Table of Contents
Roderick H. MacDonald, Jr.
Initiative for System Dynamics in the Public Sector
Center for Policy Research
Rockefeller College of Public Affairs and Policy
University at Albany
135 Western Avenue
Albany, New York 12222
Rod @isdps.org
Anne M. Dowling
Institute for Traffic Safety Management and Research
Rockefeller College of Public Affairs and Policy
University at Albany
80 Wolf Road, Suite 607
Albany, New York 12205
Abstract
One of the most difficult tasks system dynamicists have is presenting the key
concepts of system dynamics to senior decision makers quickly. The paper presents
three, very small, stock and flow models that were developed quickly and used in
presentations to senior managers of New York State government agencies to show them
the potential power of developing formal models to address key issues. The first model
shows senior managers how their view of a program’s performance could be inaccurate,
and offers an alternative explanation that was not obvious prior to model development.
The second model shows how a successful policy would appear to fail when measured
using system stocks. The third model provides an example of how a small stock and flow
model was used to obtain the confidence of an expert advisory group unfamiliar with the
system dynamics methodology. These small models represent the beginning of what the
authors hope is a growing number of small formal models that can be used to identify
insights that highlight the power of system dynamics for those working in the public
sector.
Lessons from Simple Stock and Flow Models
Introduction
One of the most powerful tools system dynamicists have is the ability to quickly
identify and map important stocks and the behavior of those stocks over time. Andersen
Page 1 of 24
and Richardson (1997) begin their group modeling interventions with simple stock and
flow models, they refer to them as concept models, in order to quickly get a group up to
speed on the use of system dynamics icons, structure generating behavior, and formal
simulation. Homer (1993) developed a formal system dynamics model to examine the
issue of the prevalence of cocaine use in the United States, yet a simple stock and flow
structure of people who have ever used cocaine shows how self-report surveys can be
inaccurate. Forrester begins World Dynamics by identifying the key stocks. Warren
(2001) argues that identifying the key stocks is important from a strategic perspective
while Randers (1980) advocates that simple models capable of simulation should be built
as quickly as possible during a formal system dynamics modeling project. Sweeney and
Sterman (2000) have found that graduate students from an elite business school have
difficulty understanding stock and flow concepts. Ossimitiz (2002) has also conducted
empirical research that indicates that the subjects tested had difficulty in stock and flow
thinking. Building on these perspectives, this paper examines three small formal stock
and flow models that were developed within hours of being given the problem statement
and that quickly provided insights to different clients.
Model 1: Waiver Slots Model
The New York State Office of Mental Health developed a pilot program for
children with psychiatric problems that would provide children and their immediate
families with intensive case management services. This program targeted children
requiring a psychiatric intervention that was less than hospitalization, but more than what
was currently available in existing programs. The program was designed to save money
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by reducing the number of psychiatric hospitalizations (these are high cost services),
while at the same time providing opportunities to meet the treatment needs of these
children.
The pilot program was designed to accommodate a maximum of 125 children. It
was structured so that children presenting themselves at hospitals in need of psychiatric
services would be evaluated based on a set of standard evaluation practices. Through the
evaluation process, these children would be divided into one of three groups: 1) children
requiring immediate psychiatric hospitalization; 2) children not needing immediate
psychiatric hospitalization, but deemed in need of intensive case management services; or
3) children not requiring any mental health services.
The program provided services to those children in Group 2, with Group 2 being
further broken down into two categories. Although the standard evaluation practices
used were considered state of the art, they were not deemed to be fool proof. It was
possible that some children deemed eligible for the intensive case management program
would not respond to this treatment and would end up requiring a psychiatric
hospitalization to meet their needs. The rest of the children entering the program would
be suitable and would respond well to this form of treatment.
Furthermore, experts setting up the program assumed that the program would
work for only two-thirds of the children. In addition, the program experts thought that it
would take four months to determine that the program was not working for a child.
Children for whom the program worked would remain in the intensive case management
treatment program for an average of nine months before being discharged.
Page 3 of 24
Since it was designed as a pilot program, an evaluation of the program was
scheduled to be conducted after the program had been in operation 18 months. The
purpose of the evaluation was to determine whether the program was functioning as
anticipated and whether it should be replicated in other parts of the state. The author was
asked to spend a few hours with the evaluation team, comment on the data that were
collected, and provide a feedback perspective on the program’s operation.
Although the experts initially anticipated that the program was going to be
appropriate for two-thirds of the children entering the program, the evaluation found that
the program was appropriate for 84 percent of the children receiving services. After
some discussion, the experts concluded that this higher rate was due to the screening
procedures used at intake. Furthermore, they decided that the screening procedures and
the personnel using them warranted closer examination to determine if this could be
replicated in other programs with similar clientele.
The stock and flow model contained in Figure 1 was quickly (about 2 hours of
listening and modeling) developed to examine how patients flowed through the system.
As this was a new program starting out with no participants and growing to a maximum
of 125, the author was originally interested in capturing the growth of the program and
thinking about the transitions that would need to occur in order to move the program
from a start-up endeavor to one that functioned in equilibrium.
The model was built based on two primary assumptions: 1) the program would
not be suitable for one-third of the participants and they would leave after four months,
and 2) the program would work for two-thirds of the clients and they would leave after
Page 4 of 24
nine months of treatment. The simulation model generated output that was very close to
that collected through the evaluation.
Figure |
Stock and Flow Model of the Waiver Program
Time in Program
for High Need
Children
Waiver Slots
x | For High Need >)
Peay te Rate of High
, Enrolled f hy ey
New Children ff Average High
Enrolled Probability of Being Total Children Need Children
High Need
f \ a
is Waiver Slots
| For Lower > O)
Rate of Lower Need Children :
Need Children Rate of Lower
Enrolled Need Children
Discharged
SX _ Tine in Program
for Lower Need
‘tes Children
Children
Openings
Time to Enroll Children
Capacity
Adjustment Time
for Openings
The simulation model showed that by month twelve (see Graph 1) the program
had reached an equilibrium whereby 85 percent of the participants were suitable for the
program and 15 percent were not suitable. Since the model did not change any intake
parameters, an explanation for this behavior had to be found elsewhere.
An analysis of the model indicated that the 85/15 percent breakdown occurred due
to the differences in the length of stay each population had in the model. Since the
Page 5 of 24
program was determined not to be suitable for a child after four months, the child was
discharged to a psychiatric hospital for more intensive services and his or her spot
became available. There was a two-thirds probability that this opening would go to a
child whose needs could be met by the program. It soon became readily apparent that
this was the reason that the program appeared to be meeting the needs of more children
than originally anticipated. The model offered a different explanation than that originally
identified (i.e., a better intake process). It showed that the leverage in this system is in
the time delays in identifying those children for whom the program is inappropriate.
Reducing these time delays results in services being provided to more children for whom
the program is suitable.
Graph 1
Fraction of Kids in Each Program
0.75 a ee
0.5
0.25 Ps
0 2 4 6 8 10 12 14 16 18
Time (Month)
Fraction of Higher Need Children : Base Run ——+——+—_+—._ Dimensionless
Fraction of Lower Need Children : Base Run -@-——-@——*-——-_ Dimensionless
Page 6 of 24
When these results were shared with the senior management team, a light bulb
went off. The team realized that it could have been dealing with a program that was
underperforming and that the reason for the underperformance might not have been
evident from the traditional types of evaluations they were performing. The end result
was that they included a system dynamics modeler on additional evaluations to seek out
similar insights.
Model 2: Tobacco Model
The New York State Health Department runs a number of anti-tobacco programs
aimed at stopping children and young adults from picking up the smoking habit as well as
getting people who currently smoke to stop. In 2001, the New York State Health
Commissioner announced that the agency’s goal was to reduce the number of smokers in
New York State by 50 percent in five years.
Data! are readily available that show 20 percent of youth between ages 11 and 17
smoke, and 22 percent of all adults smoke. Figure 2 contains a stock and flow system
dynamics model that disaggregates the population of New York State into four distinct
groups, which are determined by age and smoking status. The model is based on the
assumption that children enter the system when they turn eleven and age through the
process and live, on average, to age 74. Many people do quit smoking each year, but in
order for 20 percent of youths and 22 percents of adults to smoke, a net increase of 3,000
more adults must start smoking than quit each year.
' These data were obtained from the New York State Department of Health’s RFP number 1341466A
titled, “Independent Evaluation of the New York State Comprehensive Tobacco Use Prevention and
Control Program.”
Page 7 of 24
As an extreme simplification of the system and problems to be addressed, this
model addresses one key question: how to achieve the stated goal of reducing tobacco
dependency by 50 percent in five years. Furthermore, the model focuses on only one
policy - reducing the number of youths who start smoking (Fraction of Youth Becoming
Figure 2
Stock and Flow Structure of the Tobacco Use Aging Chain
g Frouth Who Do
Adults Who g
Not Smoke ‘ >>
ig Yo a Do Not Smoke =
Bo Ree ake Youth Who Never Adults Who do Not
ng sated Ang Ont Smoke Dying From
Natural Causes
Fraction OF Children ‘AvegeTimeto Becoming Smokers re bind
a Becoming Eleven Who Fraction of Youth age Time t9(Capnures all Programs action of Adults c Span ot
ccome Ads ‘wo Smoke St
‘Stoke : ‘med a Adult
NN + ) 7 a
a pm] Youth Who ) ‘als Who yt
<a ‘Stoke x Be Awl >
Sogn Smoking Youth ss Adults Dying fom
‘Smoke > Agog ot ‘Natural Causes:
Eleven Who Smoke). Since this policy lever was selected based on the notion that
smoking is an addiction, getting youth to not start smoking should be much simpler than
getting people who are already smoking, both youth and adults, to stop smoking. The
simple stock and flow model allowed us to reduce the Fraction of Youth Becoming
Eleven Who Smoke from its initial value of .2 to zero. Stopping youth from becoming
smokers would seem to be a very effective policy. The output in Graph 2 shows what
happens over a ten-year period when no new youth start to smoke. There is almost no
change in the total fraction that smoke. The reason for this is simple. Success is
measured in terms of stocks that have a very long residency time. It takes time for youth
to become adults and it takes time for those who already smoke to leave the system.
Therefore, a policy that would be expected to be extremely effective does not appear to
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move the system toward achieving the Health Department’s goal of reducing the number
of smokers in New York State by 50 percent in five years.
Graph 2
Total Fraction That Smoke With The No New Youth Begin Smoking Policy
0.75
0.5
0.25
0 1 2 3 4 5 6 7 8 9 10
Time (Year)
Total Fraction That Smoke : Youth Smoking Reduced +——+— Dimensionless
Graph 3 indicates that the policy does result in substantial changes in the number
of youth who smoke, but again, it takes time. An astute observer will also notice that the
Fraction of Youth Who Smoke should have gone to zero in seven years, but it does not.
This is due to the formulation in the Smoking Youth Aging Out outflow from the Youth
Who Smoke level. A queuing process or additional disaggregating would be more
appropriate, but would lead to greater detail that was not deemed appropriate for the
model’s purpose, i.e. showing Health Department officials how focusing policy
statements on obvious stocks in the system could be a mistake. Although the model has a
number of limitations, it served its purpose. The model showed how a system dynamics
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model could be useful and how measuring the effectiveness of a policy in terms of rates
is more realistic than measuring it in terms of stocks when the average residency in
stocks is long.
Graph 3
Fraction of Youth Smoking With The No New Youth Begin Smoking Policy
0.2
0.15
0.1
0.05
0 1 2 3 4 5 6 7 8 9 10
Time (Year)
Fraction of Youth Who Smoke : Youth Smoking Reduced —+— Dimensionless
Model 3: Child Safety Seats
The National Highway Traffic Safety Administration (NHTSA) recently”
announced that great strides in child passenger safety had been made due in large part to
child safety seat programs implemented at the state level. NHTSA reported that 2,658
children under 16 died in traffic crashes nation-wide in 2001, representing a 5.4 percent
? National Highway Traffic Safety Administration Press release on February 12, 2003: GHSA News
Release re New State CPS Program Assessment Tool.
Page 10 of 24
reduction from the previous record low of 2,811 set in 2000. New York State established
a child safety seat program in the late 1990s, and over the last few years it has seen
dramatic growth and development. As a result, a number of issues and challenges have
arisen with respect to managing and enhancing the program.
To examine the effects of selected laws and policies on the child passenger safety
education program in New York State, it was decided that a simulation model would be
built. The problem to be addressed by the simulation model was: “How do you reduce
trained technician turnover and increase coverage in order to maximize the number of
correctly installed child safety seats in New York State?”
The modeling project is being guided by an Advisory Board comprised of experts
in the field of child passenger safety. Board members have no specific modeling
experience and have never worked with system dynamics models. The model shown in
Figures 3 and 4 was used to introduce the Board members to the potential uses of a
system dynamics model. The model focused on the issue of correctly installed child
safety seat coverage in New York State.
In New York State, there are 2,000 certified child safety seat technicians. Each
year, through child safety seat events and at permanent fitting stations, approximately
7,000 child safety seats are fitted correctly. Furthermore, 3,000 new child safety seats are
given away and fitted into vehicles each year. Therefore, the New York State Child
Passenger Safety Education Program is responsible for insuring that 10,000 additional
children each year are riding in child safety seats that are properly installed.
In New York State, children under the age of four are required to ride in child
safety seats. The number of children under the age of four in New York State, excluding
Page 11 of 24
New York City’, is 728,000. Interviews with experts about the installation of child safety
seats indicates that 90 percent’ of all child safety seats are installed incorrectly. If it is
assumed that the population of New York State will remain relatively constant, it can be
concluded that approximately 15,000 children age out each month and that 15,000 babies
are born and will require child safety seats each month. These assumptions are obviously
wrong as the population of New York State increased from approximately 17 million in
1990 to 18.5 million in 2000 according to census data.
The stock and flow model shown in Figures 3 and 4 was developed to show the
Board how increases in the capacity of the child safety seat program would change the
fraction of child safety seats installed correctly (Fraction Installed Correctly). Using a
slider, project participants were able to increase or decrease the number of child safety
seats installed correctly to see how that change would influence the fraction of safety
seats installed correctly. In addition, it was observed that when the number of seats
installed correctly through the child safety seat program exceeds the number of children
being born each month, 100 percent compliance was still not obtained. This occurred
because of a nonlinearity in the model that reduced the effectiveness of the child safety
seat program as more people participated in the program. It was explained to the project
participants that this nonllinearity was included to capture the idea that as more and more
people participated in the program, those remaining would be more difficult to reach
and/or unwilling to participate.
* New York City was excluded as public transportation is readily available. This is not to say that children
in New York City do not ride in cars, but that calculating actual use would take more resources as this point
than are available.
* Data collected by Stephanie Zaza et al (2001) indicated that 85 percent of child safety seats were installed
incorrectly. The 90 percent figure was used as it was obtained from discussions with members of the
Advisory Board.
Page 12 of 24
Figure 3
Stock and Flow Structure for the Child Safety Seat Model
Child Seats
salad awl
People Incorrectly
Purchasing Child Child Seats No
Seats Longer Needed
Effect of Fraction Installed
Installed Correctly Incorrectly on the Ability to
‘Now Seats Installed by Program Install Correctly
Fraction of Seats cogs
Installed Correctly by
‘Owners
Policy - Number of Seats
Installed Correclty Per Month
Through Child
Program
fety Seat
Cad Sas
Soles ee)
Comet 5
New Seats Conectlytsaled
Installed Correctly Sm Child Safety Seats
wing Out
Figure 4
Additional Structure in the Child Safety Seat Model
FEffect of Fraction Installed
Fraction Installed Fraction Installed Incorrectly on the Ability to
Correctly Incorrectly Install Correctly
Effect of Fraction Installed
Incorrectly on the Ability to
Install Correctly
The participants learned that the number of safety seats installed each year
through the program was only a small fraction of all seats installed (Graph 4).
Furthermore, the simulation model was used to show project participants that the slider
Page 13 of 24
they used represented their system. In the concept model, they could increase the number
of seats installed by moving the slider (the results of increasing the number of seats
installed to 20,000 per month is shown in Graph 5). In the real world, this would require
more events, more training stations, increased utilization of technicians and/or the
training of new technicians. These were the issues that the modeling project was going to
focus on and it was the area in which the project participants were experts.
The model was simple enough that project participants could follow and
understand what was happening. It included information that they provided, real
information from sources they had confidence in, and it told a story that they could
accept. The model also introduced them to stocks, flows, information feedback and
simulation concepts that would be required for the larger modeling project in which they
were going to participate.
Page 14 of 24
Graph 4
Simulation Run With No Changes in the Number of Correctly Installed Child
0.75
0.5
0.25
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Fraction Installed Correctly : Policy Run —++——+_+—__ Dimensionless
Fraction Installed Incorrectly : Policy Run —-2-——-2-——-2——-2-_ Dimensionless
Safety Seats
Simulation Run With Policy itoring 0 Child Safety Seats to be Installed
Per Month
1
0.75
0.5
0.25
0
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Fraction Installed Correctly : Policy Run —-++—-+—_+—_+—__ Dimensionless
Fraction Installed Incorrectly : Policy Run ==®==="®="®=*=_— Dimensionless
Page 15 of 24
Conclusion
The three simple stock and flow models provided insights and valuable
information to client groups that were not obvious before the development of the model.
In the first model, a traditional evaluation indicated that the system performed much
better than expected, and attributed this finding to the ability of program managers to
develop on the job skills that allowed them, over time, to identify incoming clients more
accurately than originally anticipated. The small simulation model, however, showed
that the improvement was due to the structure of the system and not to the managers’
ability to distinguish between different types of clients. The model convinced decision
makers that their initial view was incorrect, that the structure of the system generated the
behavior they observed, not their job skills related to identifying clients more accurately.
The second model was developed to examine a publicly stated policy put forth by
the New York State Health Commissioner that set the goal of reducing tobacco use in
New York State by 50 percent in five years. Aggregating tobacco users and non-tobacco
users into four stocks, the mode was used to test a policy that stopped all youth from ever
beginning to smoke. In testing this policy, the model enabled policy makers to observed
how long it would take to achieve the stated goal. This simple model indicated that
focusing on an absolute change in stocks as a policy goal, in the short-run, is not wise.
Public policy decision makers would be better off focusing on rates of change rather than
system stocks.
The third model showed how a simple model was used to introduce the benefits of
simulation to an expert advisory group. Although small, the model included observed
Page 16 of 24
data and the expert opinions of advisory group members showing how simulation could
be used to observe the behavior of the system given a specific policy.
In sum, these three models show how simple stock and flow models can be used
to gain insights, develop trust, point clients in a different policy direction, and introduce
clients to system dynamics modeling concepts in an environment that leads to changes in
their mental models.
Page 17 of 24
Bibliography
Andersen, D. F., and G. P. Richardson. 1997. Scripts for Group Model Building. System
Dynamics Review 13(2): 107 — 129.
Forrester J. W. 1973. World Dynamics. Cambridge, Pegasus Communications, Inc.
Homer, J. B. 1993. A System Dynamics Model of National Cocaine Prevalence. System
Dynamics Review 9(1): 49 — 78.
Ossimitz, G. 2002. Stock-Flow-Thinking and Reading stock-flow-related Graphs: An
Empirical Investigation in Dynamic Thinking Abilities. System Dynamics
Conference. Palermo, Italy.
Randers, J. 1980. Guidelines for Model Conceptualization. In Elements of the System
Dynamics Method, ed J. Randers., Cambridge, Productivity Press, p. 117-138.
Sweeney, L. B. and J. D. Sterman. 2000. Bathtub dynamics: initial results of a systems
thinking inventory. System Dynamics Review. 16(2): 249-286.
Warren, K. 2002. Competitive Strategy Dynamics. Chichester, John Wiley & Sons Ltd.
Zaza S., D. A. Sleet, R. S. Thompson, D. M. Sosin, J. Bolen. 2001. Reviews of Evidence
Regarding Interventions to Increase Use of Child Safety Seats. American Journal
of Preventive Medicine 21(4S): 31 — 47.
Page 18 of 24
Appendix I
Waiver Model
Adjustment Time for Openings = 2
Units: Month
Fraction of Lower Need Children=
Waiver Slots For Lower Need Children/Total Children
Units: Dimensionless
Rate of High Need Children Enrolled=
(New Children Enrolled*Probability of Being High Need)
Units: People/Month
Capacity = 125
Units: People
Rate of Lower Need Children Enrolled=
( New Children Enrolled*(1-Probability of Being High Need))
Units: People/Month
Fraction of Higher Need Children=
Waiver Slots For High Need Children/Total Children
Units: Dimensionless
New Children Enrolled=
Openings* Initial Difficulty in Program Start Up/Time to Enroll Children
Units: People/Month
Time to Enroll Children = 1
Units: Month
Openings=
Capacity-(SMOOTH(Total Children, Adjustment Time for Openings))
Units: People
f Start Up ([(0,0)-(20,2)],(0,0),(10,1),(19,1))
Units: Dimensionless
Initial Difficulty in Program Start Up = f Start Up (Time)
Units: Dimensionless
Average High Need Children=
Waiver Slots For High Need Children/(Waiver Slots For Lower Need
Children+Waiver Slots For High Need Children)
Units: Dimensionless
Page 19 of 24
Average Length of Stay = (Average High Need Children*Time in Program for High
Need Children)+((1-Average High Need Children)*Time in Program for Lower Need
Children)
Units: Month
Probability of Being High Need = 0.33
Units: Dimensionless
Rate of High Need Children Discharged = Waiver Slots For High Need Children/Time in
Program for High Need Children
Units: People/Month
Rate of Lower Need Children Discharged = Waiver Slots For Lower Need Children/Time
in Program for Lower Need Children
Units: People/Month
Time in Program for High Need Children = 3
Units: Month
Time in Program for Lower Need Children = 9
Units: Month
Total Children = Waiver Slots For High Need Children+Waiver Slots For Lower Need
Children
Units: People
Waiver Slots For High Need Children= INTEG (
Rate of High Need Children Enrolled-Rate of High Need Children Discharged,
0.33)
Units: People
Waiver Slots For Lower Need Children= INTEG (
Rate of Lower Need Children Enrolled-Rate of Lower Need Children Discharged,
0.67)
Units: People
Page 20 of 24
Appendix II
Tobacco Model
Adults Dying from Natural Causes=
Adults Who Smoke/Average Life Span of New York State Adults
Units: People/Year
Additions to Youth Who Never Smoked=
All Children Becoming Eleven This Year*(1-Fraction Of Children Becoming
Eleven Who Smoke)
Units: People/Year
Adults Who Do Not Smoke= INTEG (
+Youth Who Never Smoked Aging Out-Adults Who do Not Smoke Dying From
Natural Causes-"Net Gain in Adults Becoming Smokers (Captures all Programs Aimed at
Adults)", Youth Who Never Smoked Aging Out*Average Life Span of New York State
Adults)
Units: People
Adults Who do Not Smoke Dying From Natural Causes=
Adults Who Do Not Smoke/Average Life Span of New York State Adults
Units: People/Year
Adults Who Smoke= INTEG (
+Smoking Youth Aging Out-Adults Dying from Natural Causes+"Net Gain in
Adults Becoming Smokers (Captures all Programs Aimed at Adults)"\Smoking Youth
Aging Out*Average Life Span of New York State Adults+0.03*Adults Who Do Not
Smoke)
Units: People
All Children Becoming Eleven This Year = 171776
Units: People/Year
Average Life Span of New York State Adults = 56
Units: Year
Average Time to Become Adults = 7
Units: Year
Fraction of Adults who Smoke=
Adults Who Smoke/(Adults Who Smoke+Adults Who Do Not Smoke)
Units: Dimensionless
Fraction Of Children Becoming Eleven Who Smoke=
0.1
Units: Dimensionless
Page 21 of 24
Fraction of Youth Who Smoke=
Youth Who Smoke/(Youth Who Smoke+Youth Who Do Not Smoke)
Units: Dimensionless
"Net Gain in Adults Becoming Smokers (Captures all Programs Aimed at Adults)"=
3000
Units: People/Year
New Youth Beginning to Smoke=
All Children Becoming Eleven This Year*Fraction Of Children Becoming Eleven
Who Smoke
Units: People/Year
Smoking Youth Aging Out=
Youth Who Smoke/Average Time to Become Adults
Units: People/Year
Total Fraction That Smoke=
(Youth Who Smoke+Adults Who Smoke)/Total Population
Units: Dimensionless
Total Population=
Adults Who Do Not Smoke+Adults Who Smoke+Youth Who Do Not
Smoke+Youth Who Smoke
Units: People
Youth Who Do Not Smoke= INTEG (
Additions to Youth Who Never Smoked-Youth Who Never Smoked Aging Out,
1.16098e+006)
Units: People
Youth Who Never Smoked Aging Out=
Youth Who Do Not Smoke/Average Time to Become Adults
Units: People/Year
Youth Who Smoke= INTEG (
New Youth Beginning to Smoke-Smoking Youth Aging Out, 290243)
Units: People
Page 22 of 24
Appendix III
Child Safety Seat Model
Average Length of Time Kids are in Safety Seats = 48
Units: Month
Child Seats Installed Correctly= INTEG (
+New Seats Installed Correctly+Installed Correctly by Program-Correctly
Installed Child Safety Seats Aging Out, New Seats Installed Per Month*Average Length
of Time Kids are in Safety Seats*Fraction of Seats Installed Correctly by Owners)
Units: Safety Seats
Child Seats Installed Incorrectly= INTEG (
+People Purchasing Child Seats-Child Seats No Longer Needed-Installed
Correctly by Program,New Seats Installed Per Month*Average Length of Time Kids are
in Safety Seats*0.9)
Units: Safety Seats
Child Seats No Longer Needed=
Child Seats Installed Incorrectly/Average Length of Time Kids are in Safety Seats
Units: Safety Seats/Month
Correctly Installed Child Safety Seats Aging Out=
Child Seats Installed Correctly/Average Length of Time Kids are in Safety Seats
Units: Safety Seats/Month
Effect of Fraction Installed Incorrectly on the Ability to Install Correctly=
f Effect of Fraction Installed Incorrectly on the Ability to Install Correctly
(Fraction Installed Incorrectly)
Units: Dimensionless
f Effect of Fraction Installed Incorrectly on the Ability to Install Correctly(
[(0,0)(1,1)],(0,0),(0.0487805,0.28 1609),(0.114983,0.62069),(0.212544,0.810345),
(0.344948 ,0.931035),(0.480836,0.97 1264),(0.634146,0.982759),(0.74216,1),(0.902439,),
d,1))
Units: Dimensionless
Fraction Installed Correctly=
Child Seats Installed Correctly/Total Seats
Units: Dimensionless
Fraction Installed Incorrectly=
Child Seats Installed Incorrectly/Total Seats
Units: Dimensionless
Page 23 of 24
Fraction of Seats Installed Correctly by Owners = 0.1
Units: Dimensionless
Installed Correctly by Program=
"Policy - Number of Seats Installed Correctly Per Month Through Child Safety
Seat Program" *Effect of Fraction Installed Incorrectly on the Ability to Install Correctly
Units: Safety Seats/Month
New Seats Installed Correctly=
New Seats Installed Per Month*Fraction of Seats Installed Correctly by Owners
Units: Safety Seats/Month
New Seats Installed Per Month = 15719
Units: Safety Seats/Month
People Purchasing Child Seats=
New Seats Installed Per Month*(1-Fraction of Seats Installed Correctly by
Owners)
Units: Safety Seats/Month
"Policy - Number of Seats Installed Correctly Per Month Through Child Safety Seat
Program" = 0
Units: Safety Seats/Month
Total Seats=
Child Seats Installed Correctly+Child Seats Installed Incorrectly
Units: Safety Seats
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