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

_____________________________________

i

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

ii

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

iii

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.

iv

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

v

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.

vi

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

1

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

2

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.

3

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 long-

term 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

4

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

5

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.

6

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.

7

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.

8

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.

9

Table 1: Installation Costs

Component

(Unit)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Irradiator Purchase Price:

(Total Dollars) 160,000 325,000 242,500

X-Ray Purchase Price:

(Total Dollars) 160,000 240,000 220,000

Cesium Site Preparation:

(Total Dollars) 5,000 10,000 7,500

X-Ray Site Preparation:

(Total Dollars) 0 50,000 18,600

Cesium Initial Legal/Licensing/RSO/Public

Health Costs:

(Total Dollars)

4,000 20,000 15,400

X-Ray Initial Legal/Licensing/RSO/Public

Health Time Costs:

(Total Dollars)

2,000 3,000 2,500

Cesium Initial Fingerprinting/Background

Check Costs:

(Total Dollars)

2,000 5,000 3,800

Cesium Installation/ /Shielding Design

Considerations:

(Total Dollars)

30,000 38,000 34,000

Cesium Transportation of Device:

(Total Dollars) 3,000 50,000 28,800

X-Ray Transportation of Device:

(Total Dollars) 0 2,600 2,000

Cesium Import Permit- Cesium Only

(Total Dollars) 7,000 7,000 7,000

Cesium Global Threat Reduction Initiative

Security Equipment/Installation:

(Total Dollars)

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

10

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

11

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.

12

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

13

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)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Security Infrastructure Maintenance:

(Annual Total Dollars) 1,000 8,600 4,900

Cesium Security Background Check:

(Annual Total Dollars) 2,400 2,400 2,400

Cesium Anticipated Security Ongoing Costs:

(Annual Total Dollars) 4,000 7,500 5,800

Cesium Service Contract/ Warranty:

(Annual Total Dollars) 1,000 14,000 6,000

X-Ray Service Contract/ Warranty:

(Annual Total Dollars) 2,000 17,000 8,500

X-Ray Year 7 Power Supply Upgrade:

(Total Dollars) 5,000 5,000 5,000

X-Ray Year 10 Power Supply Upgrade:

(Total Dollars) 10,000 10,000 10,000

Cesium Regulation Personnel:

(Annual Salaries in Dollars) 57,500 57,500 57,500

Cesium Regulation Licensing:

(Annual Total Dollars) 650 8,700 4,700

X-Ray Regulation Licensing:

(Annual Total Dollars) 3,000 8,700 5,900

Nuclear Regulatory Commission Costs Not

Covered by Licensing:

(Annual Total Dollars)

4,600 4,600 4,600

14

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.

15

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)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Blood Units Per Site Per Day:

(Average Daily Blood Units Irradiated) 0 50 25

X-Ray Blood Units Per Site Per Day:

(Average Daily Blood Units Irradiated) 0 50 25

Cesium Blood Units Per Batch:

(Average Blood Units Irradiated Per Run) 1 4 2.5

X-Ray Blood Units Per Batch:

(Average Blood Units Irradiated Per Run) 5 5 5

Cesium Wage of Technician/Operator:

(Hourly Wage in Dollars) 27 37 29

X-Ray Wage of Technician/Operator:

(Hourly Wage in Dollars) 27 37 29

Cesium Irradiation Time Per Batch:

(Run Time in Minutes Per Batch) 1.7 8.6 5

X-Ray Irradiation Time Per Batch:

(Run Time in Minutes Per Batch) 5 5 5

Price of Electricity:

(Dollars Per Kilowatt Hours) 0.076 0.1647 .1081

Cesium Kilowatts of Electricity Consumed:

(Kilowatts Consumed Per Minute of Run-Time) 0.3 0.3 0.3

X-Ray Kilowatts of Electricity Consumed:

(Kilowatts Consumed Per Minute of Run-Time) 2 2 2

X-Ray Parts Replacement:

(Average Annual Dollars) 10,000 10,000 10,000

Cesium Costs of Downtime:

(Average Annual Dollars) 2,300 2,300 2,300

X-Ray Costs of Downtime:

(Average Annual Dollars) 4,000 4,000 4,000

16

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

17

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.

18

Table 4: Termination Costs

Component

(Unit)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Physical Costs of Disposal:

(Total Dollars) 75,000 150,000

--------------

--

X-Ray Physical Costs of Disposal:

(Total Dollars) 0 2,600 1,300

Cesium Site to Vendor Disposal Fee:

(Total Dollars) 15,000 40,000

--------------

--

Cesium Site to Off-Site Recovery Project

Disposal Fee:

(Total Dollars)

0 190,000 --------------

--

Off-Site Recovery Project Costs Not Covered by

Fees:

(Total Dollars)

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 X-

ray device on the market and has multiple advantages over other models that make it a strong

19

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

20

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 x-

ray 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,

21

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

22

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

23

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 X-

ray 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

24

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

25

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.

26

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.

Trials with Lower Private Costs of Purchasing and

Operating X-Ray Irradiator

(Percentage)

Trials with Lower Social Costs of Purchasing

and Operating X-Ray Irradiator

(Percentage)

Throughput Throughput

Discount Rate 5,000 10,000 15,000 Total 5,000 10,000 15,000 Total

3% 98 98 99 98 100 100 100 100

7% 98 98 98 98 100 100 100 100

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

Table 5: New Purchase Analysis

27

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.

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

Figure 2: Private Benefits for X-ray over CsCl Irradiator Purchase

28

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

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)

Social Cost Analysis

(Percentage

Throughput Throughput

Age 5,000 10,000 15,000 Total 5,000 10,000 15,000 Total

1 53 52 51 52 56 56 57 56

5 52 54 59 55 61 62 67 63

10 50 58 61 56 70 75 76 74

15 55 60 78 67 86 88 90 88

20 57 65 78 67 98 97 99 98

25 68 78 88 78 100 100 100 100

30 98 100 100 99 100 100 100 100

Table 7: Percentage of Trials with Positive Savings from Replacement, 7 percent discount

rate

Private Cost Analysis

(Percentage)

Social Cost Analysis

(Percentage)

Throughput Throughput

Age 5,000 10,000 15,000 Total 5,000 10,000 15,000 Total

1 14 15 15 15 11 13 12 12

5 18 19 24 20 18 18 16 17

10 15 21 25 20 17 19 21 19

15 18 22 31 24 26 29 28 27

20 16 25 38 27 43 46 51 47

25 28 43 55 42 86 88 91 88

30 98 99 100 99 100 100 100 100

Table 6: Percentage of Trials with Positive Savings from Replacement, 3 percent

discount rate

29

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

30

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

31

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

32

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

33

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.

34

Figure 7: Social NPV of Switching from Cesium to X-ray, 7 percent discount rate

Figure 8: Social NPV of Switching from Cesium to X-ray, 3 percent discount rate

35

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

36

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.

37

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.

Private Cost Difference

(Dollars)

Social Cost Difference

(Dollars)

3 percent 7 percent 3 percent 7 percent

Age Average Lower 5% Average Lower 5% Average Lower 5% Average Lower 5%

1 15,000 (277,400) (116,400) (307,100) 42,300 (350,000) (196,500) (687,000)

5 23,000 (245,500) (94,500) (277,100) 77,400 (283,300) (238,600) (610,400)

10 27,800 (187,100) (83,200) (248,400) 120,600 (175,500) (198,400) (544,300)

15 35,900 (145,000) (61,600) (208,600) 183,300 (69,200) (116,800) (428,400)

20 39,000 (80,200) (37,400) (140,400) 238,300 41,600 (10,500) (259,400)

25 36,500 (33,900) (7,200) (72,900) 297,200 152,300 127,500 (38,300)

30 27,700 7,800 25,500 6,000 363,600 254,700 315,800 206,900

Table 8: Possible RDD Valuations Necessary for Replacement

38

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.

39

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

40

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

41

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.

42

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.

7 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.

8 United States Environmental Protection Agency. “Sealed Radioactive Sources.” Last updated

on June 12, 2013. Accessed via: http://www.epa.gov/radiation/source-reduction-

management/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.

43

Accessed via: http://www.nrc.gov/public-involve/conference-

symposia/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

14 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

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.

44

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.

45

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 Cesium-

137 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

46

transport, but they do not have any incentive to create a general-purpose package usable by non-

customers.

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.

47

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

48

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/

49

APPENDIX C: OSRP TOTAL 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

50

APPENDIX D: GAMMACELL 1000 ELITE/3000 ELAN

51

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

52

APPENDIX E: RAD SOURCE 3400 REVOLUTION

Technical Specifications and Costs:

53

Product Description:

54

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

55

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.

56

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/

57

APPENDIX G: COST ESTIMATES

Please refer to the Methodology section for information on how this data was obtained.

Installation Costs

Component

(Unit)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Irradiator Purchase Price:

(Total Dollars) 160,000 325,000 242,500

X-Ray Purchase Price:

(Total Dollars) 160,000 240,000 220,000

Cesium Site Preparation:

(Total Dollars) 5,000 10,000 75,000

X-Ray Site Preparation:

(Total Dollars) 0 50,000 18,600

Cesium Initial Legal/Licensing/RSO/Public

Health Costs:

(Total Dollars)

4,000 20,000 15,400

X-Ray Initial Legal/Licensing/RSO/Public

Health Time Costs:

(Total Dollars)

2,000 3,000 2,500

Cesium Initial Fingerprinting/Background

Check Costs:

(Total Dollars)

2,000 5,000 3,800

Cesium

Installation/Setup/Commissioning/Shielding

Design Considerations:

(Total Dollars)

30,000 38,000 34,000

Cesium Transportation of Device:

(Total Dollars) 3,000 50,000 28,800

X-Ray Transportation of Device:

(Total Dollars) 0 2,600 2,000

Cesium Import Permit- Cesium Only

(Total Dollars) 7,000 7,000 7,000

Cesium Global Threat Reduction Initiative

Security Equipment/Installation:

(Total Dollars)

317,800 500,000 404,800

58

Fixed Costs

Component

(Unit)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Security Infrastructure Maintenance:

(Annual Total Dollars) 1,000 8,600 4,900

Cesium Security Background Check:

(Annual Total Dollars) 2,400 2,400 2,400

Cesium Anticipated Security Ongoing Costs:

(Annual Total Dollars) 4,000 7,500 5,800

Cesium Service Contract/ Warranty:

(Annual Total Dollars) 1,000 14,000 6,000

X-Ray Service Contract/ Warranty:

(Annual Total Dollars) 2,000 17,000 8,500

X-Ray Year 7 Power Supply Upgrade:

(Total Dollars) 5,000 5,000 5,000

X-Ray Year 10 Power Supply Upgrade:

(Total Dollars) 10,000 10,000 10,000

Cesium Regulation Personnel:

(Annual Salaries in Dollars) 57,500 57,500 57,500

Cesium Regulation Licensing:

(Annual Total Dollars) 650 8,700 4,700

X-Ray Regulation Licensing:

(Annual Total Dollars) 3,000 8,700 5,900

Nuclear Regulatory Commission Costs Not

Covered by Licensing:

(Annual Total Dollars)

4,600 4,600 4,600

Variable Costs

Component

(Unit)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Blood Units Per Site Per Day:

(Average Daily Blood Units Irradiated) 0 50 25

X-Ray Blood Units Per Site Per Day:

(Average Daily Blood Units Irradiated) 0 50 25

Cesium Blood Units Per Batch:

(Average Blood Units Irradiated Per Run) 1 4 2.5

X-Ray Blood Units Per Batch:

(Average Blood Units Irradiated Per Run) 5 5 5

(Continued on Next Page) ---------------- --------------- --------------

59

Cesium Wage of Technician/Operator:

(Hourly Wage in Dollars) 27 37 29

X-Ray Wage of Technician/Operator:

(Hourly Wage in Dollars) 27 37 29

Cesium Irradiation Time Per Batch:

(Run Time in Minutes Per Batch) 1.7 8.6 5

X-Ray Irradiation Time Per Batch:

(Run Time in Minutes Per Batch) 5 5 5

Price of Electricity:

(Dollars Per Kilowatt Hours) 0.076 0.1647 .1081

Cesium Kilowatts of Electricity Consumed:

(Kilowatts Consumed Per Minute of Run-Time) 0.3 0.3 0.3

X-Ray Kilowatts of Electricity Consumed:

(Kilowatts Consumed Per Minute of Run-Time) 2 2 2

X-Ray Parts Replacement:

(Average Annual Dollars) 10,000 10,000 10,000

Cesium Costs of Downtime:

(Average Annual Dollars) 2,300 2,300 2,300

X-Ray Costs of Downtime:

(Average Annual Dollars) 4,000 4,000 4,000

Termination Costs

Component

(Unit)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Physical Costs of Disposal:

(Total Dollars) 75,000 150,000

--------------

--

X-Ray Physical Costs of Disposal:

(Total Dollars) 0 2,600 1,300

Cesium Site to Vendor Disposal Fee:

(Total Dollars) 15,000 40,000

--------------

--

Cesium Site to Off-Site Recovery Project

Disposal Fee:

(Total Dollars)

0 190,000 --------------

--

Off-Site Recovery Project Costs Not Covered by

Fees:

(Total Dollars)

75,000 920,000 --------------

--

Source: Author

60

APPENDIX H: MONTE CARLO INSTRUCTION SHEET

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.

61

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.

62

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.

63

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.

64

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)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Irradiator Purchase Price:

(Total Dollars) 160,000 325,000 242,500

X-Ray Irradiator Purchase Price:

(Total Dollars) 160,000 240,000 220,000

Value of Grant(s)/Awards:

(Total Dollars) Site Specific Site Specific Site Specific

Discount Rate:

(Annual Percent) 3 10 4

Staff Salary Costs:

(Total Salaries in Dollars) Site Specific Site Specific Site Specific

Cost of Contracting Out for Irradiated Blood:

(Cost Per Blood Unit Purchased in Dollars) 25 50 25

Operator/Technician Wage:

(Dollars Per Hour) 27 37 29

65

Variable Inputs

Component

(Unit)

Low Range

Price

Estimate

High Range

Price

Estimate

Point Price

Estimate

Cesium Estimated Costs of Device

Installation:

(Total Dollars)

51,000 130,000 90,500

X-Ray Estimated Costs of Device Installation:

(Total Dollars) 2,000 55,600 23,000

Cesium Number of Blood Units Irradiated :

(Average Annual Units of Blood Irradiated) Site Specific Site Specific Site Specific

X-Ray Number of Blood Units Irradiated :

(Average Annual Units of Blood Irradiated) Site Specific Site Specific Site Specific

Cesium Irradiation Time:

(Minutes Needed Per Batch) 1.7 8.6 5

X-Ray Irradiation Time:

(Minutes Needed Per Batch) 5 5 5

Price of Water:

(Dollars Per Gallon) .00133 .0114 .00272

Price of Electricity:

(Dollars Per Kilowatt Hour) .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

Cesium Maintenance Costs:

(Average Annual Costs) 1,000 14,000 6,000

X-Ray Maintenance Costs:

(Average Annual Costs) 23,400 23,400 23,400

Cesium Days Inoperable:

(Average Annual Days Down) 5 5 5

X-Ray Days Inoperable:

(Average Annual Days Down) 15 15 15

66

Cesium Permitting and Licensing Costs:

(Average Annual Dollars) 650 8,700 4,675

X-Ray Permitting and Licensing Costs:

(Average Annual Dollars) 3,000 8,700 5,850

Cesium Removal and Disposal Costs:

(Total Dollars) 90,000 380,000 Unknown

X-Ray Removal and Disposal Costs:

(Total Dollars) 0 2,600 Unknown

Miscellaneous Expenses:

(Average Annual Dollars) 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

67

APPENDIX I: OUTPUT TABLES

Percent of Trials with Positive Private Benefits to Replacement at 7%

(Based on Throughput)

CsCl Age

(Year)

5,000 Blood Units

(Percentage)

10,000 Blood Units

(Percentage)

15,000 Blood Units

(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

68

Percent of Trials with Positive Social Benefits to Replacement at 7%

(Based on Throughput)

CsCl Age

(Year)

5,000 Blood Units

(Percentage)

10,000 Blood Units

(Percentage)

15,000 Blood Units

(Percentage)

1 11 13 12

2 14 13 16

3 15 16 18

4 13 13 15

5 18 18 16

6 17 17 16

7 17 18 16

8 16 21 19

9 18 19 20

10 17 19 21

11 19 23 24

12 20 21 25

13 20 24 27

14 22 27 29

15 26 29 28

16 31 32 35

17 31 34 39

18 31 34 39

19 35 44 45

20 43 46 51

21 49 52 56

22 53 57 65

23 61 67 73

24 71 78 79

25 86 88 91

26 94 95 96

27 99 100 100

28 100 100 100

29 100 100 100

30 100 100 100

69

Difference between Social and Private Benefits' Replacement Rates at 7%

(Based on Throughput)

CsCl Age

(Year)

5,000 Blood Units

(Percentage)

10,000 Blood Units

(Percentage)

15,000 Blood Units

(Percentage)

1 (4) (2) (3)

2 (1) (4) (4)

3 (3) (2) (1)

4 (4) (4) (4)

5 0 (1) (7)

6 2 (2) (3)

7 2 (1) (7)

8 3 2 (5)

9 3 (1) (4)

10 2 (2) (4)

11 1 0 (6)

12 4 2 (3)

13 4 1 (2)

14 3 1 (2)

15 8 7 (3)

16 10 6 0

17 11 5 0

18 10 7 5

19 17 18 6

20 27 21 12

21 30 21 16

22 34 30 21

23 40 34 28

24 51 43 26

25 58 45 36

26 61 49 38

27 62 46 30

28 50 33 21

29 28 15 7

30 2 1 0

70

Percent of Trials with Positive Private Benefits to Replacement at 3%

(Based on Throughput)

CsCl Age

(Year)

5,000 Blood Units

(Percentage)

10,000 Blood Units

(Percentage)

15,000 Blood Units

(Percentage)

1 53 52 51

2 52 50 52

3 49 54 53

4 52 53 57

5 52 54 59

6 52 56 56

7 48 55 60

8 54 60 62

9 50 56 66

10 50 58 61

11 53 57 61

12 54 59 65

13 59 62 70

14 56 60 65

15 55 60 65

16 58 62 69

17 62 66 68

18 58 63 71

19 54 66 77

20 57 65 78

21 59 68 80

22 59 73 82

23 65 75 85

24 65 77 85

25 68 78 88

26 71 81 90

27 77 87 94

28 83 92 96

29 94 98 99

30 98 100 100

71

Percent of Trials with Positive Social Benefits to Replacement at 3%

(Based on Throughput)

CsCl Age

(Year)

5,000 Blood Units

(Percentage)

10,000 Blood Units

(Percentage)

15,000 Blood Units

(Percentage)

1 56 56 57

2 55 57 58

3 58 58 60

4 59 61 63

5 61 62 67

6 61 65 64

7 64 68 68

8 69 73 75

9 69 72 75

10 70 75 76

11 72 75 79

12 78 80 84

13 82 83 88

14 83 85 86

15 86 88 90

16 88 88 90

17 91 93 93

18 92 94 95

19 96 97 98

20 98 97 99

21 99 99 99

22 100 100 100

23 100 100 100

24 100 100 100

25 100 100 100

26 100 100 100

27 100 100 100

28 100 100 100

29 100 100 100

30 100 100 100

72

Difference between Social and Private Benefits' Replacement Rates at 3%

(Based on Throughput)

CsCl Age

(Year)

5,000 Blood Units

(Percentage)

10,000 Blood Units

(Percentage)

15,000 Blood Units

(Percentage)

1 3 4 6

2 4 7 6

3 9 5 8

4 8 8 6

5 9 8 8

6 9 8 8

7 17 12 8

8 15 14 13

9 19 16 10

10 19 18 15

11 20 18 18

12 24 21 19

13 23 20 18

14 27 25 21

15 31 28 25

16 30 27 21

17 30 27 25

18 35 30 24

19 42 31 21

20 41 33 20

21 40 31 19

22 41 27 18

23 35 25 16

24 35 23 15

25 32 22 12

26 29 19 10

27 23 13 6

28 17 8 4

29 6 3 1

30 2 0 0

73

Private Costs of Replacement at 7%

(Based on Throughput)

CsCl Age

(Year)

Mean Cost

(Dollars)

Maximum Cost

(Dollars)

Minimum Cost

(Dollars)

Lower 5% Bound

(Dollars)

1 (116,400) 381,300 (574,500) (307,100)

2 (115,800) 269,400 (467,600)

3 (107,400) 318,300 (479,700)

4 (107,300) 318,600 (549,800)

5 (94,500) 366,800 (544,600) (277,100)

6 (104,000) 260,400 (447,500)

7 (94,200) 309,400 (447,900)

8 (93,800) 315,200 (456,800)

9 (86,700) 296,900 (506,300)

10 (83,200) 310,800 (490,400) (248,400)

11 (70,900) 301,700 (396,900)

12 (74,800) 389,100 (370,000)

13 (73,100) 248,600 (402,900)

14 (63,900) 274,200 (408,500)

15 (61,600) 267,400 (331,100) (208,600)

16 (52,600) 275,200 (340,100)

17 (45,800) 249,200 (317,700)

18 (48,700) 251,700 (325,900)

19 (39,800) 243,800 (267,200)

20 (37,400) 204,400 (238,300) (140,400)

21 (31,600) 223,400 (216,300)

22 (26,800) 189,500 (194,700)

23 (20,000) 195,700 (175,200)

24 (15,400) 180,900 (155,700)

25 (7,200) 149,300 (144,200) (72,900)

26 (1,100) 142,200 (126,800)

27 4,600 136,800 (90,800)

28 11,300 107,800 (73,400)

29 18,000 78,500 (35,600)

30 25,500 70,900 (10,900) 6,000

74

Social Costs of Replacement at 7%

(Based on Throughput)

CsCl Age

(Year)

Mean Cost

(Dollars)

Maximum Cost

(Dollars)

Minimum Cost

(Dollars)

Lower 5% Bound

(Dollars)

1 (296,500) 515,500 (1,013,200) (687,000)

2 (287,700) 427,600 (952,600)

3 (265,900) 525,100 (951,000)

4 (269,200) 552,200 (934,800)

5 (238,600) 484,100 (876,500) (610,400)

6 (248,000) 464,500 (871,000)

7 (236,300) 552,400 (878,100)

8 (216,700) 498,700 (796,500)

9 (210,900) 449,500 (809,800)

10 (198,400) 451,000 (736,700) (544,300)

11 (175,100) 455,300 (747,400)

12 (168,600) 530,300 (698,500)

13 (154,100) 605,200 (735,700)

14 (132,400) 583,500 (684,300)

15 (116,800) 451,600 (656,800) (428,400)

16 (92,700) 523,000 (616,800)

17 (70,800) 548,800 (564,100)

18 (63,700) 553,700 (587,100)

19 (33,600) 515,100 (507,100)

20 (10,500) 544,400 (426,700) (259,400)

21 11,900 518,100 (398,600)

22 36,300 461,400 (359,900)

23 61,400 486,300 (298,500)

24 88,300 500,200 (262,200)

25 127,500 506,000 (170,400) (38,300)

26 158,800 504,800 (118,300)

27 193,400 495,400 (42,600)

28 232,100 495,400 14,600

29 272,500 510,800 99,200

30 315,800 529,700 153,300 206,900

75

Private Costs of Replacement at 3%

(Based on Throughput)

CsCl Age

(Year)

Mean Cost

(Dollars)

Maximum Cost

(Dollars)

Minimum Cost

(Dollars)

Lower 5% Bound

(Dollars)

1 15,000 638,600 (585,300) (277,400)

2 10,800 796,400 (529,000)

3 13,200 665,100 (516,000)

4 21,800 743,200 (537,000)

5 23,000 607,100 (548,700) (245,500)

6 18,500 676,500 (572,200)

7 20,500 637,500 (448,800)

8 33,500 489,300 (380,700)

9 31,000 482,100 (380,600)

10 27,800 575,700 (434,300) (187,100)

11 30,000 595,900 (414,100)

12 33,900 489,800 (343,600)

13 47,300 551,800 (325,800)

14 37,100 442,400 (317,400)

15 35,900 486,500 (312,800) (145,000)

16 39,400 518,300 (307,600)

17 42,600 458,900 (267,400)

18 37,800 445,000 (298,600)

19 37,300 381,100 (164,500)

20 38,700 329,000 (183,200) (80,200)

21 38,700 333,700 (152,300)

22 39,700 274,900 (134,900)

23 42,700 276,500 (107,500)

24 38,200 223,000 (119,600)

25 36,500 218,500 (92,300) (33,900)

26 35,100 192,700 (71,100)

27 33,600 171,000 (63,100)

28 32,300 137,100 (32,000)

29 30,200 101,900 (23,900)

30 27,700 70,100 (6,200) 7,800

76

Social Costs of Replacement at 3%

(Based on Throughput)

CsCl Age

(Year)

Mean Cost

(Dollars)

Maximum Cost

(Dollars)

Minimum Cost

(Dollars)

Lower 5% Bound

(Dollars)

1 42,300 949,000 (673,300) (350,000)

2 46,800 859,500 (642,300)

3 56,300 795,900 (760,400)

4 72,100 936,900 (812,900)

5 77,400 833,600 (636,900) (283,300)

6 80,400 876,700 (644,800)

7 91,600 925,900 (537,900)

8 116,900 774,000 (424,700)

9 118,600 742,900 (426,300)

10 120,600 792,900 (430,600) (176,500)

11 133,100 869,300 (414,400)

12 145,200 817,600 (414,700)

13 174,700 869,100 (407,900)

14 172,800 725,700 (347,100)

15 183,300 744,000 (366,300) (69,200)

16 192,700 851,300 (323,200)

17 203,500 744,400 (280,100)

18 214,400 694,100 (300,600)

19 224,100 788,300 (129,500)

20 238,300 650,500 (93,800) 41,600

21 248,000 679,000 (75,300)

22 260,900 648,800 (69,700)

23 275,400 626,300 (15,200)

24 286,400 606,100 (26,700)

25 297,200 583,400 33,700 152,300

26 310,700 578,000 83,800

27 323,700 573,400 117,300

28 339,000 582,800 152,800

29 350,000 547,500 191,200

30 363,600 540,500 205,900 254,700

77

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

78

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

79

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.

80

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

81

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

82

/* 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"

83

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'

84

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

85

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

86

/* 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'

87

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

88

*/

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

89

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

}

90

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

91

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

92

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

*/

93

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

94

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

95

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"

96

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()

97

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

98

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

99

*/

/* 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

100

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

101

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

102

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

103

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

*/

104

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

105

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

106

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