A stochastic model for layered defense: Ballistic missile defense and harbor protection

Asymmetrical attacks can come in multiple scenarios such as diver threats carrying improvised explosive devices to destroy critical assets, or hijacked civilian aircraft aimed to crash into critical assets in a 9-11 style approach. To defend critical assets, we need to understand the effectiveness of the defensive systems against the potential asymmetrical threats. In this paper, we propose a general methodology that characterizes a layered defense system of systems that mimics the OODA loop, i.e., a model that simulates the processes of Observation, Orientation, Decision and Action. Our model considers the capabilities of the threats such as the payload of explosives, their speeds and ranges. It also models the defensive surveillance systems such as detection and tracking performances, in addition to the capabilities of the interceptors such as speeds, weapon ranges and reaction times. The model can be used to simulate a layered defense in the sense that if a threat leaks (a leaker) through an outer defense system, it will be re-engaged by the following inner defense system if time permits. Specific applications of this model have been implemented in a number of studies of harbor protection, as well as in air defense, and even ballistic missile defense. We provide a model that integrates the defense capabilities into a globally stochastic metric called PISE (probability of integrated system effectiveness). PISE depends on a number of probabilistic parameters such as the probability of detecting and the probability of tracking a threat, the probability of neutralizing a threat given the type of weapon, and the probability of neutralization assessment. PISE is also a function of the geometry of the problem, the terrain surrounding the critical asset and the critical asset itself. This model yields a map of PISE values that allows identifying the strengths and weaknesses of the defensive systems and thereby guides the capability developers in determining solutions (Doctrine, Organization, Training, Material, Leadership, Personnel, Facilities, & Interoperability) to defend critical assets. We emphasize the fact that this paper describes a unified model that combines the underlying methodologies.