Designing Airport Checked-Baggage-Screening ... - Semantic Scholar
Designing Airport Checked-Baggage-Screening Strategies Considering System Capability and Reliability Qianmei Feng1,*, Hande Sahin1, and Kailash C. Kapur2 1
Department of Industrial Engineering, University of Houston, Houston, TX 77204, USA 2 Industrial Engineering, University of Washington, Seattle, WA 98195, USA
Abstract Emerging image-based technologies are critical components of airport security for screening checked baggage. Since these new technologies differ widely in cost and accuracy, a comprehensive mathematical framework should be developed for selecting technology or combination of technologies for efficient 100% baggage screening. This paper addresses the problem of setting threshold values of these screening technologies and determining the optimal combination of technologies in a two-level screening system by considering system capability and human reliability. Probability and optimization techniques are used to quantify and evaluate the cost- and risk-effectiveness of various deployment configurations, which is captured by using a system life-cycle cost model that incorporates the deployment cost, operating cost, and costs associated with system decisions. Two system decision rules are studied for a two-level screening system. For each decision rule, two different optimization approaches are formulated and investigated from practitioner’s perspective. Numerical examples for different decision rules, optimization approaches and system arrangements are demonstrated.
Keywords Airport baggage screening; Risk analysis; Threshold values; System capability and reliability; Switching probability
* Corresponding author. Tel.: 1 713 743 2870; Fax: 1 713 743 4190; Email: [email protected]
2
1. Introduction In the wake of terrorism against air transportation, there have been significant changes in both policy and operational environments of aviation security activities that include passenger and baggage screening systems. In accordance with the requirements exposited in the Aviation and Transportation Security Act (ATSA) of 2001, the Transportation Security Administration (TSA) is charged to deploy 100% screening of all checked baggage for explosives by either Explosive Detection Systems (EDS) or Explosive Trace Detection (ETD) machines [1,2]. To meet the requirement of 100% screening, TSA procured and installed about 1,600 EDS and 7,200 ETD machines at over 400 airports through June 2006 [3]. Nevertheless, the significant economic and operational concerns regarding these currently used technologies, such as the prohibitory costs, high error rates and low processing rates, have led TSA to plan improvements in the design of the baggage screening systems and also consider new technologies that offer the opportunity for higher performance and lower cost [4]. To enhance national and even international security, it is critical to design effective baggage screening strategies for maximizing system security under limited resources. Especially for Checked-Baggage-Screening (CBS) systems, the concern of the potential risk associated with error rates of baggage screening systems, namely false alarm and false clear rates, is extremely important. Airport CBS strategies are complex and sensitive in nature due to political, social, and economic consequences of a potential terrorist attack. Hence, all relevant risks, costs and benefits to baggage screening systems and strategies must be appraised in a multi-objective framework [5]. Pertinent metrics should be developed to evaluate the cost, effectiveness, maturity, and efficiency of devices to ensure that they achieve the maximum payoff in improving security for funds spent.
3
Design and analysis of inspection policies for aviation security systems have been studied in literature. Kobza and Jacobson [6] and Jacobson et al. [7] assessed risk and cost-effectiveness of aviation security systems by considering the false alarm and false clear rates as performance measures. To optimally deploy baggage screening security devices at airports, Virta et al. studied the impact of transferring passengers on the outgoing selectee rate by introducing a method for calculating the outgoing selectee rates [8]. The model developed by Virta et al. focused on modeling tradeoffs between screening only the selectee checked-baggage and screening both selectee and nonselectee checked-baggage for a single EDS device, where a cost model was also used to measure the cost and benefit associated with various security configurations [9]. Jacobson et al. extended this work to 100% screening, where tradeoffs between using single-device and two-device systems were studied by utilizing the expected direct cost model [10]. Candalino et al. determined the best selection of technology and optimal number of baggage screening security devices that minimize the expected total cost of the baggage screening strategy by using a cost model including both the direct costs and the indirect costs associated with system errors [11]. In addition to previous studies on risk and cost-benefit analysis, the concern of setting threshold values for continuous security responses were addressed in [12] and [13] for both single-level screening systems as well as two-level screening systems. A comprehensive total cost function was introduced that includes costs associated, not only with purchasing and operating the baggage screening security devices, but also with system decisions, namely false alarms and false clears. The existing study on evaluating the baggage screening systems appears to concentrate exclusively on system capability, without considering system reliability issues associated with specific deployment options. This paper incorporates the influence of human reliability on the deployment strategies, since it affects both the system life-cycle cost and the system false alarm
4
and false clear rates. With the consideration of human reliability, this paper aims to select the optimal baggage screening strategy by assessing the risk and cost-effectiveness of various baggage screening technologies and the combination of these technologies. The optimal threshold values to classify threat and non-threat items are determined for the continuous security responses. The proposed methodology, which is previously applied in manufacturing areas for quality improvement [14,15], combines optimization and statistical techniques for designing effective baggage screening systems. System life-cycle cost, instead of system annual cost [12,13], is developed, which provides a long-term assessment of the cost-effectiveness of a project or a system [16]. For a two-level screening system, two system decision rules are studied, based on which the bags can takes different paths through the system. For each decision rule, two different optimization approaches are formulated and investigated from practitioner’s perspective. The first model aims to minimize the life-cycle cost under the constraint of prespecified false clear rate. The second model minimizes the false clear rate subject to budget constraint on the tangible life-cycle cost of the system. The organization of this paper is as follows. Section 2 presents the principles underlying the model formulation of the problem, followed by the two-level system architecture in Section 3. In Section 4, the life-cycle cost model is formulated. Section 5 introduces two optimization models based on different motivations. In Section 6, numerical examples for sixteen possible arrangements of devices are studied, and analyses are presented for two optimization models. Section 7 concludes the paper providing additional discussions.
2. Problem Formulation The currently used technologies at most U.S. airports for baggage screening are EDS and ETD. However, the constraints on operational efficiency and security levels have prompted TSA
5
to consider alternative technologies based on applications in Europe and Israel, which were also discussed at the Aviation Security Technology Conference in Atlantic City in 2001 [4]. These alternative technologies that utilize automated X-ray imaging include Backscatter X-ray (BX), Coherent Scattering (CS), Dual-energy X-ray (DX), and Multiview Tomography (MVT), among others. The differences of these technologies, such as purchasing cost, operating cost, processing rate and accuracy, should be taken into account when deciding which technology or combination of technologies to deploy. For four image-based screening technologies, i.e., EDS, BX, DX, and MVT, this paper studies the deployment of two-level screening strategies. Continuous responses provided as an output at each level are combined into the system response function. A probability utility function is developed to represent purchasing cost, operating cost, processing rate, and system decision costs associated with risks for evaluating different combinations of these technologies. 2.1. Continuous Responses Image-based screening devices usually provide continuous security responses, such as the matching ratio between the screened item and the image of a known threat item [12,13]. Let X represent the continuous security response from a screening device, and X takes values in [0, 1], where a response close to 0 and 1 suggests a non-threat item and a threat item, respectively [7]. Other values of continuous responses can be rescaled such that 0 ≤ X ≤ 1 [12]. The conditional probability density functions, given a threat or a non-threat item, must be estimated in order to set the screening threshold value that classifies threat items from non-threat ones. A binary variable Z is used to denote the actual status of an item with Z=0 indicating a nonthreat item and Z=1 indicating a threat item. Let f X |Z =1 ( x ) and f X |Z =0 ( x ) represent the conditional probability density functions, given a threat item and a non-threat item, respectively. f X |Z =1 ( x )
6
exhibits a non-decreasing shape and f X |Z =0 (x ) shows a non-increasing shape for 0 ≤ X ≤ 1. These conditional probability density functions can be estimated using sampling procedures over various threat or non-threat items, such as the static grid estimation procedure [7]. In this paper, a family of beta distributions is utilized to model the security responses, since it exhibits many forms including decreasing, unimodal right-skewed, symmetric, uniform, U-shaped, unimodal left-skewed, and increasing shapes [17]. The probability density function of a beta distribution with parameters ρ and τ, Beta (ρ, τ), is given by f ( x | ρ ,τ ) =
Γ(ρ +τ )
Γ ( ρ ) Γ (τ )
x ρ −1 (1 − x )
τ −1
, for 0 ≤ x ≤ 1, ρ > 0,τ > 0 ,
(1)
where Γ(.) is a gamma function. The parameters of beta distribution can be estimated using classical statistical approach on sampling data or utilizing Bayesian inferential method based on both sampling data and prior information. 2.2. Two Types of Errors Like in any other inspection processes, two types of errors can occur in a baggage screening system. The system can allow either a false clear, when a threat item to pass through undetected, or a false alarm, when a non-threat item is not allowed to gain access. Both false alarm and false clear rates impact airport operations negatively. False alarms lead to additional steps being taken, which ultimately affect the cost-effectiveness of the system, whereas false clears have catastrophic social and economic consequences. Ideally, the false clear rate of a baggage screening system should be very close to 0. Additionally, the system can return correct responses, in the form of a true clear by correctly determining that an item does not pose a threat or a true alarm by correctly detecting a threat item.
7
False alarm and false clear rates are determined to a large extend by the upper specification limit or the threshold value, u, on continuous security responses. Bearing a greater security response than the threshold value, an item is specified as a threat item, and the response variable is transformed into an alarm. The general formulation of false alarm and false clear probabilities are:
α ( u ) = P ( alarm|non-threat item ) = P ( X > u | Z = 0 ) =
∫
f X |Z =0 ( x ) dx ,
(2)
x >u
β ( u ) = P ( clear|threat item ) = P ( X ≤ u | Z = 1) =
∫
f X |Z =1 ( x ) dx .
(3)
x ≤u
False alarm and false clear probabilities are affected in the opposite way, i.e. false clear rate can be reduced to the detriment of false alarm rate. Therefore, setting the optimal threshold values to balance two misclassification errors considering all associated costs and risks is an important design issue for enhancing airport security.
3. Two-Level Screening System Architecture In practice, 100% screening on checked baggage is usually performed by deploying one or two levels of screening devices. Previous studies show that two-level screening systems outperform one-level screening systems in terms of security levels, measurement errors and total system costs [6,12]. Therefore, this paper studies a screening strategy consisting of two levels of baggage screening devices. Only one type of device is deployed per level, where the number of devices at each level can be determined by the device capacity and the baggage volume. 3.1. Switching Probability Existing research on evaluating baggage screening systems appears to concentrate exclusively on system capability, without considering system reliability issues associated with
8
both equipment and human (operators), which influence the system performance in significant ways. Human reliability directly influences system availability and accuracy, as well as the performance in terms of system decisions and the overall life-cycle cost. Human performance may degrade due to fatigue and decreased vigilance of the operator. For example, in a multilevel screening system, an item needs to be transferred by an operator to the subsequent screening device. The probability that the item can be successfully switched significantly affects the system performance as shown in Figure 1 and Figure 2. This paper investigates the effects of the switching probability, PS, on the system performance. 3.2. Decision Rules for Two-Level Screening In a two-level screening system, system decisions must be distinguished from the decisions at each level. All bags are inspected at Level 1, and then controlled sampling is used to determine the bags to be inspected at Level 2. In controlled sampling, the decision whether or not to inspect an item at Level 2 may depend on two decision rules, where a system alarm can be defined in two ways [17]: Rule 1: A system alarm is triggered when both devices signal alarms on an item; Rule 2: A system alarm is triggered when any one of the two devices signals an alarm on an item. Although Rule 1 is currently used at most U.S. airports [10], this paper studies both Rule 1 and Rule 2 in order to select the most cost-effective one for implementation in practice. Rule 1: System configuration and system errors Using this rule, the system false alarm probability can be reduced to the detriment of the false clear probability by utilizing additional levels of screening. The two-level screening system configuration for this rule is illustrated in Figure 1. Assumptions of the two-level system using Rule 1 are:
9
All items are screened at Level 1, and only the items that are not cleared from posing a risk, i.e. that trigger an alarm, are switched to be inspected at Level 2.
System alarm is triggered, only if the item triggers an alarm at both levels. More specifically, an item not signaling an alarm at Level 1 does not need to be screened at Level 2 and cleared by the system.
The items to be inspected at Level 2 are determined by the parameters of controlled sampling for Rule 1, which are the probability of alarm at Level 1 for an item and the switching probability.
The alarmed items that fail to be conveyed to Level 2 due to the switching failure will be classified as cleared items. Bags
Device 1 1
No
Alarm? Bags
Device 1 K1
Yes No
Switching? Yes
System Clear
Device 2 1
Alarm?
No
Device 2 K2
Yes System Alarm
Figure 1. Two-Level Screening System Using Rule 1 Based on these assumptions, system false alarm and system false clear probabilities are:
α = P ( system false alarm ) = P ( system alarm | non-threat item ) = P ( L1 alarm ∩ switch works ∩ L2 alarm | non-threat item )
(4)
10
β = P ( system false clear ) = P ( system clear | threat item ) = P ( L1 no alarm| threat item ) + P ( L1 alarm ∩ switch fails | threat item )
(5)
+ P ( L1 alarm ∩ switch works ∩ L2 no alarm | threat item ) where L1 and L2 indicate Level 1 and Level 2, respectively. The upper specifications are set for the continuous security responses from two devices, denoted by u = (u1 , u 2 ) . If the value of a security response is greater than the upper specification T
( X i > u i for i = 1; 2), the i th level signals an alarm. The responses from two levels on the same item are assumed to be independent. Hence, the false alarm and false clear probabilities in Equations (4) and (5) can be calculated as:
α (u ) = PS
∫ ∫f
X 1 |Z = 0
(x1 ) f X |Z =0 (x 2 ) dx1dx 2 ,
(6)
2
x2 > u 2 x1 > u1
β (u ) =
∫f
x1 ≤ u1
X 1 | Z =1
(x1 ) dx1 + (1 − PS ) ∫ f X |Z =1 (x1 ) dx1 + PS ∫ ∫ f X |Z =1 (x1 ) f X |Z =1 (x2 ) dx1 dx 2 . 1
x1 > u1
1
2
(7)
x2 ≤ u 2 x1 > u1
Rule 2: System configuration and system errors
Using Rule 2, any individual alarm in the system will trigger the system alarm. Therefore, system false alarm rate will be increased to the benefit of the system false clear rate by implementing an additional level of screening device. The system configuration for this rule is depicted in Figure 2. The assumptions of system configuration using Rule 2 are:
All bags are screened at Level 1, and only bags that do not trigger alarms are to be switched for further inspection at Level 2.
A system alarm is triggered when any one of devices signals alarm on an item. It means that an item triggering alarm at Level 1 triggers a system alarm and does not need to be screened at Level 2.
11
The parameters of controlled sampling for Rule 2 are the probability of no alarm at Level 1 for an item and the switching probability.
As in Rule 1, the items that fail to be switched are cleared of posing risk. Bags
Device 1 1
Yes
Alarm? Bags
Device 1
Alarm K1
No
Device 2
Switching?
Yes
1
Alarm?
Yes
Device 2 K2
No
No
Clear
Figure 2. Two-Level Screening System Using Rule 2 Accordingly, the probabilities of committing two types of system errors are:
α = P ( system false alarm ) = P ( system alarm | non-threat item ) = P ( L1 alarm | non-threat item )
(8)
+ P ( L1 no alarm ∩ switch works ∩ L2 alarm | non-threat item )
β = P ( system false clear ) = P ( system clear | threat item ) = P ( L1 no alarm ∩ switch works ∩ L2 no alarm | threat item )
(9)
+ P ( L1 no alarm ∩ switch fails | threat item ) Using the upper specifications, the false alarm and false clear probabilities can be calculated as:
α (u ) =
∫f
x1 > u1
β (u ) = PS
X 1 |Z = 0
(x1 ) dx1 + PS ∫ ∫ f X |Z =0 (x1 ) f X |Z =0 dx1 dx 2 , 1
2
(10)
x2 > u 2 x1 ≤ u1
∫ ∫f
x2 ≤ u 2 x1 ≤ u1
X 1 | Z =1
(x1 ) f X |Z =1 (x2 ) dx1 dx 2 + (1 − PS ) ∫ f X |Z =1 (x1 ) dx1 . 2
1
x1 < u1
(11)
12
4. Formulation of Life-Cycle Cost Model
The new and existing technologies used for baggage screening are significantly differentiated by initial investment costs, operating costs, processing rates, and both false alarm and false clear rates. Multiple cost factors should be considered when determining the optimal combination strategy of devices. System cost models are extensively used in literature to evaluate the performance and effectiveness of baggage screening systems. Previous work on measuring the performance of CBS systems deployed the system annual cost [6,12,13]. In this research, a life-cycle cost model is utilized as the performance metric that combines all these important factors and facilitates the evaluation and selection of the optimal combination of technologies. Although these two measurements of system cost are essentially the same, the system life-cycle cost analysis is particularly suitable for the evaluation of alternatives that satisfy a required level of performance but that may have different initial investment costs, operating costs, maintenance and repair costs; and possibly different usage lives [19]. 4.1. Cost Parameters
The sources of life-cycle cost include three main components: deployment cost, operating cost, and system decision cost. The deployment cost of security devices includes both the initial purchasing cost and the maintenance cost such as periodical maintenance to prevent machine breakdowns. The values of both purchasing cost and maintenance cost are assumed to be deterministic that can be obtained from manufacturers. The operating cost consists of inspection cost and switching cost. The inspection cost is the cost of screening each bag with the aid of security personnel, and the value is assumed to be deterministic that can be estimated based on the labor cost and cost of regular equipment operation such as power consumption. The switching cost is defined as the additional cost of transmitting bags to the subsequent screening device when needed, which is random depending
13
on the parameters of controlled sampling including the switching probability and the probability of alarm from Level 1. System decision costs of screening systems arise from different risks. False alarms lead to additional procedures, which cause inconvenience to passengers and increased costs. Efforts need to be carried out to clear a true alarm as well. Such steps can range from having the bag reinspected to the evacuation of all or a portion of a terminal. A false clear occurs when a threat item is actually present but the system fails to detect it. This can result in destructive economic and social consequences. A true clear incurs the least cost, since it requires only regular inspection due to volume processing. Costs associated with system decisions are stochastic depending on the random nature of the events, but the expected values can be obtained based on prior information on airport operations. The notations used to identify the parameters of cost components are listed as follows: 1. Deployment cost of security devices: CD: Purchasing cost of a device CM: Maintenance cost per year of a device 2. Operating cost of security devices: CI: Inspection cost per baggage screened CS: Cost of switching a bag to the subsequent device 3. Costs associated with system decisions: Cα: Cost of a false alarm, or cost of wrongly indicating a threat Cβ: Cost of a false clear, or cost of passing a threat item CTA: Cost of a true alarm, or cost of correctly identifying a threat and addressing it CTC: Cost of a true clear, or cost of passing a non-threat item
14
4.2. Probability Parameters
System decision probabilities and switching probability are significant elements of probability parameters. Additionally, the probability of threat has an indisputable effect on the cost model. The probability that a bag contains a threat item, PT = P(Z = 1), may change according to the specific threat information of the national and international security. For instance, the probability PT may relate to the color-coded threat levels provided by a security warning system: PT is 1 out of 1010 under Code Yellow, and 1 out of 109 under Code Orange [12,13]. 4.3. Volume Parameters
The processing rate of a device is another significant factor in that it affects the volume parameters of the cost model, and ultimately determines the number of devices needed for the system. Given as the number of screened bags per hour, the processing rates are estimated for an EDS machine as 150~200, for a DX machine as approximately 1,500, and for an MVT machine as 1,200~1,800. The annual processing capacity of a device, NC, can be calculated as “processing rate × operating hours per year.” The number of machines required at each level depends on the items to be screened and the processing rate of the technology to be deployed at that particular level. Let Ni indicate the number of items to be screened at the ith level. Then, the number of devices required at the ith level, Ki, can be calculated as K i = ⎡N i / N C ⎤ . Since all checked baggage is subject to inspection at Level 1, N1 equals the maximum volume of checked baggage each year, denoted by N. However, N2 depends on the parameters of controlled sampling and differentiates between two decision rules. Using Rule 1, only the bags triggering an alarm at Level 1 are screened at Level 2. Let PA1 be the alarm probability from Level 1, and we have
PA1 = P( X 1 > u1 | Z = 0)P(Z = 0) + P( X 1 > u1 | Z = 1)P(Z = 1) ,
(12)
15
where P(Z = 1) = PT . For Rule 1, N 2 = N PA1 PS . Similarly, let PNA1 denote the probability that a bag does not trigger an alarm at Level 1 when using Rule 2, and we have PNA1 = P( X 1 < u1 | Z = 0 )P(Z = 0) + P( X 1 < u1 | Z = 1)P(Z = 1) .
(13)
Then, the number of the items to be screened at Level 2 using Rule 2 is N 2 = N PNA1 PS . 4.4. Time Parameters
Time parameters delineate the total life cycle of a particular system. A machine may be replaced every T1 years due to regulation and maintenance policies, or wear out due to mechanical erosion in T2 years. T1 is assumed to be deterministic, whereas T2 is the expected lifetime of a device, which is available to be gathered from manufacturers. Therefore, the lifecycle service time of a device is determined by min(T1 , T2 ) . Let T1i and T2i be the number of years until the replacement and the expected life time of the ith level, respectively. The life-cycle service time of the two-level screening system is determined by min (T1i , T2i ) . i =1,2
Based on the setting of all parameters, the expected life-cycle cost (ELCC) for a two-level system using Rule 1 is expressed as: 2 2 ⎛ 2 ⎞ ELCC1 ( u ) = ∑ K i CDi + ⎜ ∑ K i CM i + ∑ CI i N i + Cs PS PA1 N + ESDC ( u ) ⎟ min (T1i , T2i ) , i =1 i =1 ⎝ i =1 ⎠ i =1,2
(14)
where ESDC (u ) denotes the expected annual system decision cost such that: ESDC (u ) = Cα α (u )(1 − PT ) N + C β β (u ) PT N + C TC (1 − α (u ))(1 − PT ) N + C TA (1 − β (u )) PT N . Similarly, the expected life cycle cost for a two-level system using Rule 2 is stated as: 2 2 ⎛ 2 ⎞ ELCC2 ( u ) = ∑ K i CDi + ⎜ ∑ K i CM i + ∑ CI i N i + Cs PS PNA1 N + ESDC ( u ) ⎟ min (T1i , T2i ) . (15) i =1,2 i =1 i =1 ⎝ i =1 ⎠
16
5. Optimization Models 5.1. Model 1: Expected Life-Cycle Cost Optimization
This optimization problem is modeled through minimizing the expected life-cycle cost of the screening system. The motivation is to use the minimal budget to satisfy the federal agency’s requirement that all screening devices meet a pre-specified false clear standard [7]. Accordingly, a constraint needs to be satisfied, such that β ( u ) ≤ ε , where ε is the pre-specified false clear probability. The set of optimal threshold values are the ones that minimize the expected life-cycle cost of the system. Therefore, a constrained nonlinear optimization model is formulated as: min { ELCC ( u )} u
subject to β ( u ) ≤ ε .
(16)
5.2. Model 2: False Clear Rate Optimization
The deployment of a baggage screening system is usually constrained by budget provided at an airport. Under the budget constraint, the threshold values can be set as low as possible to decrease the false clear rate and accordingly, to increase security level. Therefore, in the second optimization model, the problem of choosing threshold values is formulated to minimize the false clear probability under the budget constraint set on the system life-cycle cost. In most situations, false clears result in catastrophic social and economical consequences, which make the cost of false clear intangible. Although a large number can be assigned to the false clear cost, it is quite challenging to specify a specific value. Hence, the tangible life-cycle cost is used in the budget constraint, which does not include the false clear cost, and is denoted by ELCC ′ (u) . The optimization model to minimize the false clear rate with budget constraint is developed as: min β ( u ) u
subject to ELCC ′ ( u ) ≤ B0 ,
(17)
17
where B0 is the maximum available budget set by federal agencies for an airport. Both constrained nonlinear problems can be solved by implementing a Sequential Quadratic Programming (SQP) method provided by a MATLAB function fmincon [20]. The SQP algorithm is chosen because it outperforms many other methods in terms of efficiency, accuracy and percentage of successful solutions [21,22].
6. System Analysis with Numerical Examples In this section, four cases are analyzed for two optimization approaches using two decision rules. Each case examines sixteen arrangements of four image-based technologies that provide continuous security responses: Explosive Detection System (EDS), Backscatter X-ray (BX), Dual-energy X-ray (DX), and Multiview Tomography (MVT). The data are classified into two categories as system parameters and device parameters. The expected values of system parameters, including the costs associated with system decisions, switching cost (CS), probability of threat (PT) and switching probability (PS) are summarized in Table 1. The pre-specified false clear probability (ε) and budget (B0) are also provided. The annual maximum volume of checked baggage, N, is assumed to be 2,625,000. Table 1. System Parameters System parameters N Cα Cβ CTC CTA CS PT PS ε B0
Expected values 2,625,000 $9.16 $3E+10 $0 $1,000,000 $0.01 1.00E-09 0.995 1% $4E+7
18
Device parameters provided in Table 2 include the purchasing cost (CD), the maintenance cost (CM), the inspection cost (CI), the lifetime of device (T1 and T2), and the processing rate (bag/hour) for each of the four devices. The annual processing capacity (NC) and the number of devices required at Level 1 (K1) are calculated based on the processing rate of each technology. Data reported in the tables are representative and obtained from [4] and [10], and the exact values can be secured from manufacturers and TSA. Table 2. Device Parameters Device Parameters
EDS
BX
DX
MVT
ρ (NT)
1
1
1
1
τ (NT)
7
5
4
6
CD
$800,000 $333,333 $500,000 $1,000,000
CM
$125,000 $41,667
$62,500
$80,000
CI
$0.19
$0.09
$0.03
$0.12
T1
10 years
10 years
10 years
10 years
T2
10 years
10 years
10 years
10 years
Nc
394,200
547,500
3,285,000 3,285,000
Processing Rate 180 bags/h 250 bags/h 1500 bags/h 1500 bags/h K1
7
5
1
1
The conditional probability distributions of security responses are modeled using beta distributions. Table 3 provides the parameters of beta distributions for various devices that are chosen to reflect the relative accuracy levels of four technologies. EDS is assumed to have the highest accuracy among these technologies, followed by MVT, BX, and DX, respectively. For instance, the conditional probability distribution for MVT given a threat item is defined as X | Z = 1 ~ Beta (6,1). The shapes of beta distributions are shown in Figure 3. The exact values of these values in real applications can be obtained by statistical estimation based on real data or Bayesian approach based on both prior information and sampling data.
19
Table 3. Parameters in Beta Distributions
Figure 3. Shapes of Beta Distributions For all sixteen arrangements of four technologies, models in (16) and (17) using Rule 1 and Rule 2, respectively, are encoded using MATLAB and solved using sequential quadratic programming methods provided by MATLAB function fmincon.
6.1. Model 1 (Expected Life-Cycle Cost Optimization)
Using the model in (16), the optimal threshold values of security responses (u*) are determined to identify the baggage screening strategies that minimize the expected life-cycle cost of the screening system. Figure 4 and Figure 5 present the optimization results of sixteen arrangements for Rule 1 and Rule 2, respectively. Optimal false alarm probabilities (α*), false clear probabilities (β*), and ELCC* values are illustrated in the figures.
20
LCC($)
α and β alpha
0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00
4.50E+07
beta LCC
4.00E+07 3.50E+07 3.00E+07 2.50E+07 2.00E+07 1.50E+07 1.00E+07
EDS- EDS- EDS- EDS- BX- BX- BX- BX- DX- DX- DX- DX- MVT- MVT- MVT- MVTBX DX MVT EDS EDS DX MVT BX EDS BX MVT DX EDS BX DX MVT
Figure 4. Solutions of Model 1 using Rule 1 LCC($)
α and β 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00
alpha beta LCC
4.50E+07 4.00E+07 3.50E+07 3.00E+07 2.50E+07 2.00E+07 1.50E+07 1.00E+07
EDS- EDS- EDS- EDS- BX- BX- BX- BX- DX- DX- DX- DX- MVT- MVT- MVT- MVTBX DX MVT EDS EDS DX MVT BX EDS BX MVT DX EDS BX DX MVT
Figure 5. Solutions of Model 1 using Rule 2 The results suggest that on average, EDS group has the highest expected life-cycle cost for both decision rules mainly due to relatively high purchasing cost and operating cost of multiple EDS devices. EDS group also results in the lowest false alarm and false clear rates due to the high level of accuracy represented in the beta distribution. All arrangements of BX, DX, and MVT groups for both decision rules provide lower expected cost, except for the BX-DX and DX-DX for Rule 1. However, false alarm and false clear probabilities in other groups are higher than those provided in EDS group. Another observation is that MVT group has the highest cost-
21
effective performance for both Rule 1 and Rule 2, which is mainly due to the fast processing rate and relatively high accuracy of MVT technology. Using Rule 1, MVT-EDS provides the lowest expected life-cycle cost ($1.37 ×107 ) among sixteen arrangements. Therefore, MVT-EDS is the optimal deployment strategy, even though EDS-EDS combination has slightly lower false alarm and false clear (0.0029 and 0.0061) probabilities than those of MVT-EDS (0.0046 and 0.0067). When Rule 2 is deployed, MVTMVT configuration results in the lowest expected life-cycle cost ($1.35 ×107 ) having slightly higher false alarm and false clear rates (0.0090 and 0.0021) than EDS-EDS arrangement (0.0035 and 0.0008). For both decision rules, this indicates that the difference in the expected cost between these two optimal solutions and EDS-EDS comes from the higher deployment and operating costs of EDS devices. Further study shows that average expected costs for device arrangements as well as optimal expected costs do not widely change depending on the decision rules. It can also be observed that Rule 2 outperforms Rule 1 in terms of the security level provided, i.e. false alarm and false clear rates. Therefore, deploying Rule 2 in a two-level screening system is more effective in order to increase the security level. Sensitivity Analysis
The receiver operating characteristic (ROC) curve is used to analyze the sensitivity for the optimal arrangements, MVT-EDS for Rule 1 and MVT-MVT for Rule 2, respectively. In signal detection theory, ROC analysis provides tools to select possibly optimal models and to analyze cost/benefit of diagnostic decision making. ROC curve plots the fraction of true clear vs. the fraction of false alarm for a binary classifier system as its discrimination threshold is varied.
22
As shown in Figure 6 and Figure 7, ROC curves are formed by the most upper-left points. A point on the curve corresponds to the optimal setting of false alarm and false clear rates under different cost parameters. Under the current cost parameters, the optimal solution for MVT-EDS in Model 1 using Rule 1 is indicated in Figure 6, and the optimal solution for MVT-MVT in Model 1 using Rule 2 is shown in Figure 7. u=(0.3132, 0.3605) α=0.0046 β=0.0067
1-β 1
ROC Curve for Rule 1 (MVT-EDS, Ps=0.995)
0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.9
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
α
Figure 6. ROC Curves for MVT-EDS in Model 1 using Rule 1 u=(0.5880, 0.5985) α=0.0090 β=0.0021
1-β 1
ROC Curve for Rule 2 (MVT-MVT, Ps=0.995)
0.995 0.99 0.985 0.98 0.975 0.97 0.965 0.96 0.955 0.95
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
α
Figure 7. ROC Curves for MVT-MVT in Model 1 using Rule 2
23
6.2. Model 2 (False Clear Rate Optimization)
For the model in (17), the optimal threshold values of security responses (u*) are determined to identify the baggage screening strategies that minimize the false clear probability (β*) with the constrained budget. The optimal values of false alarm and false clear rates for Rule 1 and Rule 2 are presented in Figure 8 and Figure 9, respectively. As seen in the figures, EDS group shows lower probabilities compared to the other groups, which is similarly indicated by the results of Model 1. The optimal device configurations that minimize the false clear rate are EDSEDS (0.0051) for Rule 1 and EDS-MVT (0.0000113) for Rule 2. The overall high performance of EDS group in enhancing the security level is mainly due to the high accuracy level. For Model 2, the tradeoff between the security level and the budget constraint needs to be studied, because the risk due to the misclassification errors can be reduced by increasing budget. As shown in Figures 10 and 11, increasing the budget constraint tends to lead to lower false clear rates and consequently lower risks. Another observation is that for the same pre-specified lifecycle cost, Rule 2 provides significantly lower false clear probabilities. Thus, deploying a controlled sampling method defined in Rule 2 is more effective if solely minimizing the false clear rate with a budget constraint is the concern. 0.16 0.15 0.14
alpha beta
0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 EDS- EDS- EDS- EDS- BX- BXBX DX MVT EDS EDS DX
BX- BX- DX- DXMVT BX EDS BX
DX- DX- MVT- MVT- MVT- MVTMVT DX EDS BX DX MVT
Figure 8. Solutions of Model 2 using Rule 1
24 beta
0.0030
0.0025
0.1600
alpha
0.1400
beta alpha
0.1200 0.0020
0.1000 0.0800
0.0015
0.0600
0.0010
0.0400 0.0005
0.0200 0.0000
0.0000 EDS- EDS- EDS- EDS- BX- BX- BX- BX- DX- DX- DX- DX- MVT- MVT- MVT- MVTBX DX MVT EDS EDS DX MVT BX EDS BX MVT DX EDS BX DX MVT
Figure 9. Solutions of Model 2 using Rule 2 β* 0.0065 0.0060
β*
α* 0.0700
α*
0.0600 0.0500
0.0055
0.0400
0.0050
0.0300 0.0200
0.0045
0.0100
0.0040
0.0000 2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
Budget (x10^7)
Figure 10. Sensitivity Analysis for EDS-EDS in Model 2 using Rule 1 β* 0.0008 0.0007
α* β* α*
0.1200 0.1000
0.0006 0.0800
0.0005 0.0004
0.0600
0.0003
0.0400
0.0002 0.0200
0.0001 0.0000
0.0000 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 Budget (x10^7)
Figure 11. Sensitivity Analysis for EDS-MVT in Model 2 using Rule 2
25
7. Conclusions As alternatives of the currently deployed EDS technology, emerging image-based technologies (e.g. DX, BX, and MVT) will serve as critical components of airport security. Since these new technologies are widely different in cost and accuracy provided, a comprehensive mathematical framework is developed for selecting technology or combination of technologies for efficient 100% baggage screening. This paper considers the problem of setting threshold levels of these screening technologies and determining the optimal combination of technologies in a two-level system. Probability and optimization techniques are used to quantify and evaluate the cost- and risk-effectiveness of various deployment configurations. The cost-effectiveness is captured by using a cost model that incorporates the deployment cost, operating cost, and costs associated with system decisions. The objective of the first optimization model is to minimize the cost under the false clear rate constraint. The risk is measured by the probability of system false clears, which is to be minimized in the second optimization model subject to the available budget. Both optimization models are solved for two different decision rules of controlled sampling. The results presented suggest that for a two-level system, Rule 2 outperforms Rule 1 in terms of the security level provided, i.e. false alarm and false clear rates. Therefore, deploying Rule 2 in a two-level screening system is more effective in order to increase the security level. MVT group has the highest cost-effective performance for both Rule 1 and Rule 2, which is mainly due to the fast processing rate and relatively high accuracy of MVT technology. EDS group performs the highest effectiveness in reducing the risk primarily due to the high accuracy level provided by the technology. The random nature of reliability and maintainability of equipment will be considered in future work. The equipment reliability significantly affects the life-cycle cost and maintenance
26
schedule of screening systems. Therefore, it is critical to capture the reliability of equipment as well as human reliability in evaluating different deployment options. Furthermore, the human reliability may differentiate between two decision rules, since the baggage volume to be switched and the perception of security responses will be different. It should also be noted that the above conclusions are drawn based on the representative data for system and device parameters. The system and device information should be verified with device manufacturers and TSA in practice. The values for beta parameters can be estimated for each technology based on real data. Acknowledgements The first author would like to acknowledge the support from the Office of Contracts and Grants at the University of Houston. References [1]
Transportation Security Administration (TSA). (2006). Recommended Security Guidelines for Airport Planning, Design and Construction. Available at http://www.tsa.gov/assets/pdf/airport_security_design_guidelines.pdf. Accessed July 20, 2007.
[2]
U.S. Government Accountability Office (GAO). (2006). Aviation Security: TSA Oversight of Checked Baggage Screening Procedures Could be Strengthened. Report Number GAO06-869. Available at http://www.gao.gov/new.items/d06869.pdf. Accessed July 20, 2007.
[3]
Berrick, C. A. (2006). Aviation Security: TSA Has Strengthened Efforts to Plan for the Optimal Deployment of Checked Baggage Screening Systems, but Funding Uncertainties Remain. Report Number GAO-06-875T. Washington, DC: United States Government Accountability Office (GAO).
[4]
Butler, V., Poole, R. W. (2002). Re-Thinking Checked-Baggage Screening. Policy Study, 297. Los Angeles: Reason Foundation.
[5]
Haimes, Y. Y. (2004). Risk Modeling, Assessment, and Management. New Jersey: John Wiley & Sons.
[6]
Kobza, J. E., Jacobson, S. H. (1997). Probability Models for Access Security System Architectures. Journal of the Operational Research Society, 48, 255-263.
27
[7] [8] [9]
Jacobson, S. H., Kobza, J. E., Easterling, A. S. (2001). A Detection Theoretic Approach to Modeling Aviation Security Problems Using the Knapsack Problem. IIE Transactions, 33, 747-759. Virta, J.E., Jacobson, S.H., Kobza, J.E. (2002). Outgoing Selectee Rates at Hub Airports. Reliability Engineering and System Safety, 76(2), 155-165. Virta, J. L., Jacobson, S. H., Kobza, J. E. (2003). Analyzing the Cost of Screening Selectee and Non-Selectee Baggage. Risk Analysis, 23(5), 897-908.
[10] Jacobson, S. H., Karnani, T., Kobza, J. E., Ritchie, L. (2006). A Cost-Benefit Analysis of Alternative Device Configurations for Aviation-Checked Baggage Security Screening. Risk Analysis, 26(2), 297-310. [11] Candalino, T. J., Kobza, J. E., Jacobson, S. H. (2004). Designing optimal aviation baggage screening strategies using simulated annealing. Computers & Operations Research, 31, 1753-1767. [12] Feng, Q. (2007). On Determining Specifications and Selection of Alternative Technologies for Airport Baggage Screening. Risk Analysis. 27(5), 1-11. [13] Feng, Q., Sahin, H. (2007). Selection of Alternative Technologies for Airport CheckedBaggage-Security Systems. Proceedings of the 2007 Industrial Engineering Research Conference. [14] Feng, Q., Kapur, K.C. (2006). Economic Development of Specifications for 100% Inspection Based on Asymmetric Quality Loss Functions. IIE Transactions, 38(8), 659669. [15] Feng, Q., Kapur, K.C. (2006). Economic Design of Specifications for 100% Inspection with Imperfect Measurement Systems. Quality Technology and Quantitative Management, 3(2), 127-144. [16] Emblemsvag, J. (2003). Life-cycle Costing: Using Activity-based Costing and Monte Carlo Methods to Manage Future Costs and Risks, Hoboken, N.J. John Wiley & Sons, Inc. [17] Martz, H. F., Waller, R. A. (1982). Bayesian Reliability Analysis. John Wiley & Sons, New York, NY. [18] Kobza, J. E., Jacobson, S. H. (1996). Addressing the Dependency Problem in Access Security System Architecture Design. Risk Analysis, 16(2), 801-812. [19] Fuller, S.K., Petersen S. R. (1995). Life-Cycle Costing Manual for the Federal Energy Management Program. U.S. Department of Commerce. [20] The MathWorks, Inc. (2006). Optimization Toolbox User's Guide. Version 3.1, Natick, MA.
28
[21] Nocedal, J., Wright, S.J. (2006). Numerical Optimization. 2nd ed. Springer-Verlag, New York, NY. [22] Powell, M.J.D. (1983). Variable Metric Methods for Constrained Optimization. Mathematical Programming: The State of the Art (A. Bachem, M. Grotschel and B.Korte, eds), 288-311, Springer-Verlag, New York, NY.
Department of Industrial Engineering, University of Houston, Houston, TX 77204, USA 2 Industrial Engineering, University of Washington, Seattle, WA 98195, USA
Abstract Emerging image-based technologies are critical components of airport security for screening checked baggage. Since these new technologies differ widely in cost and accuracy, a comprehensive mathematical framework should be developed for selecting technology or combination of technologies for efficient 100% baggage screening. This paper addresses the problem of setting threshold values of these screening technologies and determining the optimal combination of technologies in a two-level screening system by considering system capability and human reliability. Probability and optimization techniques are used to quantify and evaluate the cost- and risk-effectiveness of various deployment configurations, which is captured by using a system life-cycle cost model that incorporates the deployment cost, operating cost, and costs associated with system decisions. Two system decision rules are studied for a two-level screening system. For each decision rule, two different optimization approaches are formulated and investigated from practitioner’s perspective. Numerical examples for different decision rules, optimization approaches and system arrangements are demonstrated.
Keywords Airport baggage screening; Risk analysis; Threshold values; System capability and reliability; Switching probability
* Corresponding author. Tel.: 1 713 743 2870; Fax: 1 713 743 4190; Email: [email protected]
2
1. Introduction In the wake of terrorism against air transportation, there have been significant changes in both policy and operational environments of aviation security activities that include passenger and baggage screening systems. In accordance with the requirements exposited in the Aviation and Transportation Security Act (ATSA) of 2001, the Transportation Security Administration (TSA) is charged to deploy 100% screening of all checked baggage for explosives by either Explosive Detection Systems (EDS) or Explosive Trace Detection (ETD) machines [1,2]. To meet the requirement of 100% screening, TSA procured and installed about 1,600 EDS and 7,200 ETD machines at over 400 airports through June 2006 [3]. Nevertheless, the significant economic and operational concerns regarding these currently used technologies, such as the prohibitory costs, high error rates and low processing rates, have led TSA to plan improvements in the design of the baggage screening systems and also consider new technologies that offer the opportunity for higher performance and lower cost [4]. To enhance national and even international security, it is critical to design effective baggage screening strategies for maximizing system security under limited resources. Especially for Checked-Baggage-Screening (CBS) systems, the concern of the potential risk associated with error rates of baggage screening systems, namely false alarm and false clear rates, is extremely important. Airport CBS strategies are complex and sensitive in nature due to political, social, and economic consequences of a potential terrorist attack. Hence, all relevant risks, costs and benefits to baggage screening systems and strategies must be appraised in a multi-objective framework [5]. Pertinent metrics should be developed to evaluate the cost, effectiveness, maturity, and efficiency of devices to ensure that they achieve the maximum payoff in improving security for funds spent.
3
Design and analysis of inspection policies for aviation security systems have been studied in literature. Kobza and Jacobson [6] and Jacobson et al. [7] assessed risk and cost-effectiveness of aviation security systems by considering the false alarm and false clear rates as performance measures. To optimally deploy baggage screening security devices at airports, Virta et al. studied the impact of transferring passengers on the outgoing selectee rate by introducing a method for calculating the outgoing selectee rates [8]. The model developed by Virta et al. focused on modeling tradeoffs between screening only the selectee checked-baggage and screening both selectee and nonselectee checked-baggage for a single EDS device, where a cost model was also used to measure the cost and benefit associated with various security configurations [9]. Jacobson et al. extended this work to 100% screening, where tradeoffs between using single-device and two-device systems were studied by utilizing the expected direct cost model [10]. Candalino et al. determined the best selection of technology and optimal number of baggage screening security devices that minimize the expected total cost of the baggage screening strategy by using a cost model including both the direct costs and the indirect costs associated with system errors [11]. In addition to previous studies on risk and cost-benefit analysis, the concern of setting threshold values for continuous security responses were addressed in [12] and [13] for both single-level screening systems as well as two-level screening systems. A comprehensive total cost function was introduced that includes costs associated, not only with purchasing and operating the baggage screening security devices, but also with system decisions, namely false alarms and false clears. The existing study on evaluating the baggage screening systems appears to concentrate exclusively on system capability, without considering system reliability issues associated with specific deployment options. This paper incorporates the influence of human reliability on the deployment strategies, since it affects both the system life-cycle cost and the system false alarm
4
and false clear rates. With the consideration of human reliability, this paper aims to select the optimal baggage screening strategy by assessing the risk and cost-effectiveness of various baggage screening technologies and the combination of these technologies. The optimal threshold values to classify threat and non-threat items are determined for the continuous security responses. The proposed methodology, which is previously applied in manufacturing areas for quality improvement [14,15], combines optimization and statistical techniques for designing effective baggage screening systems. System life-cycle cost, instead of system annual cost [12,13], is developed, which provides a long-term assessment of the cost-effectiveness of a project or a system [16]. For a two-level screening system, two system decision rules are studied, based on which the bags can takes different paths through the system. For each decision rule, two different optimization approaches are formulated and investigated from practitioner’s perspective. The first model aims to minimize the life-cycle cost under the constraint of prespecified false clear rate. The second model minimizes the false clear rate subject to budget constraint on the tangible life-cycle cost of the system. The organization of this paper is as follows. Section 2 presents the principles underlying the model formulation of the problem, followed by the two-level system architecture in Section 3. In Section 4, the life-cycle cost model is formulated. Section 5 introduces two optimization models based on different motivations. In Section 6, numerical examples for sixteen possible arrangements of devices are studied, and analyses are presented for two optimization models. Section 7 concludes the paper providing additional discussions.
2. Problem Formulation The currently used technologies at most U.S. airports for baggage screening are EDS and ETD. However, the constraints on operational efficiency and security levels have prompted TSA
5
to consider alternative technologies based on applications in Europe and Israel, which were also discussed at the Aviation Security Technology Conference in Atlantic City in 2001 [4]. These alternative technologies that utilize automated X-ray imaging include Backscatter X-ray (BX), Coherent Scattering (CS), Dual-energy X-ray (DX), and Multiview Tomography (MVT), among others. The differences of these technologies, such as purchasing cost, operating cost, processing rate and accuracy, should be taken into account when deciding which technology or combination of technologies to deploy. For four image-based screening technologies, i.e., EDS, BX, DX, and MVT, this paper studies the deployment of two-level screening strategies. Continuous responses provided as an output at each level are combined into the system response function. A probability utility function is developed to represent purchasing cost, operating cost, processing rate, and system decision costs associated with risks for evaluating different combinations of these technologies. 2.1. Continuous Responses Image-based screening devices usually provide continuous security responses, such as the matching ratio between the screened item and the image of a known threat item [12,13]. Let X represent the continuous security response from a screening device, and X takes values in [0, 1], where a response close to 0 and 1 suggests a non-threat item and a threat item, respectively [7]. Other values of continuous responses can be rescaled such that 0 ≤ X ≤ 1 [12]. The conditional probability density functions, given a threat or a non-threat item, must be estimated in order to set the screening threshold value that classifies threat items from non-threat ones. A binary variable Z is used to denote the actual status of an item with Z=0 indicating a nonthreat item and Z=1 indicating a threat item. Let f X |Z =1 ( x ) and f X |Z =0 ( x ) represent the conditional probability density functions, given a threat item and a non-threat item, respectively. f X |Z =1 ( x )
6
exhibits a non-decreasing shape and f X |Z =0 (x ) shows a non-increasing shape for 0 ≤ X ≤ 1. These conditional probability density functions can be estimated using sampling procedures over various threat or non-threat items, such as the static grid estimation procedure [7]. In this paper, a family of beta distributions is utilized to model the security responses, since it exhibits many forms including decreasing, unimodal right-skewed, symmetric, uniform, U-shaped, unimodal left-skewed, and increasing shapes [17]. The probability density function of a beta distribution with parameters ρ and τ, Beta (ρ, τ), is given by f ( x | ρ ,τ ) =
Γ(ρ +τ )
Γ ( ρ ) Γ (τ )
x ρ −1 (1 − x )
τ −1
, for 0 ≤ x ≤ 1, ρ > 0,τ > 0 ,
(1)
where Γ(.) is a gamma function. The parameters of beta distribution can be estimated using classical statistical approach on sampling data or utilizing Bayesian inferential method based on both sampling data and prior information. 2.2. Two Types of Errors Like in any other inspection processes, two types of errors can occur in a baggage screening system. The system can allow either a false clear, when a threat item to pass through undetected, or a false alarm, when a non-threat item is not allowed to gain access. Both false alarm and false clear rates impact airport operations negatively. False alarms lead to additional steps being taken, which ultimately affect the cost-effectiveness of the system, whereas false clears have catastrophic social and economic consequences. Ideally, the false clear rate of a baggage screening system should be very close to 0. Additionally, the system can return correct responses, in the form of a true clear by correctly determining that an item does not pose a threat or a true alarm by correctly detecting a threat item.
7
False alarm and false clear rates are determined to a large extend by the upper specification limit or the threshold value, u, on continuous security responses. Bearing a greater security response than the threshold value, an item is specified as a threat item, and the response variable is transformed into an alarm. The general formulation of false alarm and false clear probabilities are:
α ( u ) = P ( alarm|non-threat item ) = P ( X > u | Z = 0 ) =
∫
f X |Z =0 ( x ) dx ,
(2)
x >u
β ( u ) = P ( clear|threat item ) = P ( X ≤ u | Z = 1) =
∫
f X |Z =1 ( x ) dx .
(3)
x ≤u
False alarm and false clear probabilities are affected in the opposite way, i.e. false clear rate can be reduced to the detriment of false alarm rate. Therefore, setting the optimal threshold values to balance two misclassification errors considering all associated costs and risks is an important design issue for enhancing airport security.
3. Two-Level Screening System Architecture In practice, 100% screening on checked baggage is usually performed by deploying one or two levels of screening devices. Previous studies show that two-level screening systems outperform one-level screening systems in terms of security levels, measurement errors and total system costs [6,12]. Therefore, this paper studies a screening strategy consisting of two levels of baggage screening devices. Only one type of device is deployed per level, where the number of devices at each level can be determined by the device capacity and the baggage volume. 3.1. Switching Probability Existing research on evaluating baggage screening systems appears to concentrate exclusively on system capability, without considering system reliability issues associated with
8
both equipment and human (operators), which influence the system performance in significant ways. Human reliability directly influences system availability and accuracy, as well as the performance in terms of system decisions and the overall life-cycle cost. Human performance may degrade due to fatigue and decreased vigilance of the operator. For example, in a multilevel screening system, an item needs to be transferred by an operator to the subsequent screening device. The probability that the item can be successfully switched significantly affects the system performance as shown in Figure 1 and Figure 2. This paper investigates the effects of the switching probability, PS, on the system performance. 3.2. Decision Rules for Two-Level Screening In a two-level screening system, system decisions must be distinguished from the decisions at each level. All bags are inspected at Level 1, and then controlled sampling is used to determine the bags to be inspected at Level 2. In controlled sampling, the decision whether or not to inspect an item at Level 2 may depend on two decision rules, where a system alarm can be defined in two ways [17]: Rule 1: A system alarm is triggered when both devices signal alarms on an item; Rule 2: A system alarm is triggered when any one of the two devices signals an alarm on an item. Although Rule 1 is currently used at most U.S. airports [10], this paper studies both Rule 1 and Rule 2 in order to select the most cost-effective one for implementation in practice. Rule 1: System configuration and system errors Using this rule, the system false alarm probability can be reduced to the detriment of the false clear probability by utilizing additional levels of screening. The two-level screening system configuration for this rule is illustrated in Figure 1. Assumptions of the two-level system using Rule 1 are:
9
All items are screened at Level 1, and only the items that are not cleared from posing a risk, i.e. that trigger an alarm, are switched to be inspected at Level 2.
System alarm is triggered, only if the item triggers an alarm at both levels. More specifically, an item not signaling an alarm at Level 1 does not need to be screened at Level 2 and cleared by the system.
The items to be inspected at Level 2 are determined by the parameters of controlled sampling for Rule 1, which are the probability of alarm at Level 1 for an item and the switching probability.
The alarmed items that fail to be conveyed to Level 2 due to the switching failure will be classified as cleared items. Bags
Device 1 1
No
Alarm? Bags
Device 1 K1
Yes No
Switching? Yes
System Clear
Device 2 1
Alarm?
No
Device 2 K2
Yes System Alarm
Figure 1. Two-Level Screening System Using Rule 1 Based on these assumptions, system false alarm and system false clear probabilities are:
α = P ( system false alarm ) = P ( system alarm | non-threat item ) = P ( L1 alarm ∩ switch works ∩ L2 alarm | non-threat item )
(4)
10
β = P ( system false clear ) = P ( system clear | threat item ) = P ( L1 no alarm| threat item ) + P ( L1 alarm ∩ switch fails | threat item )
(5)
+ P ( L1 alarm ∩ switch works ∩ L2 no alarm | threat item ) where L1 and L2 indicate Level 1 and Level 2, respectively. The upper specifications are set for the continuous security responses from two devices, denoted by u = (u1 , u 2 ) . If the value of a security response is greater than the upper specification T
( X i > u i for i = 1; 2), the i th level signals an alarm. The responses from two levels on the same item are assumed to be independent. Hence, the false alarm and false clear probabilities in Equations (4) and (5) can be calculated as:
α (u ) = PS
∫ ∫f
X 1 |Z = 0
(x1 ) f X |Z =0 (x 2 ) dx1dx 2 ,
(6)
2
x2 > u 2 x1 > u1
β (u ) =
∫f
x1 ≤ u1
X 1 | Z =1
(x1 ) dx1 + (1 − PS ) ∫ f X |Z =1 (x1 ) dx1 + PS ∫ ∫ f X |Z =1 (x1 ) f X |Z =1 (x2 ) dx1 dx 2 . 1
x1 > u1
1
2
(7)
x2 ≤ u 2 x1 > u1
Rule 2: System configuration and system errors
Using Rule 2, any individual alarm in the system will trigger the system alarm. Therefore, system false alarm rate will be increased to the benefit of the system false clear rate by implementing an additional level of screening device. The system configuration for this rule is depicted in Figure 2. The assumptions of system configuration using Rule 2 are:
All bags are screened at Level 1, and only bags that do not trigger alarms are to be switched for further inspection at Level 2.
A system alarm is triggered when any one of devices signals alarm on an item. It means that an item triggering alarm at Level 1 triggers a system alarm and does not need to be screened at Level 2.
11
The parameters of controlled sampling for Rule 2 are the probability of no alarm at Level 1 for an item and the switching probability.
As in Rule 1, the items that fail to be switched are cleared of posing risk. Bags
Device 1 1
Yes
Alarm? Bags
Device 1
Alarm K1
No
Device 2
Switching?
Yes
1
Alarm?
Yes
Device 2 K2
No
No
Clear
Figure 2. Two-Level Screening System Using Rule 2 Accordingly, the probabilities of committing two types of system errors are:
α = P ( system false alarm ) = P ( system alarm | non-threat item ) = P ( L1 alarm | non-threat item )
(8)
+ P ( L1 no alarm ∩ switch works ∩ L2 alarm | non-threat item )
β = P ( system false clear ) = P ( system clear | threat item ) = P ( L1 no alarm ∩ switch works ∩ L2 no alarm | threat item )
(9)
+ P ( L1 no alarm ∩ switch fails | threat item ) Using the upper specifications, the false alarm and false clear probabilities can be calculated as:
α (u ) =
∫f
x1 > u1
β (u ) = PS
X 1 |Z = 0
(x1 ) dx1 + PS ∫ ∫ f X |Z =0 (x1 ) f X |Z =0 dx1 dx 2 , 1
2
(10)
x2 > u 2 x1 ≤ u1
∫ ∫f
x2 ≤ u 2 x1 ≤ u1
X 1 | Z =1
(x1 ) f X |Z =1 (x2 ) dx1 dx 2 + (1 − PS ) ∫ f X |Z =1 (x1 ) dx1 . 2
1
x1 < u1
(11)
12
4. Formulation of Life-Cycle Cost Model
The new and existing technologies used for baggage screening are significantly differentiated by initial investment costs, operating costs, processing rates, and both false alarm and false clear rates. Multiple cost factors should be considered when determining the optimal combination strategy of devices. System cost models are extensively used in literature to evaluate the performance and effectiveness of baggage screening systems. Previous work on measuring the performance of CBS systems deployed the system annual cost [6,12,13]. In this research, a life-cycle cost model is utilized as the performance metric that combines all these important factors and facilitates the evaluation and selection of the optimal combination of technologies. Although these two measurements of system cost are essentially the same, the system life-cycle cost analysis is particularly suitable for the evaluation of alternatives that satisfy a required level of performance but that may have different initial investment costs, operating costs, maintenance and repair costs; and possibly different usage lives [19]. 4.1. Cost Parameters
The sources of life-cycle cost include three main components: deployment cost, operating cost, and system decision cost. The deployment cost of security devices includes both the initial purchasing cost and the maintenance cost such as periodical maintenance to prevent machine breakdowns. The values of both purchasing cost and maintenance cost are assumed to be deterministic that can be obtained from manufacturers. The operating cost consists of inspection cost and switching cost. The inspection cost is the cost of screening each bag with the aid of security personnel, and the value is assumed to be deterministic that can be estimated based on the labor cost and cost of regular equipment operation such as power consumption. The switching cost is defined as the additional cost of transmitting bags to the subsequent screening device when needed, which is random depending
13
on the parameters of controlled sampling including the switching probability and the probability of alarm from Level 1. System decision costs of screening systems arise from different risks. False alarms lead to additional procedures, which cause inconvenience to passengers and increased costs. Efforts need to be carried out to clear a true alarm as well. Such steps can range from having the bag reinspected to the evacuation of all or a portion of a terminal. A false clear occurs when a threat item is actually present but the system fails to detect it. This can result in destructive economic and social consequences. A true clear incurs the least cost, since it requires only regular inspection due to volume processing. Costs associated with system decisions are stochastic depending on the random nature of the events, but the expected values can be obtained based on prior information on airport operations. The notations used to identify the parameters of cost components are listed as follows: 1. Deployment cost of security devices: CD: Purchasing cost of a device CM: Maintenance cost per year of a device 2. Operating cost of security devices: CI: Inspection cost per baggage screened CS: Cost of switching a bag to the subsequent device 3. Costs associated with system decisions: Cα: Cost of a false alarm, or cost of wrongly indicating a threat Cβ: Cost of a false clear, or cost of passing a threat item CTA: Cost of a true alarm, or cost of correctly identifying a threat and addressing it CTC: Cost of a true clear, or cost of passing a non-threat item
14
4.2. Probability Parameters
System decision probabilities and switching probability are significant elements of probability parameters. Additionally, the probability of threat has an indisputable effect on the cost model. The probability that a bag contains a threat item, PT = P(Z = 1), may change according to the specific threat information of the national and international security. For instance, the probability PT may relate to the color-coded threat levels provided by a security warning system: PT is 1 out of 1010 under Code Yellow, and 1 out of 109 under Code Orange [12,13]. 4.3. Volume Parameters
The processing rate of a device is another significant factor in that it affects the volume parameters of the cost model, and ultimately determines the number of devices needed for the system. Given as the number of screened bags per hour, the processing rates are estimated for an EDS machine as 150~200, for a DX machine as approximately 1,500, and for an MVT machine as 1,200~1,800. The annual processing capacity of a device, NC, can be calculated as “processing rate × operating hours per year.” The number of machines required at each level depends on the items to be screened and the processing rate of the technology to be deployed at that particular level. Let Ni indicate the number of items to be screened at the ith level. Then, the number of devices required at the ith level, Ki, can be calculated as K i = ⎡N i / N C ⎤ . Since all checked baggage is subject to inspection at Level 1, N1 equals the maximum volume of checked baggage each year, denoted by N. However, N2 depends on the parameters of controlled sampling and differentiates between two decision rules. Using Rule 1, only the bags triggering an alarm at Level 1 are screened at Level 2. Let PA1 be the alarm probability from Level 1, and we have
PA1 = P( X 1 > u1 | Z = 0)P(Z = 0) + P( X 1 > u1 | Z = 1)P(Z = 1) ,
(12)
15
where P(Z = 1) = PT . For Rule 1, N 2 = N PA1 PS . Similarly, let PNA1 denote the probability that a bag does not trigger an alarm at Level 1 when using Rule 2, and we have PNA1 = P( X 1 < u1 | Z = 0 )P(Z = 0) + P( X 1 < u1 | Z = 1)P(Z = 1) .
(13)
Then, the number of the items to be screened at Level 2 using Rule 2 is N 2 = N PNA1 PS . 4.4. Time Parameters
Time parameters delineate the total life cycle of a particular system. A machine may be replaced every T1 years due to regulation and maintenance policies, or wear out due to mechanical erosion in T2 years. T1 is assumed to be deterministic, whereas T2 is the expected lifetime of a device, which is available to be gathered from manufacturers. Therefore, the lifecycle service time of a device is determined by min(T1 , T2 ) . Let T1i and T2i be the number of years until the replacement and the expected life time of the ith level, respectively. The life-cycle service time of the two-level screening system is determined by min (T1i , T2i ) . i =1,2
Based on the setting of all parameters, the expected life-cycle cost (ELCC) for a two-level system using Rule 1 is expressed as: 2 2 ⎛ 2 ⎞ ELCC1 ( u ) = ∑ K i CDi + ⎜ ∑ K i CM i + ∑ CI i N i + Cs PS PA1 N + ESDC ( u ) ⎟ min (T1i , T2i ) , i =1 i =1 ⎝ i =1 ⎠ i =1,2
(14)
where ESDC (u ) denotes the expected annual system decision cost such that: ESDC (u ) = Cα α (u )(1 − PT ) N + C β β (u ) PT N + C TC (1 − α (u ))(1 − PT ) N + C TA (1 − β (u )) PT N . Similarly, the expected life cycle cost for a two-level system using Rule 2 is stated as: 2 2 ⎛ 2 ⎞ ELCC2 ( u ) = ∑ K i CDi + ⎜ ∑ K i CM i + ∑ CI i N i + Cs PS PNA1 N + ESDC ( u ) ⎟ min (T1i , T2i ) . (15) i =1,2 i =1 i =1 ⎝ i =1 ⎠
16
5. Optimization Models 5.1. Model 1: Expected Life-Cycle Cost Optimization
This optimization problem is modeled through minimizing the expected life-cycle cost of the screening system. The motivation is to use the minimal budget to satisfy the federal agency’s requirement that all screening devices meet a pre-specified false clear standard [7]. Accordingly, a constraint needs to be satisfied, such that β ( u ) ≤ ε , where ε is the pre-specified false clear probability. The set of optimal threshold values are the ones that minimize the expected life-cycle cost of the system. Therefore, a constrained nonlinear optimization model is formulated as: min { ELCC ( u )} u
subject to β ( u ) ≤ ε .
(16)
5.2. Model 2: False Clear Rate Optimization
The deployment of a baggage screening system is usually constrained by budget provided at an airport. Under the budget constraint, the threshold values can be set as low as possible to decrease the false clear rate and accordingly, to increase security level. Therefore, in the second optimization model, the problem of choosing threshold values is formulated to minimize the false clear probability under the budget constraint set on the system life-cycle cost. In most situations, false clears result in catastrophic social and economical consequences, which make the cost of false clear intangible. Although a large number can be assigned to the false clear cost, it is quite challenging to specify a specific value. Hence, the tangible life-cycle cost is used in the budget constraint, which does not include the false clear cost, and is denoted by ELCC ′ (u) . The optimization model to minimize the false clear rate with budget constraint is developed as: min β ( u ) u
subject to ELCC ′ ( u ) ≤ B0 ,
(17)
17
where B0 is the maximum available budget set by federal agencies for an airport. Both constrained nonlinear problems can be solved by implementing a Sequential Quadratic Programming (SQP) method provided by a MATLAB function fmincon [20]. The SQP algorithm is chosen because it outperforms many other methods in terms of efficiency, accuracy and percentage of successful solutions [21,22].
6. System Analysis with Numerical Examples In this section, four cases are analyzed for two optimization approaches using two decision rules. Each case examines sixteen arrangements of four image-based technologies that provide continuous security responses: Explosive Detection System (EDS), Backscatter X-ray (BX), Dual-energy X-ray (DX), and Multiview Tomography (MVT). The data are classified into two categories as system parameters and device parameters. The expected values of system parameters, including the costs associated with system decisions, switching cost (CS), probability of threat (PT) and switching probability (PS) are summarized in Table 1. The pre-specified false clear probability (ε) and budget (B0) are also provided. The annual maximum volume of checked baggage, N, is assumed to be 2,625,000. Table 1. System Parameters System parameters N Cα Cβ CTC CTA CS PT PS ε B0
Expected values 2,625,000 $9.16 $3E+10 $0 $1,000,000 $0.01 1.00E-09 0.995 1% $4E+7
18
Device parameters provided in Table 2 include the purchasing cost (CD), the maintenance cost (CM), the inspection cost (CI), the lifetime of device (T1 and T2), and the processing rate (bag/hour) for each of the four devices. The annual processing capacity (NC) and the number of devices required at Level 1 (K1) are calculated based on the processing rate of each technology. Data reported in the tables are representative and obtained from [4] and [10], and the exact values can be secured from manufacturers and TSA. Table 2. Device Parameters Device Parameters
EDS
BX
DX
MVT
ρ (NT)
1
1
1
1
τ (NT)
7
5
4
6
CD
$800,000 $333,333 $500,000 $1,000,000
CM
$125,000 $41,667
$62,500
$80,000
CI
$0.19
$0.09
$0.03
$0.12
T1
10 years
10 years
10 years
10 years
T2
10 years
10 years
10 years
10 years
Nc
394,200
547,500
3,285,000 3,285,000
Processing Rate 180 bags/h 250 bags/h 1500 bags/h 1500 bags/h K1
7
5
1
1
The conditional probability distributions of security responses are modeled using beta distributions. Table 3 provides the parameters of beta distributions for various devices that are chosen to reflect the relative accuracy levels of four technologies. EDS is assumed to have the highest accuracy among these technologies, followed by MVT, BX, and DX, respectively. For instance, the conditional probability distribution for MVT given a threat item is defined as X | Z = 1 ~ Beta (6,1). The shapes of beta distributions are shown in Figure 3. The exact values of these values in real applications can be obtained by statistical estimation based on real data or Bayesian approach based on both prior information and sampling data.
19
Table 3. Parameters in Beta Distributions
Figure 3. Shapes of Beta Distributions For all sixteen arrangements of four technologies, models in (16) and (17) using Rule 1 and Rule 2, respectively, are encoded using MATLAB and solved using sequential quadratic programming methods provided by MATLAB function fmincon.
6.1. Model 1 (Expected Life-Cycle Cost Optimization)
Using the model in (16), the optimal threshold values of security responses (u*) are determined to identify the baggage screening strategies that minimize the expected life-cycle cost of the screening system. Figure 4 and Figure 5 present the optimization results of sixteen arrangements for Rule 1 and Rule 2, respectively. Optimal false alarm probabilities (α*), false clear probabilities (β*), and ELCC* values are illustrated in the figures.
20
LCC($)
α and β alpha
0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00
4.50E+07
beta LCC
4.00E+07 3.50E+07 3.00E+07 2.50E+07 2.00E+07 1.50E+07 1.00E+07
EDS- EDS- EDS- EDS- BX- BX- BX- BX- DX- DX- DX- DX- MVT- MVT- MVT- MVTBX DX MVT EDS EDS DX MVT BX EDS BX MVT DX EDS BX DX MVT
Figure 4. Solutions of Model 1 using Rule 1 LCC($)
α and β 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00
alpha beta LCC
4.50E+07 4.00E+07 3.50E+07 3.00E+07 2.50E+07 2.00E+07 1.50E+07 1.00E+07
EDS- EDS- EDS- EDS- BX- BX- BX- BX- DX- DX- DX- DX- MVT- MVT- MVT- MVTBX DX MVT EDS EDS DX MVT BX EDS BX MVT DX EDS BX DX MVT
Figure 5. Solutions of Model 1 using Rule 2 The results suggest that on average, EDS group has the highest expected life-cycle cost for both decision rules mainly due to relatively high purchasing cost and operating cost of multiple EDS devices. EDS group also results in the lowest false alarm and false clear rates due to the high level of accuracy represented in the beta distribution. All arrangements of BX, DX, and MVT groups for both decision rules provide lower expected cost, except for the BX-DX and DX-DX for Rule 1. However, false alarm and false clear probabilities in other groups are higher than those provided in EDS group. Another observation is that MVT group has the highest cost-
21
effective performance for both Rule 1 and Rule 2, which is mainly due to the fast processing rate and relatively high accuracy of MVT technology. Using Rule 1, MVT-EDS provides the lowest expected life-cycle cost ($1.37 ×107 ) among sixteen arrangements. Therefore, MVT-EDS is the optimal deployment strategy, even though EDS-EDS combination has slightly lower false alarm and false clear (0.0029 and 0.0061) probabilities than those of MVT-EDS (0.0046 and 0.0067). When Rule 2 is deployed, MVTMVT configuration results in the lowest expected life-cycle cost ($1.35 ×107 ) having slightly higher false alarm and false clear rates (0.0090 and 0.0021) than EDS-EDS arrangement (0.0035 and 0.0008). For both decision rules, this indicates that the difference in the expected cost between these two optimal solutions and EDS-EDS comes from the higher deployment and operating costs of EDS devices. Further study shows that average expected costs for device arrangements as well as optimal expected costs do not widely change depending on the decision rules. It can also be observed that Rule 2 outperforms Rule 1 in terms of the security level provided, i.e. false alarm and false clear rates. Therefore, deploying Rule 2 in a two-level screening system is more effective in order to increase the security level. Sensitivity Analysis
The receiver operating characteristic (ROC) curve is used to analyze the sensitivity for the optimal arrangements, MVT-EDS for Rule 1 and MVT-MVT for Rule 2, respectively. In signal detection theory, ROC analysis provides tools to select possibly optimal models and to analyze cost/benefit of diagnostic decision making. ROC curve plots the fraction of true clear vs. the fraction of false alarm for a binary classifier system as its discrimination threshold is varied.
22
As shown in Figure 6 and Figure 7, ROC curves are formed by the most upper-left points. A point on the curve corresponds to the optimal setting of false alarm and false clear rates under different cost parameters. Under the current cost parameters, the optimal solution for MVT-EDS in Model 1 using Rule 1 is indicated in Figure 6, and the optimal solution for MVT-MVT in Model 1 using Rule 2 is shown in Figure 7. u=(0.3132, 0.3605) α=0.0046 β=0.0067
1-β 1
ROC Curve for Rule 1 (MVT-EDS, Ps=0.995)
0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.9
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
α
Figure 6. ROC Curves for MVT-EDS in Model 1 using Rule 1 u=(0.5880, 0.5985) α=0.0090 β=0.0021
1-β 1
ROC Curve for Rule 2 (MVT-MVT, Ps=0.995)
0.995 0.99 0.985 0.98 0.975 0.97 0.965 0.96 0.955 0.95
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
α
Figure 7. ROC Curves for MVT-MVT in Model 1 using Rule 2
23
6.2. Model 2 (False Clear Rate Optimization)
For the model in (17), the optimal threshold values of security responses (u*) are determined to identify the baggage screening strategies that minimize the false clear probability (β*) with the constrained budget. The optimal values of false alarm and false clear rates for Rule 1 and Rule 2 are presented in Figure 8 and Figure 9, respectively. As seen in the figures, EDS group shows lower probabilities compared to the other groups, which is similarly indicated by the results of Model 1. The optimal device configurations that minimize the false clear rate are EDSEDS (0.0051) for Rule 1 and EDS-MVT (0.0000113) for Rule 2. The overall high performance of EDS group in enhancing the security level is mainly due to the high accuracy level. For Model 2, the tradeoff between the security level and the budget constraint needs to be studied, because the risk due to the misclassification errors can be reduced by increasing budget. As shown in Figures 10 and 11, increasing the budget constraint tends to lead to lower false clear rates and consequently lower risks. Another observation is that for the same pre-specified lifecycle cost, Rule 2 provides significantly lower false clear probabilities. Thus, deploying a controlled sampling method defined in Rule 2 is more effective if solely minimizing the false clear rate with a budget constraint is the concern. 0.16 0.15 0.14
alpha beta
0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 EDS- EDS- EDS- EDS- BX- BXBX DX MVT EDS EDS DX
BX- BX- DX- DXMVT BX EDS BX
DX- DX- MVT- MVT- MVT- MVTMVT DX EDS BX DX MVT
Figure 8. Solutions of Model 2 using Rule 1
24 beta
0.0030
0.0025
0.1600
alpha
0.1400
beta alpha
0.1200 0.0020
0.1000 0.0800
0.0015
0.0600
0.0010
0.0400 0.0005
0.0200 0.0000
0.0000 EDS- EDS- EDS- EDS- BX- BX- BX- BX- DX- DX- DX- DX- MVT- MVT- MVT- MVTBX DX MVT EDS EDS DX MVT BX EDS BX MVT DX EDS BX DX MVT
Figure 9. Solutions of Model 2 using Rule 2 β* 0.0065 0.0060
β*
α* 0.0700
α*
0.0600 0.0500
0.0055
0.0400
0.0050
0.0300 0.0200
0.0045
0.0100
0.0040
0.0000 2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
Budget (x10^7)
Figure 10. Sensitivity Analysis for EDS-EDS in Model 2 using Rule 1 β* 0.0008 0.0007
α* β* α*
0.1200 0.1000
0.0006 0.0800
0.0005 0.0004
0.0600
0.0003
0.0400
0.0002 0.0200
0.0001 0.0000
0.0000 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 Budget (x10^7)
Figure 11. Sensitivity Analysis for EDS-MVT in Model 2 using Rule 2
25
7. Conclusions As alternatives of the currently deployed EDS technology, emerging image-based technologies (e.g. DX, BX, and MVT) will serve as critical components of airport security. Since these new technologies are widely different in cost and accuracy provided, a comprehensive mathematical framework is developed for selecting technology or combination of technologies for efficient 100% baggage screening. This paper considers the problem of setting threshold levels of these screening technologies and determining the optimal combination of technologies in a two-level system. Probability and optimization techniques are used to quantify and evaluate the cost- and risk-effectiveness of various deployment configurations. The cost-effectiveness is captured by using a cost model that incorporates the deployment cost, operating cost, and costs associated with system decisions. The objective of the first optimization model is to minimize the cost under the false clear rate constraint. The risk is measured by the probability of system false clears, which is to be minimized in the second optimization model subject to the available budget. Both optimization models are solved for two different decision rules of controlled sampling. The results presented suggest that for a two-level system, Rule 2 outperforms Rule 1 in terms of the security level provided, i.e. false alarm and false clear rates. Therefore, deploying Rule 2 in a two-level screening system is more effective in order to increase the security level. MVT group has the highest cost-effective performance for both Rule 1 and Rule 2, which is mainly due to the fast processing rate and relatively high accuracy of MVT technology. EDS group performs the highest effectiveness in reducing the risk primarily due to the high accuracy level provided by the technology. The random nature of reliability and maintainability of equipment will be considered in future work. The equipment reliability significantly affects the life-cycle cost and maintenance
26
schedule of screening systems. Therefore, it is critical to capture the reliability of equipment as well as human reliability in evaluating different deployment options. Furthermore, the human reliability may differentiate between two decision rules, since the baggage volume to be switched and the perception of security responses will be different. It should also be noted that the above conclusions are drawn based on the representative data for system and device parameters. The system and device information should be verified with device manufacturers and TSA in practice. The values for beta parameters can be estimated for each technology based on real data. Acknowledgements The first author would like to acknowledge the support from the Office of Contracts and Grants at the University of Houston. References [1]
Transportation Security Administration (TSA). (2006). Recommended Security Guidelines for Airport Planning, Design and Construction. Available at http://www.tsa.gov/assets/pdf/airport_security_design_guidelines.pdf. Accessed July 20, 2007.
[2]
U.S. Government Accountability Office (GAO). (2006). Aviation Security: TSA Oversight of Checked Baggage Screening Procedures Could be Strengthened. Report Number GAO06-869. Available at http://www.gao.gov/new.items/d06869.pdf. Accessed July 20, 2007.
[3]
Berrick, C. A. (2006). Aviation Security: TSA Has Strengthened Efforts to Plan for the Optimal Deployment of Checked Baggage Screening Systems, but Funding Uncertainties Remain. Report Number GAO-06-875T. Washington, DC: United States Government Accountability Office (GAO).
[4]
Butler, V., Poole, R. W. (2002). Re-Thinking Checked-Baggage Screening. Policy Study, 297. Los Angeles: Reason Foundation.
[5]
Haimes, Y. Y. (2004). Risk Modeling, Assessment, and Management. New Jersey: John Wiley & Sons.
[6]
Kobza, J. E., Jacobson, S. H. (1997). Probability Models for Access Security System Architectures. Journal of the Operational Research Society, 48, 255-263.
27
[7] [8] [9]
Jacobson, S. H., Kobza, J. E., Easterling, A. S. (2001). A Detection Theoretic Approach to Modeling Aviation Security Problems Using the Knapsack Problem. IIE Transactions, 33, 747-759. Virta, J.E., Jacobson, S.H., Kobza, J.E. (2002). Outgoing Selectee Rates at Hub Airports. Reliability Engineering and System Safety, 76(2), 155-165. Virta, J. L., Jacobson, S. H., Kobza, J. E. (2003). Analyzing the Cost of Screening Selectee and Non-Selectee Baggage. Risk Analysis, 23(5), 897-908.
[10] Jacobson, S. H., Karnani, T., Kobza, J. E., Ritchie, L. (2006). A Cost-Benefit Analysis of Alternative Device Configurations for Aviation-Checked Baggage Security Screening. Risk Analysis, 26(2), 297-310. [11] Candalino, T. J., Kobza, J. E., Jacobson, S. H. (2004). Designing optimal aviation baggage screening strategies using simulated annealing. Computers & Operations Research, 31, 1753-1767. [12] Feng, Q. (2007). On Determining Specifications and Selection of Alternative Technologies for Airport Baggage Screening. Risk Analysis. 27(5), 1-11. [13] Feng, Q., Sahin, H. (2007). Selection of Alternative Technologies for Airport CheckedBaggage-Security Systems. Proceedings of the 2007 Industrial Engineering Research Conference. [14] Feng, Q., Kapur, K.C. (2006). Economic Development of Specifications for 100% Inspection Based on Asymmetric Quality Loss Functions. IIE Transactions, 38(8), 659669. [15] Feng, Q., Kapur, K.C. (2006). Economic Design of Specifications for 100% Inspection with Imperfect Measurement Systems. Quality Technology and Quantitative Management, 3(2), 127-144. [16] Emblemsvag, J. (2003). Life-cycle Costing: Using Activity-based Costing and Monte Carlo Methods to Manage Future Costs and Risks, Hoboken, N.J. John Wiley & Sons, Inc. [17] Martz, H. F., Waller, R. A. (1982). Bayesian Reliability Analysis. John Wiley & Sons, New York, NY. [18] Kobza, J. E., Jacobson, S. H. (1996). Addressing the Dependency Problem in Access Security System Architecture Design. Risk Analysis, 16(2), 801-812. [19] Fuller, S.K., Petersen S. R. (1995). Life-Cycle Costing Manual for the Federal Energy Management Program. U.S. Department of Commerce. [20] The MathWorks, Inc. (2006). Optimization Toolbox User's Guide. Version 3.1, Natick, MA.
28
[21] Nocedal, J., Wright, S.J. (2006). Numerical Optimization. 2nd ed. Springer-Verlag, New York, NY. [22] Powell, M.J.D. (1983). Variable Metric Methods for Constrained Optimization. Mathematical Programming: The State of the Art (A. Bachem, M. Grotschel and B.Korte, eds), 288-311, Springer-Verlag, New York, NY.
