Costs-Annual social costs of irradiator disposal by the
Off-Site Source Recovery Project.

Cesium Selected Lifespan- Selected number of lifespan years for use of a Cesium
irradiator.

X-Ray Selected Lifespan- Selected number of lifespan years for use of a X-Ray
irradiator.
Input Estimates
If exact data is unknown for some inputs, we have also provided estimates for inputs.
Fixed Inputs
Component
(Unit)
Cesium Irradiator Purchase Price:
(Total Dollars)
X-Ray Irradiator Purchase Price:
(Total Dollars)
Value of Grant(s)/Awards:
(Total Dollars)
Discount Rate:
(Annual Percent)
Staff Salary Costs:
(Total Salaries in Dollars)
Cost of Contracting Out for Irradiated Blood:
(Cost Per Blood Unit Purchased in Dollars)
Operator/Technician Wage:
(Dollars Per Hour)
64
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
160,000
325,000
242,500
160,000
240,000
220,000
Site Specific
Site Specific
Site Specific
3
10
4
Site Specific
Site Specific
Site Specific
25
50
25
27
37
29
Variable Inputs
Low Range
Price
Estimate
High Range
Price
Estimate
Point Price
Estimate
51,000
130,000
90,500
2,000
55,600
23,000
Site Specific
Site Specific
Site Specific
Site Specific
Site Specific
Site Specific
1.7
8.6
5
5
5
5
.00133
.0114
.00272
.076
.1647
.1081
Cesium Annual Electricity Usage:
(Average Annual Kilowatt Hours Consumed)
Site Specific
Site Specific
Site Specific
X-Ray Annual Electricity Usage:
(Average Annual Kilowatt Hours Consumed)
Site Specific
Site Specific
Site Specific
X-Ray Annual Water Usage:
(Average Annual Gallons Consumed)
Site Specific
Site Specific
Site Specific
Estimated Cost of NRC Security Compliance:
(Average Annual Dollars)
7,350
18,450
12,900
1,000
14,000
6,000
23,400
23,400
23,400
5
5
5
15
15
15
Component
(Unit)
Cesium Estimated Costs of Device
Installation:
(Total Dollars)
X-Ray Estimated Costs of Device Installation:
(Total Dollars)
Cesium Number of Blood Units Irradiated :
(Average Annual Units of Blood Irradiated)
X-Ray Number of Blood Units Irradiated :
(Average Annual Units of Blood Irradiated)
Cesium Irradiation Time:
(Minutes Needed Per Batch)
X-Ray Irradiation Time:
(Minutes Needed Per Batch)
Price of Water:
(Dollars Per Gallon)
Price of Electricity:
(Dollars Per Kilowatt Hour)
Cesium Maintenance Costs:
(Average Annual Costs)
X-Ray Maintenance Costs:
(Average Annual Costs)
Cesium Days Inoperable:
(Average Annual Days Down)
X-Ray Days Inoperable:
(Average Annual Days Down)
65
Cesium Permitting and Licensing Costs:
(Average Annual Dollars)
X-Ray Permitting and Licensing Costs:
(Average Annual Dollars)
Cesium Removal and Disposal Costs:
(Total Dollars)
X-Ray Removal and Disposal Costs:
(Total Dollars)
Miscellaneous Expenses:
(Average Annual Dollars)
650
8,700
4,675
3,000
8,700
5,850
90,000
380,000
Unknown
0
2,600
Unknown
Site Specific
Site Specific
Site Specific
Global Threat Reduction Initiative Security
and Equipment:
(Average Annual Dollars)
317,800
500,000
404,800
Nuclear Regulatory Commission Costs Not
Covered by Licensing:
(Average Annual Dollars)
Unknown
Unknown
1600
Off-Site Source Recovery Project Costs:
(Total Dollars)
7,000
920,000
Unknown
Source: Author
66
APPENDIX I: OUTPUT TABLES
Percent of Trials with Positive Private Benefits to Replacement at 7%
(Based on Throughput)
CsCl Age 5,000 Blood Units 10,000 Blood Units 15,000 Blood Units
(Year)
(Percentage)
(Percentage)
(Percentage)
1
14
15
15
2
14
16
20
3
17
18
19
4
17
17
19
5
18
19
24
6
15
19
19
7
15
19
23
8
14
20
24
9
15
21
24
10
15
21
25
11
18
22
30
12
16
20
28
13
16
23
29
14
19
27
31
15
18
22
31
16
21
26
34
17
20
29
39
18
21
27
34
19
18
26
38
20
16
25
38
21
19
31
39
22
19
28
44
23
20
33
45
24
20
35
53
25
28
43
55
26
34
46
59
27
37
54
70
28
50
67
79
29
72
85
93
30
98
99
100
67
Percent of Trials with Positive Social Benefits to Replacement at 7%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5,000 Blood Units
(Percentage)
11
14
15
13
18
17
17
16
18
17
19
20
20
22
26
31
31
31
35
43
49
53
61
71
86
94
99
100
100
100
10,000 Blood Units
(Percentage)
13
13
16
13
18
17
18
21
19
19
23
21
24
27
29
32
34
34
44
46
52
57
67
78
88
95
100
100
100
100
68
15,000 Blood Units
(Percentage)
12
16
18
15
16
16
16
19
20
21
24
25
27
29
28
35
39
39
45
51
56
65
73
79
91
96
100
100
100
100
Difference between Social and Private Benefits' Replacement Rates at 7%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5,000 Blood Units
(Percentage)
(4)
(1)
(3)
(4)
0
2
2
3
3
2
1
4
4
3
8
10
11
10
17
27
30
34
40
51
58
61
62
50
28
2
10,000 Blood Units
(Percentage)
(2)
(4)
(2)
(4)
(1)
(2)
(1)
2
(1)
(2)
0
2
1
1
7
6
5
7
18
21
21
30
34
43
45
49
46
33
15
1
69
15,000 Blood Units
(Percentage)
(3)
(4)
(1)
(4)
(7)
(3)
(7)
(5)
(4)
(4)
(6)
(3)
(2)
(2)
(3)
0
0
5
6
12
16
21
28
26
36
38
30
21
7
0
Percent of Trials with Positive Private Benefits to Replacement at 3%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5,000 Blood Units
(Percentage)
53
52
49
52
52
52
48
54
50
50
53
54
59
56
55
58
62
58
54
57
59
59
65
65
68
71
77
83
94
98
10,000 Blood Units
(Percentage)
52
50
54
53
54
56
55
60
56
58
57
59
62
60
60
62
66
63
66
65
68
73
75
77
78
81
87
92
98
100
70
15,000 Blood Units
(Percentage)
51
52
53
57
59
56
60
62
66
61
61
65
70
65
65
69
68
71
77
78
80
82
85
85
88
90
94
96
99
100
Percent of Trials with Positive Social Benefits to Replacement at 3%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5,000 Blood Units
(Percentage)
56
55
58
59
61
61
64
69
69
70
72
78
82
83
86
88
91
92
96
98
99
100
100
100
100
100
100
100
100
100
10,000 Blood Units
(Percentage)
56
57
58
61
62
65
68
73
72
75
75
80
83
85
88
88
93
94
97
97
99
100
100
100
100
100
100
100
100
100
71
15,000 Blood Units
(Percentage)
57
58
60
63
67
64
68
75
75
76
79
84
88
86
90
90
93
95
98
99
99
100
100
100
100
100
100
100
100
100
Difference between Social and Private Benefits' Replacement Rates at 3%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5,000 Blood Units
(Percentage)
3
4
9
8
9
9
17
15
19
19
20
24
23
27
31
30
30
35
42
41
40
41
35
35
32
29
23
17
6
2
10,000 Blood Units
(Percentage)
4
7
5
8
8
8
12
14
16
18
18
21
20
25
28
27
27
30
31
33
31
27
25
23
22
19
13
8
3
0
72
15,000 Blood Units
(Percentage)
6
6
8
6
8
8
8
13
10
15
18
19
18
21
25
21
25
24
21
20
19
18
16
15
12
10
6
4
1
0
Private Costs of Replacement at 7%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Mean Cost
(Dollars)
(116,400)
(115,800)
(107,400)
(107,300)
(94,500)
(104,000)
(94,200)
(93,800)
(86,700)
(83,200)
(70,900)
(74,800)
(73,100)
(63,900)
(61,600)
(52,600)
(45,800)
(48,700)
(39,800)
(37,400)
(31,600)
(26,800)
(20,000)
(15,400)
(7,200)
(1,100)
4,600
11,300
18,000
25,500
Maximum Cost
(Dollars)
381,300
269,400
318,300
318,600
366,800
260,400
309,400
315,200
296,900
310,800
301,700
389,100
248,600
274,200
267,400
275,200
249,200
251,700
243,800
204,400
223,400
189,500
195,700
180,900
149,300
142,200
136,800
107,800
78,500
70,900
73
Minimum Cost
(Dollars)
(574,500)
(467,600)
(479,700)
(549,800)
(544,600)
(447,500)
(447,900)
(456,800)
(506,300)
(490,400)
(396,900)
(370,000)
(402,900)
(408,500)
(331,100)
(340,100)
(317,700)
(325,900)
(267,200)
(238,300)
(216,300)
(194,700)
(175,200)
(155,700)
(144,200)
(126,800)
(90,800)
(73,400)
(35,600)
(10,900)
Lower 5% Bound
(Dollars)
(307,100)
(277,100)
(248,400)
(208,600)
(140,400)
(72,900)
6,000
Social Costs of Replacement at 7%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Mean Cost
(Dollars)
(296,500)
(287,700)
(265,900)
(269,200)
(238,600)
(248,000)
(236,300)
(216,700)
(210,900)
(198,400)
(175,100)
(168,600)
(154,100)
(132,400)
(116,800)
(92,700)
(70,800)
(63,700)
(33,600)
(10,500)
11,900
36,300
61,400
88,300
127,500
158,800
193,400
232,100
272,500
315,800
Maximum Cost
(Dollars)
515,500
427,600
525,100
552,200
484,100
464,500
552,400
498,700
449,500
451,000
455,300
530,300
605,200
583,500
451,600
523,000
548,800
553,700
515,100
544,400
518,100
461,400
486,300
500,200
506,000
504,800
495,400
495,400
510,800
529,700
74
Minimum Cost
(Dollars)
(1,013,200)
(952,600)
(951,000)
(934,800)
(876,500)
(871,000)
(878,100)
(796,500)
(809,800)
(736,700)
(747,400)
(698,500)
(735,700)
(684,300)
(656,800)
(616,800)
(564,100)
(587,100)
(507,100)
(426,700)
(398,600)
(359,900)
(298,500)
(262,200)
(170,400)
(118,300)
(42,600)
14,600
99,200
153,300
Lower 5% Bound
(Dollars)
(687,000)
(610,400)
(544,300)
(428,400)
(259,400)
(38,300)
206,900
Private Costs of Replacement at 3%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Mean Cost
(Dollars)
15,000
10,800
13,200
21,800
23,000
18,500
20,500
33,500
31,000
27,800
30,000
33,900
47,300
37,100
35,900
39,400
42,600
37,800
37,300
38,700
38,700
39,700
42,700
38,200
36,500
35,100
33,600
32,300
30,200
27,700
Maximum Cost
(Dollars)
638,600
796,400
665,100
743,200
607,100
676,500
637,500
489,300
482,100
575,700
595,900
489,800
551,800
442,400
486,500
518,300
458,900
445,000
381,100
329,000
333,700
274,900
276,500
223,000
218,500
192,700
171,000
137,100
101,900
70,100
Minimum Cost
(Dollars)
(585,300)
(529,000)
(516,000)
(537,000)
(548,700)
(572,200)
(448,800)
(380,700)
(380,600)
(434,300)
(414,100)
(343,600)
(325,800)
(317,400)
(312,800)
(307,600)
(267,400)
(298,600)
(164,500)
(183,200)
(152,300)
(134,900)
(107,500)
(119,600)
(92,300)
(71,100)
(63,100)
(32,000)
(23,900)
(6,200)
75
Lower 5% Bound
(Dollars)
(277,400)
(245,500)
(187,100)
(145,000)
(80,200)
(33,900)
7,800
Social Costs of Replacement at 3%
(Based on Throughput)
CsCl Age
(Year)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Mean Cost
(Dollars)
42,300
46,800
56,300
72,100
77,400
80,400
91,600
116,900
118,600
120,600
133,100
145,200
174,700
172,800
183,300
192,700
203,500
214,400
224,100
238,300
248,000
260,900
275,400
286,400
297,200
310,700
323,700
339,000
350,000
363,600
Maximum Cost
(Dollars)
949,000
859,500
795,900
936,900
833,600
876,700
925,900
774,000
742,900
792,900
869,300
817,600
869,100
725,700
744,000
851,300
744,400
694,100
788,300
650,500
679,000
648,800
626,300
606,100
583,400
578,000
573,400
582,800
547,500
540,500
Minimum Cost
(Dollars)
(673,300)
(642,300)
(760,400)
(812,900)
(636,900)
(644,800)
(537,900)
(424,700)
(426,300)
(430,600)
(414,400)
(414,700)
(407,900)
(347,100)
(366,300)
(323,200)
(280,100)
(300,600)
(129,500)
(93,800)
(75,300)
(69,700)
(15,200)
(26,700)
33,700
83,800
117,300
152,800
191,200
205,900
76
Lower 5% Bound
(Dollars)
(350,000)
(283,300)
(176,500)
(69,200)
41,600
152,300
254,700
APPENDIX J: STATA CODE
clear all
capture log close
set more off
*set trace on
cd u:\CBA //comment this out if not on Kyle's WinStat account
*Saving for Allison's simulations, change path if other user
*log using \\tsclient\Macint1\Users\allison\Documents\data_analysis_log.log, replace
/*
Monte Carlo Simulation - 1000 trials for each age of irradiator
1) Compares the expected lifetime costs of a new CsCl blood irradiator
vs. a new X-ray irradiator.
2) Compares operating a given age irradiator to replacing that irradiator
in the current year with an X-ray irradiator.
Previous versions:
Ver N7K
Ver N10K Ver N13A Ver N13K Ver N14A Ver N19A
Ver N21 Kyle
Edit: Redo of debugging
Edit: Commenting
77
Edit: Significant changes to calculations of life cycle costs
Add: filter cost and power source cost in X_AVC
(only life cycle cost calc, not year of replacement)
Ver N22 Kyle & Allison
Drop: Future replacement year calculation loop
Edit: Simplify
Edit: In process of updating replacement analysis
Ver N25
Add: Social Cost Calculations
Change: Spoke with Weimer. Intend to run 1000 trials at each irradiator
age instead of having randomly generated ages.
To do:
Carry over changes to life cycle cost into immediate replacement loop
UPDATE variable values!
*/
/* New Irradiator Analysis
1) Variable Initializations
2) Private and Social costs calculations for Installation, Annual
Fixed, Annual Variable and Termination
3) Comparision of cesium and X-ray
78
4) Saves initial 1000 observations to dataset
*/
set obs 3000
/*
Beginning of Variable Declarations
*/
gen discountRate = 0.03
gen highDiscountRate = 0.07
gen CS_GTRI_upgradeYear = round(8*runiform()) // assumes upgrades w/in 8 yrs
gen CS_GTRI_upgradeCost = (250000 + 250000*runiform()) ///
/ (1+d) ^ CS_GTRI_upgradeYear // Mean value of 375000
/*
Binary variables for the replacement choices at various points.
These variables will be essential to our analysis.
Declared up here mainly for transparency.
*/
gen replace_withX = 0
gen replace_withX_soc = 0
/*
User characteristics
Analysis generally pertains to hospitals and blood centers.
79
Large users are likely to have lower operating costs. */
gen largeCenterPercent = .45 // 33% sites have 2+ sealed sources, addl sites may have other
controlled devices
gen centerSize = 0 //small=0 large=1
replace centerSize = 1 if runiform() < largeCenterPercent
drop largeCenterPercent
gen throughput = 5000 // tests three levels of throughput
replace throughput = 10000 in 1001/2000
replace throughput = 15000 in 2001/3000
gen ComplianceSalary = 50000 + 50000*runiform() // often RSO, or Med Physicist
gen CompExtraHours = 50*(2+8*runiform()) // 2-10hrs/wk @ small; 1-6 @ large
replace CompExtraHours = 50*(1+5*runiform()) if centerSize == 1
gen compLabor = ComplianceSalary*CompExtraHours/50/40
gen medTechWage = 27.15 + 4*(runiform()+runiform())/2 //national average is 29.15
gen costElectric = rnormal(10.81, 1.2) // kwh; roughly [7.6,16.47]
gen costWater = rnormal(0.00272,0.00045)
* per gal; roughly [.0015,.0040]
gen costBlood = 25
/*
Irradiator characteristics
*/
gen CS_age = 0
80
gen CS_purPrice = 207000 + 165000*((runiform() + runiform())/2)
gen CS_expLife = 30
gen CS_loadTime = 2.3 + 2*runiform() // Yr 1 range: [2.3,4.3] Yr30: [4.6,8.6]
gen addlTimePYr = CS_loadTime/30 // linear approximation of time increase/half-life
gen CS_loadSize = 2 + round(2*runiform()) // 50% have capacity of 3 bags
gen CS_loadWater = 0
gen CS_loadElectric = .005 // kwh
gen CS_numWorkers = 2+round(10*runiform())
replace CS_numWorkers = 15+round(30*runiform()) if centerSize == 1
gen CS_daysDown = 5
/* Based on Rad Source 3400 Revolution X-ray Irradiator
*/
gen X_expLife = 12
gen X_purPrice = 100000 + 200000*((runiform() + runiform())/2)
gen X_bulbLife = 10000 // cycles
gen X_bulbCost = 10000
gen X_powerCost = 10000 // recommended $5k upgrade @ yr7; $10k repair @yr10
gen X_loadTime = 5
gen X_loadSize = 5
gen X_loadWater = 0 // in gal
gen X_loadElectric = .0333 // kwh
gen X_daysDown = 15
81
/*
Installation Cost Variables */
gen CS_I_trans = 5000 + 8860*((runiform() + runiform())/2) +25000*runiform() // container and
security
gen CS_I_regComp = 3100 + 12000 + 4000 // license + admin + Reli&Trust
gen CS_import = 0 // included in price or regComp
gen CS_I_security = 0 // no private costs
gen CS_sitePrep = 5000 + 5000*runiform()
gen X_I_trans = 2600*((runiform() + runiform())/2)
gen X_sitePrep = 40000*((runiform() + runiform())/2)
/*
Annual Fixed Cost Variables */
gen CS_Sec_maintenance = 2000 + 8700*runiform() // maintaining security infrastructure
gen CS_Sec_accessControl = 126.60 * CS_numWorkers // fingerprinting Reli&Trust
gen CS_Sec_services = 4000 + 4000*runiform() // cost for inhouse or contract security labor
gen CS_A_security = CS_Sec_m + CS_Sec_a + CS_Sec_s
local min = 1000
local mode = 4500
local max = 14500
local variable = "CS_AF_maintenance"
82
local cutoff=(`mode'-`min')/(`max'-`min')
generate Tri_temp = uniform()
generate `variable' = `min' + sqrt(Tri_temp*(`mode'-`min')*(`max'-`min')) if Tri_temp<`cutoff'
replace `variable' = `max' - sqrt((1-Tri_temp)*(`max'-`mode')*(`max'-`min')) if
Tri_temp>=`cutoff'
drop Tri_temp
gen CS_A_license = 700 + 8000*runiform() // range from Iowa @ 650/yr to NRC fee of 8700
replace CS_A_license = CS_A_license/3 if centerSize == 1
gen CS_S_addlNRCCosts = .185*CS_A_lic // captures 10% of NRC costs not covered by
licences and fees. 60% recovered from licenses.
gen CS_regComp = CS_A_lic + compLabor
gen CS_S_regComp = CS_regComp + CS_S_addlNRCCosts
local min = 2000
local mode = 6500
local max = 17000
local variable = "X_AF_maintenance"
local cutoff=(`mode'-`min')/(`max'-`min')
generate Tri_temp = uniform()
generate `variable' = `min' + sqrt(Tri_temp*(`mode'-`min')*(`max'-`min')) if Tri_temp<`cutoff'
replace `variable' = `max' - sqrt((1-Tri_temp)*(`max'-`mode')*(`max'-`min')) if
Tri_temp>=`cutoff'
83
drop Tri_temp
gen X_regComp = 0 // CS_regComp treated as marginal difference from this baseline
/*
Termination Cost Variables
Scrap value of devices captured in disposal variable
*/
gen privateDisposal = runiform()
// Assume OSRP collects devices after a storage period
gen CS_disposal = 0
replace CS_disposal = 75000 + 75000*runiform() if privateDisposal < .1
gen CS_S_disposal = 75000 + 75000*runiform()
replace CS_S_disposal = 0 if privateDisposal < .1
gen expediated = runiform()
gen CS_T_trans = 0
replace CS_T_trans = 50000 + 140000*runiform() if expediated < .2
replace CS_T_trans = 15000 + 25000*runiform() if privateDisposal < .1 // container and
security
drop expediated
gen CS_ST_trans = 60000
replace CS_ST_trans = 10000 if CS_T_trans > 0
replace CS_ST_trans = 0 if privateDisposal < .1
gen CS_storage = 15000 // opportunity cost of space and cost of maintaining security while
waiting for OSRP
84
replace CS_storage = 0 if CS_T_trans > 0
replace CS_storage = 1000 if privateDisposal < .1
gen CS_S_storage = 100000 + 700000*runiform() // may cost as much as 800,000 to store an
irradiator worth of material
replace CS_S_storage = 0 if privateDisposal < .1
gen X_T_trans = 3000*runiform()
gen X_ST_trans = X_T_trans
gen X_disposal = 0
gen X_S_disposal = X_disposal
gen X_storage = 0
gen X_S_storage = X_storage
/*
Life Cycle Cost Comparison for New Irradiator Installation
*/
gen CS_IC = CS_purPrice + CS_I_trans + CS_I_regComp + CS_import + ///
CS_I_sec + CS_sitePrep
gen CS_SIC = CS_IC
gen X_IC = X_purPrice + X_I_trans + X_sitePrep
gen X_SIC = X_IC
85
/*
CS & X-ray Annual fixed cost loops
*/
gen CS_PVAFC = 0
gen CS_SPVAFC = 0
local year = 1
while `year' <= CS_expLife {
gen CS_AFC`year' = (CS_A_sec + CS_AF_maint + CS_regComp) / (1+d)^`year'
gen CS_SAFC`year' = (CS_A_sec + CS_AF_maint + CS_S_regComp) / (1+d)^`year'
replace CS_PVAFC = CS_PVAFC + CS_AFC`year'
replace CS_SPVAFC = CS_SPVAFC + CS_SAFC`year'
drop CS_AFC`year' CS_SAFC`year'
local year = `year' + 1
}
gen X_PVAFC = 0
local year = 1
while `year' <= X_expLife {
gen X_AFC`year' = (X_AF_maint + X_regComp) / (1+d)^`year'
replace X_PVAFC = X_PVAFC + X_AFC`year'
drop X_AFC`year'
86
local year = `year' + 1
}
gen X_SPVAFC = X_PVAFC
/* CS AVC
*/
gen CS_PVAVC = 0
gen CS_hoursPerUnit = CS_loadTime / CS_loadSize / 60
gen CS_irradCost_labor = medTechWage * CS_hoursPerUnit
gen CS_irradCost_water = costWater * CS_loadWater / CS_loadSize
gen CS_irradCost_electric = costElectric * CS_loadElectric / CS_loadSize
gen CS_irradCostPerUnit = 0
gen CS_irradCost = 0
*gen CS_downtimeCost = throughput * costBlood * CS_daysDown / 365
gen Tri_temp = uniform()
gen CS_downtimeCost = 0 + sqrt(Tri_temp*(2300)*(8000)) if Tri_temp<(2300/8000)
replace CS_downtimeCost = 8000 - sqrt((1-Tri_temp)*(8000-2300)*(8000)) if
Tri_temp>=(2300/8000)
drop Tri_temp
local year = 1
while `year' <= CS_expLife {
/*
Update loadTime
87
*/
replace CS_loadTime = CS_loadTime + addlTimePYr
/*
Find cost of irradiating the hospitals throughput
*/
replace CS_hoursPerUnit
= CS_loadTime / CS_loadSize / 60
replace CS_irradCost_labor = medTechWage * CS_hoursPerUnit
replace CS_irradCostPerUnit = CS_irradCost_l + CS_irradCost_w + CS_irradCost_e
replace CS_irradCost = CS_irradCostPerUnit * throughput
/*
Discount and Sum
*/
gen CS_AVC`year' = (CS_irradCost + CS_downtimeCost)/(1+d)^`year'
replace CS_PVAVC = CS_PVAVC + CS_AVC`year'
/*
Prep Loop
*/
drop CS_AVC`year'
local year = `year' + 1
}
gen CS_SPVAVC = CS_PVAVC
/*
X AVC
*/
gen X_PVAVC = 0
88
gen X_hoursPerUnit = X_loadTime / X_loadSize / 60
gen X_irradCost_labor = medTechWage * X_hoursPerUnit
gen X_irradCost_water = costWater * X_loadWater / X_loadSize
gen X_irradCost_electric = costElectric * X_loadElectric / X_loadSize
gen X_irradCostPerUnit = X_irradCost_l + X_irradCost_w + X_irradCost_e
gen X_irradCost = X_irradCostPerUnit*throughput
*gen X_downtimeCost = throughput * costBlood * X_daysDown / 365
gen Tri_temp = uniform()
gen X_downtimeCost = 0 + sqrt(Tri_temp*(4100)*(12000)) if Tri_temp<(4100/12000)
replace X_downtimeCost = 12000 - sqrt((1-Tri_temp)*(12000-4100)*(12000)) if
Tri_temp>=(4100/12000)
drop Tri_temp
local year = 1
local bulbCycles = 0
while `year' <= X_expLife {
gen X_AVC`year' = X_irradCost + X_downtimeCost
/*
Bulb Replace Test
*/
if `bulbCycles' > X_bulbLife {
local bulbCycles = `bulbCycles' - X_bulbLife
replace X_AVC`year' = X_AVC`year' + X_bulbCost
}
89
else {
local bulbCycles = `bulbCycles' + throughput/X_loadSize
}
/*
Power Supply Maintanence
*/
replace X_AVC`year' = X_AVC`year' + (X_powerCost/2) if `year' == 7
replace X_AVC`year' = X_AVC`year' + (X_powerCost) if `year' == 10
/*
Discount and Sum
*/
replace X_AVC`year' = X_AVC`year' / (1+d)^`year'
replace X_PVAVC = X_PVAVC + X_AVC`year'
/*
Prep for next loop
*/
drop X_AVC`year'
local year = `year' + 1
}
gen X_SPVAVC = X_PVAVC
gen CS_TC = CS_T_trans + CS_disposal + CS_storage
gen CS_STC = CS_TC + CS_ST_trans + CS_S_disposal + CS_S_storage
gen CS_PVTC = CS_TC
/ ( 1+ d) ^ CS_expLife
90
gen CS_SPVTC = CS_STC / ( 1+ d) ^ CS_expLife
gen X_TC = X_T_trans + X_disposal + X_storage
gen X_STC = X_TC
gen X_PVTC = X_TC / ( 1+ d) ^ X_expLife
gen X_SPVTC = X_STC / ( 1+ d) ^ X_expLife
gen CS_PVC = CS_IC + CS_PVAFC + CS_PVAVC + CS_PVTC
gen CS_SPVC = CS_SIC + CS_SPVAFC + CS_SPVAVC + CS_SPVTC ///
+ CS_GTRI_upgradeCost // Should happen reasonably soon for many users
gen CS_EUAC = CS_PVC*d*(1+d)^CS_expLife/((1+d)^CS_expLife - 1)
gen CS_SEUAC = CS_SPVC*d*(1+d)^CS_expLife/((1+d)^CS_expLife - 1)
gen X_PVC = X_IC + X_PVAFC + X_PVAVC + X_PVTC
gen X_SPVC = X_PVC
gen X_EUAC = X_PVC*d*(1+d)^X_expLife/((1+d)^X_expLife - 1)
gen X_SEUAC = X_SPVC*d*(1+d)^X_expLife/((1+d)^X_expLife - 1)
replace replace_withX = 1 if CS_EUAC > X_EUAC
replace replace_withX_soc = 1 if CS_SEUAC > X_SEUAC
save MonteCarloSim.dta, replace
91
bysort throughput: egen EUAC = mean(X_EUAC)
bysort throughput: egen SEUAC = mean(X_SEUAC)
replace X_EUAC = EUAC
replace X_SEUAC = SEUAC
drop in 2/1000
drop in 3/1001
drop in 4/l
keep X_EUAC X_SEUAC
save EUACandSEUAC.dta, replace
clear
/*
Replacement Analysis
Only enters loop if the X-rays are competitive with Cesium in the above lifecycle
calculation
Calculates the cost of operating a cesium irradiator over its remaining expected life
Calculates the cost of replacing a cesium irradiator immediately in the current year
and then operating x-ray irradiators over the their lifetime
If replacement immediately is cost effective then ends the loop
and changes that binary analysis variable
*/
92
local age = 1
while `age' <= 30 { // 30 is current value of CS_expLife
set obs 3000
gen CS_age = `age'
/* Reinitialize all variables */
gen discountRate = 0.03
gen highDiscountRate = 0.07
gen CS_GTRI_upgradeYear = round(8*runiform()) // assumes upgrades w/in 8 yrs
gen CS_GTRI_upgradeCost = (250000 + 250000*runiform()) ///
/ (1+d) ^ CS_GTRI_upgradeYear // Mean value of 375000
gen replace_withX = 0
gen replace_withX_soc = 0
gen largeCenterPercent = .45
gen centerSize = 0 //small=0 large=1
replace centerSize = 1 if runiform() < largeCenterPercent
drop largeCenterPercent
gen throughput = 5000
replace throughput = 10000 in 1001/2000
93
replace throughput = 15000 in 2001/3000
gen ComplianceSalary = 50000 + 50000*runiform() // often RSO, or Med Physicist
gen CompExtraHours = 50*(2+8*runiform()) // 2-10hrs/wk @ small; 1-6 @ large
replace CompExtraHours = 50*(1+5*runiform()) if centerSize == 1
gen compLabor = ComplianceSalary*CompExtraHours/50/40
gen medTechWage = 27.15 + 4*(runiform()+runiform())/2 //national average is 29.15
gen costElectric = rnormal(10.81, 1.2) // kwh; roughly [7.6,16.47]
gen costWater = rnormal(.00272,.00045)
* per gal; roughly [.0015,.0040]
gen costBlood = 25
gen CS_purPrice = 207000 + 165000*((runiform() + runiform())/2)
gen CS_expLife = 30
gen CS_loadTime = 2.3 + 2*runiform()
gen addlTimePYr = CS_loadTime/30 // linear approximation of time increase/half-life
replace CS_loadTime = CS_loadTime + addlTimePYr*CS_age
gen CS_loadSize = 2 + round(2*runiform()) // 50% have capacity of 3 bags
gen CS_loadWater = 0
gen CS_loadElectric = .005 // kwh
gen CS_numWorkers = round(10*runiform())
replace CS_numWorkers = 15+round(30*runiform()) if centerSize == 1
gen CS_daysDown = 5
94
gen X_expLife = 12
gen X_purPrice = 100000 + 200000*((runiform() + runiform())/2)
gen X_bulbLife = 10000 // cycles
gen X_bulbCost = 10000 //
gen X_powerCost = 10000 //
gen X_loadTime = 3 + 4*runiform() // in minutes
gen X_loadSize = 4 + 4*((runiform() + runiform())/2)
gen X_loadWater = 2.6 // in gallons // UPDATE
gen X_loadElectric = .2 // what units? UPDATE
gen X_daysDown = 15
gen X_I_trans = 2600*((runiform() + runiform())/2)
gen X_sitePrep = 40000*((runiform() + runiform())/2)
gen CS_Sec_maintenance = 2000 + 8700*runiform() // physical infrastructure
gen CS_Sec_accessControl = 126.60 * CS_numWorkers //dollars
gen CS_Sec_services = 4000 + 4000*runiform()
gen CS_A_security = CS_Sec_m + CS_Sec_a + CS_Sec_s
local min = 1000
local mode = 4500
local max = 14500
local variable = "CS_AF_maintenance"
95
local cutoff=(`mode'-`min')/(`max'-`min')
generate Tri_temp = uniform()
generate `variable' = `min' + sqrt(Tri_temp*(`mode'-`min')*(`max'-`min')) if
Tri_temp<`cutoff'
replace `variable' = `max' - sqrt((1-Tri_temp)*(`max'-`mode')*(`max'-`min')) if
Tri_temp>=`cutoff'
drop Tri_temp
gen CS_A_license = 700 + 8000*runiform() // range from Iowa @ 650/yr to NRC fee of
8700
replace CS_A_license = CS_A_license/3 if centerSize == 1
gen CS_S_addlNRCCosts = .185*CS_A_lic // captures 10% of NRC costs not covered
by licences and fees. 60% recovered from licenses.
gen CS_regComp = CS_A_lic + compLabor
gen CS_S_regComp = CS_regComp + CS_S_addlNRCCosts
local min = 2000
local mode = 6500
local max = 17000
local variable = "X_AF_maintenance"
local cutoff=(`mode'-`min')/(`max'-`min')
generate Tri_temp = uniform()
96
generate `variable' = `min' + sqrt(Tri_temp*(`mode'-`min')*(`max'-`min')) if
Tri_temp<`cutoff'
replace `variable' = `max' - sqrt((1-Tri_temp)*(`max'-`mode')*(`max'-`min')) if
Tri_temp>=`cutoff'
drop Tri_temp
gen X_regComp = 0
gen privateDisposal = runiform()
// Assume OSRP collects devices after a storage period
gen CS_disposal = 0
replace CS_disposal = 75000 + 75000*runiform() if privateDisposal < .1
gen CS_S_disposal = 75000 + 75000*runiform()
replace CS_S_disposal = 0 if privateDisposal < .1
gen expediated = runiform()
gen CS_T_trans = 0
replace CS_T_trans = 50000 + 140000*runiform() if expediated < .2
replace CS_T_trans = 15000 + 25000*runiform() if privateDisposal < .1 //
container and security
drop expediated
gen CS_ST_trans = 60000
replace CS_ST_trans = 10000 if CS_T_trans > 0
replace CS_ST_trans = 0 if privateDisposal < .1
97
gen CS_storage = 15000 // opportunity cost of space and cost of maintaining security
while waiting for OSRP
replace CS_storage = 0 if CS_T_trans > 0
replace CS_storage = 1000 if privateDisposal < .1
gen CS_S_storage = 100000 + 700000*runiform() // may cost as much as 800,000 to
store an irradiator worth of material
replace CS_S_storage = 0 if privateDisposal < .1
gen X_T_trans = 3000*runiform()
gen X_ST_trans = X_T_trans
gen X_disposal = 0
gen X_S_disposal = X_disposal
gen X_storage = 0
gen X_S_storage = X_storage
gen R_PVC = 0
gen R_SPVC = 0
gen R_EUAC = 0
gen R_SEUAC = 0
gen remainingYears = CS_expLife - CS_age
/*
Calculation of the costs of operating Cesium for the rest of its life
98
*/
/*
Annual Fixed Costs for Remaining Years
*/
gen CS_PVAFC = 0
gen CS_SPVAFC = 0
local year = 1
while `year' <= (remainingYears+1) {
gen CS_AFC`year' = (CS_A_sec + CS_AF_maint + CS_regComp) / (1+d)^`year'
gen CS_SAFC`year' = (CS_A_sec + CS_AF_maint + CS_S_regComp) /
(1+d)^`year'
replace CS_PVAFC = CS_PVAFC + CS_AFC`year'
replace CS_SPVAFC = CS_SPVAFC + CS_SAFC`year'
drop CS_AFC`year' CS_SAFC`year'
local year = `year' + 1
}
/*
Calculate Annual Variable Costs for Remaining years
*/
gen CS_PVAVC = 0
99
gen CS_hoursPerUnit= CS_loadTime / CS_loadSize / 60 // this is for the current age, gets
reset in loop below
gen CS_irradCost_labor = medTechWage * CS_hoursPerUnit // also gets reset
gen CS_irradCost_water = costWater * CS_loadWater / CS_loadSize
gen CS_irradCost_electric = costElectric * CS_loadElectric / CS_loadSize
gen CS_irradCostPerUnit = 0
gen CS_irradCost = 0
*gen CS_downtimeCost = costBlood * throughput * CS_daysDown / 365
gen Tri_temp = uniform()
gen CS_downtimeCost = 0 + sqrt(Tri_temp*(2300)*(8000)) if Tri_temp<(2300/8000)
replace CS_downtimeCost = 8000 - sqrt((1-Tri_temp)*(8000-2300)*(8000)) if
Tri_temp>=(2300/8000)
drop Tri_temp
local year = 1
while `year' <= (remainingYears+1) {
replace CS_loadTime = CS_loadTime + addlTimePYr
replace CS_hoursPerUnit
= CS_loadTime / CS_loadSize / 60
replace CS_irradCost_labor = medTechWage * CS_hoursPerUnit
replace CS_irradCostPerUnit = CS_irradCost_l + CS_irradCost_w +
CS_irradCost_e
replace CS_irradCost = CS_irradCostPerUnit * throughput
100
gen CS_AVC`year' = (CS_irradCost + CS_downtimeCost) / (1+d)^`year'
replace CS_PVAVC = CS_PVAVC + CS_AVC`year'
drop CS_AVC`year'
local year = `year' + 1
}
gen CS_SPVAVC = CS_PVAVC
/*Calculate Termination Costs at sooner date
*/
gen CS_TC = CS_T_trans + CS_disposal + CS_storage
gen CS_STC = CS_TC + CS_ST_trans + CS_S_disposal + CS_S_storage
gen CS_PVTC = CS_TC
/ ( 1+ d) ^ remainingYears
gen CS_SPVTC = CS_STC / ( 1+ d) ^ remainingYears
/*Total and find EUAC*/
gen CS_PVC = CS_PVAFC + CS_PVAVC + CS_PVTC
gen CS_SPVC = CS_SPVAFC + CS_SPVAVC + CS_SPVTC ///
+ CS_GTRI_upgradeCost // Should happen reasonably soon for many users
gen CS_EUAC = CS_PVC*d*(1+d)^(remainingYears) ///
/((1+d)^remainingYears - 1)
replace CS_EUAC = CS_PVC if remainingYears ==0
101
gen CS_SEUAC = CS_SPVC*d*(1+d)^(remainingYears) ///
/((1+d)^remainingYears - 1)
replace CS_SEUAC = CS_SPVC if remainingYears ==0
/*Calculate the Cost of Replacing Cesium with X-Ray in Year `i'
*/
gen R_IC = X_sitePrep
gen R_PVAFC = 0
gen R_PVAVC = 0
gen R_PVTC = CS_T_trans + CS_disposal + CS_storage
gen R_SPVTC = R_PVTC + CS_ST_trans + CS_S_disposal + CS_S_storage
gen X_hoursPerUnit = X_loadTime / X_loadSize / 60
gen X_irradCost_labor = medTechWage * X_hoursPerUnit
gen X_irradCost_water = costWater * X_loadWater / X_loadSize
gen X_irradCost_electric = costElectric * X_loadElectric / X_loadSize
gen X_irradCostPerUnit = X_irradCost_l + X_irradCost_w + X_irradCost_e
gen X_irradCost = X_irradCostPerUnit*throughput
*gen X_downtimeCost = costBlood * throughput * X_daysDown / 365
gen Tri_temp = uniform()
gen X_downtimeCost = 0 + sqrt(Tri_temp*(4100)*(12000)) if Tri_temp<(4100/12000)
replace X_downtimeCost = 12000 - sqrt((1-Tri_temp)*(12000-4100)*(12000)) if
Tri_temp>=(4100/12000)
drop Tri_temp
102
gen ryears = remainingYears
gen addlDiscYears = 0
while ryears >= X_expLife {
replace R_IC = R_IC + (X_purPrice + X_I_trans) / (1+d)^addlDiscYears
gen R_PVAFC_oneLife = 0
local year = 1
while `year' <= X_expLife {
gen R_AFC`year' = (X_AF_maint + X_regComp)/(1+d)^`year'
replace R_PVAFC_oneLife = R_PVAFC_oneLife + R_AFC`year'
drop R_AFC`year'
local year = `year' + 1
}
replace R_PVAFC = R_PVAFC + R_PVAFC_oneLife / (1+d)^addlDiscYears
gen R_PVAVC_oneLife = 0
local year = 1
local bulbCycles = X_bulbLife*runiform()
while `year' <= X_expLife {
gen R_AVC`year' = X_irradCost + X_downtimeCost
/*
Bulb Replace Test
*/
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if `bulbCycles' > X_bulbLife {
local bulbCycles = `bulbCycles' - X_bulbLife
replace R_AVC`year' = R_AVC`year' + X_bulbCost
}
else {
local bulbCycles = `bulbCycles' + throughput/X_loadSize
}
/*
Power Supply Replace Test
*/
replace R_AVC`year' = R_AVC`year' + (X_powerCost/2) if `year' == 7
replace R_AVC`year' = R_AVC`year' + X_powerCost if `year' == 10
replace R_AVC`year' = R_AVC`year' / (1+d)^`year'
replace R_PVAVC_oneLife = R_PVAVC_oneLife + R_AVC`year'
drop R_AVC`year'
local year = `year' + 1
}
replace R_PVAVC = R_PVAVC + R_PVAVC_oneLife / (1+d)^addlDiscYears
replace R_PVTC = R_PVTC + (X_T_trans + X_disposal ///
+ X_storage) / (1+d)^addlDiscYears
replace R_SPVTC = R_SPVTC + (X_T_trans + X_disposal ///
+ X_storage) / (1+d)^addlDiscYears
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replace addlDiscYears = addlDiscYears + X_expLife
replace ryears = ryears - X_expLife
drop R_PVAFC_oneLife R_PVAVC_oneLife
}
gen R_SIC = R_IC
gen R_SPVAFC = R_PVAFC
gen R_SPVAVC = R_PVAVC
replace R_PVC = R_IC + R_PVAFC + R_PVAVC + R_PVTC
replace R_SPVC = R_SIC + R_SPVAFC + R_SPVAVC + R_SPVTC
/*
This accounts for the remaining years of life of a cesium irradiator
when they are fewer than one whole lifecycle of an X-ray
*/
append using EUACandSEUAC
replace X_EUAC = X_EUAC[3001] if throughput == 5000
replace X_EUAC = X_EUAC[3002] if throughput == 10000
replace X_EUAC = X_EUAC[3003] if throughput == 15000
replace X_SEUAC = X_SEUAC[3001] if throughput == 5000
replace X_SEUAC = X_SEUAC[3002] if throughput == 10000
replace X_SEUAC = X_SEUAC[3003] if throughput == 15000
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local i = 1
while `i' <= ryears {
replace R_PVC = R_PVC + (X_EUAC/(1+d)^(remainingYears - ryears + `i'))
replace R_SPVC = R_SPVC + (X_SEUAC/(1+d)^(remainingYears - ryears + `i'))
local i = `i' + 1
}
drop in 3001/3003
replace R_EUAC = R_PVC*d*((1+d)^ remainingYears) /((1+d)^remainingYears - 1)
replace R_SEUAC = R_SPVC*d*(1+d)^ remainingYears /((1+d)^ remainingYears - 1)
replace replace_withX = 1 if CS_EUAC > R_EUAC
replace replace_withX_soc = 1 if CS_SEUAC > R_SEUAC
append using MonteCarloSim.dta
save MonteCarloSim.dta, replace
clear
local age = `age' + 1
}
Source: Author
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