Simple probability models for assessing the value of information in defense against missile attack

Suitable and timely information can enhance the effectiveness of a weapon system. This article presents simple models of an air defense situation that illustrates the expected payoff from a reduction in uncertainty by utilization of the products of sensor and C3/I capabilities. Our model is of a single defensive unit (e.g., roughly resembling a Patriot battery) that assists in defending a high‐value area against massed missile attack, perhaps by SCUD‐like missiles. The defense engages each attacking missile in turn. The defense battery makes use of information available so as to plan the defensive resource allocation; application of that resource is possible only over a fixed known time interval. With minimal damage assessment available, termed INVISIBLE KILL, the defense allocates an equal time to each of a subset of all missiles so as to maximize the expected number killed; the size of the subset engaged depends upon the probability distribution of lethality time—the random time to kill an attacking missile acquired and engaged by the defense. If more information is available, that is, kills are observable, called VISIBLE KILL, the defense pursues a threshold policy: The time of engagement with a particular missile is limited (to τ); if kill is observed before τ defense attention switches (after a delay) to a new potential target. Suppose finally that still more information is available: The defense can order the lethality times in advance (this does not require that those times be actually known) and can also observe kills; call this COMPLETE INFORMATION. Then under some circumstances defense can prosecute substantially shorter time tasks first, crowding the majority of the kills into the earliest part of the window of opportunity of length T, leading to an advantage over the other policies. This capability is artificial, but the results supply an upper bound on defense capability as a function of the variability of lethality times. The above situations merely illustrate the impact of information in a time‐constrained context. Numerous variations in the formulations are likely to be of interest, and of even more relevance. We hope that this article stimulates the analysis of a variety of such formulations. © 1995 John Wiley & Sons, Inc. This article is a US Government work and, as such, is in the public domain in the United States of America.