In this article, we consider a model for an airport security system in which the declaration of a threat is based on the joint responses of inspection devices. This is in contrast to the typical system in which each check station independently declares a passenger as having a threat or not having a threat. In our framework the declaration of threat/no-threat is based upon the passenger scores at the check stations he/she goes through. To do this we use concepts from classification theory in the field of multivariate statistics analysis and focus on the main objective of minimizing the expected cost of misclassification. The corresponding correct classification and misclassification probabilities can be obtained by using a simulation-based method. After computing the overall false alarm and false clear probabilities, we compare our joint response system with two other independently operated systems. A model that groups passengers in a manner that minimizes the false alarm probability while maintaining the false clear probability within specifications set by a security authority is considered. We also analyze the staffing needs at each check station for such an inspection scheme. An illustrative example is provided along with sensitivity analysis on key model parameters. A discussion is provided on some implementation issues, on the various assumptions made in the analysis, and on potential drawbacks of the approach.