A detection theoretic approach to modeling aviation security problems using the knapsack problem

Designers, operators and users of multiple-device, access-control security systems are challenged by the false alarm, false clear tradeoff. Given a particular access control security system, and a prescribed false clear standard, there is an optimal (minimal) false alarm rate that can be achieved. The objective of this research is to develop a new methodology for determining this false alarm rate. A static grid estimation procedure is used to estimate the joint conditional probability density functions for the security device responses. The concept of a system response function is introduced and the problem of determining a system response function that minimizes the false alarm rate, while meeting the false clear standard, is formulated as a decision problem and proven to be NP-complete. A Greedy Algorithm and a Dynamic Programming algorithm are presented to address this problem. Computational results using simulated security data are reported. These results are compared to analytical results obtained for a pre-specified system response function form. Directions for future research are also discussed.