Post on 19-Jun-2015
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Is the Rate of Events of Terrorism Increasing?
Brandon R. Theiss, PEBrandon.Theiss@Rutgers.edu
About the Data Set
• The Global Terrorism Database (GTD) is an open-source database including information on terrorist events around the world from 1970 through 2012 (with additional annual updates planned for the future). Unlike many other event databases, the GTD includes systematic data on domestic as well as transnational and international terrorist incidents that have occurred during this time period and now includes more than 113,000 cases.
http://www.start.umd.edu/gtd/
How Terrorist Event Defined
• The GTD defines a terrorist attack as the threatened or actual use of illegal force and violence by a non state actor to attain a political, ‐economic, religious, or social goal through fear, coercion, or intimidation. In practice this means in order to consider an incident for inclusion in the GTD, all three of the following attributes must be present:• The incident must be intentional – the result of a conscious calculation on the
part of a perpetrator.• The incident must entail some level of violence or threat of violence including ‐
property violence, as well as violence against people.• The perpetrators of the incidents must be sub national actors. ‐ This database
does not include acts of state terrorism.
A note about 1993
• The original Pinkerton Global Intelligence Services (PGIS) data, upon which the 1970-1997 GTD data are based, consisted of hard-copy index cards, which were subsequently coded electronically by START researchers. Unfortunately, the set of cards for 1993 was lost prior to PGIS handing the data over to START
Limiting the Data
• Only Events that happened in the USA• Only Serious Events• At least one injury or• At least one fatality or• >$500,000 in Damage (inflation adjusted)
• Reduced to 160 observations
How to make sense of this data?
Industrial Engineering Approach to Analyzing Data• Control Charts- Shewhart charts are used to determine the extent of
common cause variation and identify possible points that have an assignable tool. It is a tool that allows for the critical few to be separated from the trivially many• CUSUM Chart - typically used for monitoring change detection• EWMA Chart - tracks the exponentially-weighted moving average of all prior
sample means• C- Chart - used to monitor the total number of events occurring in a given unit
of time
Dec-09Dec-05Dec-01Dec-97Dec-93Dec-89Dec-85Dec-81Dec-77Dec-73Jan-70
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Date
Events
Time Series Plot of Events
Events 1970- 2012
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Decade
Count
172526
92Count of Events by Decade
Number of Events by Decade
J an-10Jan-06Jan-02Jan-98Jan-94Jan-90Jan-86Jan-82Jan-78Jan-74Jan-70
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Date
Cum
ula
tive S
um
0UCL=1.60LCL=-1.60
CUSUM Chart of Events
Does a CUSUM chart Indicate a Change?
Not very useful as the chart signals on every point!
J an-10Jan-06Jan-02Jan-98Jan-94Jan-90Jan-86Jan-82Jan-78Jan-74Jan-70
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Date
EWM
A
__X=0.333
UCL=0.732
LCL=-0.066
EWMA Chart of Events
What about the EWMA?
Does present a meaningful signal. However for greater than expected number of events
λ=0.2
J an-10Jan-06Jan-02Jan-98Jan-94Jan-90Jan-86Jan-82Jan-78Jan-74Jan-70
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ple
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_C=0.333
UCL=2.063
LCL=0
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C Chart of Events
What about the C Chart?
Signals on fewer points than EWMA. Still only signals for greater number of events
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Date
Elapse
d
Time Series Plot of Elapsed
Looking at the time between terrorism events (inter arrival rate)
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Elapsed
Frequency
Histogram of Elapsed
Inter Arrival Rate
Has the general appearance of a Poisson or Geometric Distribution with outliers
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/199
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/198
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1980
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1970
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ple
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_C=86.2UCL=114.0LCL=58.3
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C Chart of Elapsed
C Chart of Inter Arrival Rate
Signals on the majority of points! Not very useful
G Control Charts
• Developed and evaluated for the monitoring the number of cases between hospital acquired infections and other adverse health events• Also can be used to monitor the number of days between events • Used to analyze rare events• Assumes that the data follows a geometric-type distribution• Assumes that the opportunities are reasonably constant.
1/2/
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Date
Days
Betw
een E
vents
CL=57.8
UCL=559.3
LCL=0
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2222222222222222222222222
G Chart of DateEvent Probability = 0.012
G Chart of Inter Arrival Rate
Signals when there is a large number of days between events
Category81
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Chart of Observed and Expected Values
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ibute
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alu
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Chart of Contribution to the Chi-Square Value by Category
Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Count N DF Chi-Sq P-Value158 26 259.591 0.000
Compared to a Geometric Distribution with a probability of 0.0117232
Does the inter arrival rate follow a Geometric Distribution?
2000199019801970
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Decade
Elapse
d
202.588149.958
113.76939.7582
Boxplot of Elapsed
Is the number of days between events constant across decades?
Kruskal-Wallis Test on Elapsed
Decade N Median Ave Rank Z1970 91 20.00 59.8 -6.301980 26 104.00 102.6 2.811990 24 110.00 108.1 3.332000 17 91.00 109.2 2.84Overall 158 79.5
H = 40.01 DF = 3 P = 0.000H = 40.02 DF = 3 P = 0.000 (adjusted for ties)
Is the difference statistically significant?
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een E
vents
CL=27 CL=81 CL=78CL=143
UCL=268
UCL=781 UCL=753
UCL=1371
LCL=0 LCL=0 LCL=0 LCL=0
1970 1980 1990 2000
222222222222222222
G Chart of Date by DecadeEvent Probability = 0.024, 0.008, 0.009, 0.005
Dividing the arrival rate into stages by decade
ObamaBush IIClintonBushReaganCarterFordNixon
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President
Count
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Chart of President
The Number of Events by President in Office
ObamaBush IIClintonBushReaganCarterFordNixon
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President
Elapse
d
211204.214
121.944
222.25
138.526
57.2482.181825.9516
Boxplot of Elapsed
The Inter Arrival Rate by President in Office
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Days
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een E
vents
CL=18CL=52 CL=40 CL=99CL=119 CL=74CL=159UCL=177
UCL=500UCL=386
UCL=950
UCL=1141
UCL=716
UCL=1526
LCL=0LCL=0 LCL=0 LCL=0LCL=0 LCL=0LCL=0
Ford Carter Reagan BushClinton Bush IINixon
222222222
G Chart of Date by PresidentEvent Probability = 0.037, 0.013, 0.017, ..., 0.004
Dividing the arrival rate into stages by President in Office
Restricting To Only Events With Fatalities
Dec-09Dec-05Dec-01Dec-97Dec-93Dec-89Dec-85Dec-81Dec-77Dec-73Jan-70
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Mon-Year
Events
Time Series Plot of Events
59 events where at least one individual was killed
Fatal Events 1970- 2012
J an-10J an-06J an-02J an-98J an-94J an-90J an-86J an-82J an-78J an-74J an-70
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ple
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_C=0.123
UCL=1.173
LCL=0
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C Chart of Events
C Chart of Fatal Events by Month
Again signal that the 1970s had unusually high occurrences of terrorism
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Elapse
d
Time Series Plot of Elapsed
Looking at the time between fatal events (inter arrival rate)
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Frequency
Histogram of Elapsed With Fatalities
Inter Arrival Rate of Fatal Events
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Sam
ple
Count
_C=233UCL=278LCL=187
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1111
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11111111
111111111111
C Chart of Elapsed
C Chart of Fatal Events
Signals on almost every point!
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8/7/
1987
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Date
Days
Betw
een E
vents
CL=173
UCL=1658
LCL=0
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222
G Chart of DateEvent Probability = 0.004
G Chart of Fatal Events
Signals again that the 1970s had a high rate of events. Also signals that the ’00 had a lower rate
2000199019801970
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Decade
Count
2
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Chart of Decade
Fatal Events by Decade
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12/31/
1972
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Date
Days
Betw
een E
vents
CL=63 CL=177CL=397
UCL=610
UCL=1697
UCL=3791
LCL=0 LCL=0 LCL=0
1970 1980 1990
22
G Chart of Date by DecadeEvent Probability = 0.011, 0.004, 0.002
G Chart of Fatal Events by Decade
ObamaBush IIClintonBushReaganCarterFordNixon
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President
Elapse
d2818
803
548419.5
274.444168.111
274
55.8889
Boxplot of Elapsed
Fatal Events by President in Office
7/27
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Date
Days
Betw
een E
vents
CL=40CL=412
CL=131 CL=225CL=267CL=569UCL=386
UCL=3940
UCL=1262
UCL=2150UCL=2553
UCL=5437
LCL=0LCL=0 LCL=0 LCL=0LCL=0LCL=0
Nixon FordCarter Reagan Bush Clinton
22
G Chart of Date by PresidentEvent Probability = 0.017, 0.002, 0.005, ..., 0.001
G Chart of Fatal Events by Decade
Conclusion
• Social and Political Science Researchers are presented with challenges of analyzing large data sets• Industrial Engineering Tools Techniques and methods can be
effectively used to analyze these data in novel ways• Like in a traditional industrial engineering context, using and analyzing
data with the proper tool can result in better outcomes for the customer
Questions?
Contact Information:Brandon R. Theiss, PE
Rutgers School of Law- CamdenBrandon.Theiss@Rutgers.edu
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Histogram of Elapsed
Panel variable: Decade
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Histogram of ElapsedDecade = 1970
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CL=27.2
UCL=268.0
LCL=022
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G Chart of DateEvent Probability = 0.024
Category25
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Chart of Observed and Expected Values
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d V
alu
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Chart of Contribution to the Chi-Square Value by Category
Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: C-Obs
N DF Chi-Sq P-Value91 24 37.7535 0.037