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Article Excerpt
1. Introduction
The terrorist attacks on September 11, 2001, prompted significant policy and operational changes in aviation security systems. One of the important changes is that 100% of checked baggage at all commercial airports throughout the US must be screened by using techniques such as Explosive Detection Systems (EDSs) and Explosive Trace Detection (ETD) machines (TSA, 2006; USGAO, 2006). Nevertheless, the significant economic and operational limitations regarding currently used EDS and ETD technologies, such as the prohibitive costs, high error rates and low processing rates, have led the Transportation Security Administration (TSA) to consider new screening technologies and procedures that may offer a higher security level and lower cost for aviation screening systems (Butler and Poole, 2002).
The design and analysis of aviation security systems have been reported in the literature. Kobza and Jacobson (1997) and Jacobson et al. (2001) assessed the risk and cost-effectiveness of aviation security systems by considering the false alarm and false clear rates as performance measures. Virta et al. (2003) assessed trade-offs between screening only the selectee checked-baggage and screening both selectee and non-selectee baggage for a single EDS device. Jacobson et al. (2006) extended this work to 100% screening, where trade-offs between using single-device and two-device systems were studied by utilizing the expected direct cost model. Candalino et al. (2004) determined the best selection of technology and optimal number of screening devices that minimize the expected total cost of the entire system by using a cost model including both the direct cost and the indirect cost associated with system errors. McLay et al. (2007) utilized passenger prescreening information to develop screening strategies that maximize system security subject to system capability, as well as evaluating the effectiveness of passenger prescreening. In addition to the previous studies on risk and cost-benefit analysis, the concern of setting threshold values for continuous security responses were addressed for both single-level and two-level screening systems (Feng, 2007; Feng and Sahin, 2007). Feng et al (2009) developed a two-level screening system by incorporating the concepts of system capability and human reliability for two different decision rules. Sahin and Feng (2009) extended this two-level screening system by combining passenger prescreening information.
As discussed in the previous studies, risk in security screening is associated with false alarm and false clear rates of screening devices and procedures. A false alarm is triggered when a non-threat item is not allowed to gain access, and a false clear occurs when a threat item passes through undetected. An ideal baggage screening system should be error free. However, inspection errors are inevitable mainly due to the inherent design of screening devices, fluctuation of environmental elements and human errors (Feng and Kapur, 2006; Feng, 2007). The true status of an item is unknown a priori, and it is a binary random variable, zero or one (non-threat or threat). However, the operator may have prior subjective knowledge about the probability that an item is a threat, based on the color-coded threat level provided by national security warning systems or other sources. Therefore, the problem of designing screening procedures can be approached using Bayesian analysis, which allows the incorporation of prior knowledge with present data into a statistical analysis.
This paper develops Bayesian analysis models for both single-level and sequential multiple-level baggage screening systems. The Bayesian approach has been applied for quality inspection in manufacturing and software engineering. Bonett and Woodward (1994) designed a sequential defect removal sampling plan, where each product was examined by two or more inspectors. The number of defects discovered provides prior information to estimate the number of defects still remaining in the product. Rallis and Lansdowne (2001) proposed a Poisson prior distribution for the serial inspection of software systems. Using the Bayesian method, they conducted a quantitative assessment of sequential testing and correction cycles, and determined the confidence that all defects are detected. Chun and Sumichrast (2007) proposed three conditions that are desirable properties for a prior probability distribution of the number of defects in a product. For the negative binomial distribution prior, which is the only satisfying distribution, the effects of various parameters on the Bayesian estimate were examined.
Existing studies in aviation security screening have been conducted using classical probability modeling methods without incorporating the prior subject knowledge. To utilize the prior subjective knowledge about the threat level, this paper proposes to use Bayesian analysis to model baggage screening problems, which provides a new perspective on the design and evaluation of aviation security systems. Broadly speaking, the Bayesian approach is fundamentally sound and flexible, produces clear and direct inferences and makes use of all available information. Furthermore, the Bayesian approach allows us to make a probability statement about the true status of an item, which is not permitted in the classical approach.
Using the Bayesian approach, the operator's prior knowledge about the status of a bag is represented by a probability mass function. We then develop the posterior distributions for single-level and multiple-level screening, respectively. To evaluate the performance for Bayesian screening, two metrics are implemented: (i) system risk bounded to the posterior mean of undetected threats; and (ii) system direct cost per bag that incorporates purchasing costs, operating costs and processing rates. By evaluating the trade-off between system risk and system cost for different screening technologies or combinations of them, the objective is to select the cost-effective screening devices and procedures for single-level and multiple-level systems.
The paper is organized as follows. Section 2 introduces model formulation of the Bayesian screening method by providing prior distributions and posterior distributions for single-level and multiple-level systems. In Section 3, cost-effectiveness and risk analyses of screening technologies for a single-level screening system are studied. For a multiple-level system, Section 4 presents the system decision rules and numerical analysis using the example of a two-level system. Section 5 summarizes the paper with additional discussions.
2. Model formulation for Bayesian screening
The prior distribution that represents prior knowledge about the status of an item will be described first. Based on the prior distribution, we will then develop the posterior distributions for single-level and multiple-level screening, respectively.
2.1. Prior distribution
The true status of an item, Z, (e.g., a checked bag) is a binary random variable that can be represented as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Although the value of Z is unknown a priori, the distribution of Z is known to be a Bernoulli distribution with parameter p, which is the probability that an item is truly a threat:
P(Z|p) = [p.sup.z][(1 - p).sup.[1 -...
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