In March 2011, MDA Director Lt. Gen. Patrick O’Reilly told a House of Representatives hearing that “Today, 30 operational GBIs protect the United States against a medium ICBM raid size launched from current regional threats.”[1]  Leaving aside the fact the current Ground-Based Midcourse (GMD) system interceptors (GBIs) have never actually been tested against an ICBM target, this raises the question: How many attacking missiles comprise “a medium ICBM raid size” against the GMD system?  And this question then suggests the further question: How many GBI interceptors is the MDA planning to fire at each attacking missile?

This second question is particularly interesting in light of the recent MDA and DoD claims that they intended to modify already deploy GBI interceptors to “at least double” their effectiveness [see question 2 and its answer in May 21 post “A multiple choice quiz”].  This would seem to imply that the effectiveness of the current interceptors may not be too high.

Answers to both these questions are suggested by the following exchange between Representative Trent Franks and Gen. O’Reilly before the same committee several months earlier:[2]

Rep. Franks: “I know there’s no way to anticipate when they will have them.  But when would you anticipate being able to — if it’s just one, I know the rate issues is always a second question, but if it’s just one ICBM coming from Tehran to New York, when would we be able to, with high likelihood, be able to intercept that?  And I know that that’s still redundant coverage, but when would we be able to gain that redundant coverage?”

Gen. O’Reilly: “Sir, due to the number of interceptors in which we have, the probability will be well in the high 90s today of the GMD system being able to intercept that today.  And again our calculations along the same line says the number would have to be greater than seven simultaneously launched to start lowering that.  And that’s today.”

Gen. O’Reilly’s statement indicates that the GMD system is expected to maintain its effectiveness against up to a total of seven simultaneously attacking missiles. This seems to suggest that a “medium ICBM raid size” is at most about seven missiles. Moreover, it also indicates that GMD’s claimed effectiveness of well into the “high 90s” is based on firing four interceptors per target.  If more eight or more missiles are fired simultaneously at least one attacking missile will have fewer than four interceptors fired at it. 

So what does this tell us about what MDA is assuming about the individual effectiveness of each interceptor?  The simplest model is to assume that interceptors are fired in a salvo, that is, all the interceptors are fired before the outcome of the first intercept attempt is known, and that each interceptor’s probability of kill is independent of the others.  In principle, it might be possible to wait until the outcome of the first intercept attempt is known before launching additional interceptors.  The ability to use such a shoot-look-shoot strategy (more likely a shoot-look-shoot-shoot-shoot and maybe another shoot) depends on the particulars of the engagement scenarios and on the ability to the defense to rapidly and accurately assess the outcome of the first intercept attempt.  If such a strategy is assumed for the GMD system, and there is no public evidence I am aware of that it is [whereas one of the claimed advantages of phase four of the European Phased Adaptive Approach is that it would reduce the number of GMD interceptors required per attacking ICBM by enabling such a strategy, with the first intercept attempt or two taken by Europe-based SM-3 IIB interceptors], it would somewhat reduce the required effectiveness of each individual interceptor.  The assumption that the kill probability of each interceptor is independent of all the others makes possible the attainment of very high kill probabilities by firing multiple interceptors possible.  If there were a significant probability that all the interceptors would fail for the same reason, then there would be an upper limit on the system’s effectiveness, no matter how many interceptors were fired.

If we therefore simply assume a salvo launch of interceptors with independent kill probabilities, we get the figure below, which shows the required kill probability of kill for the interceptor as a function of the overall system effectiveness for salvo launches of two and four interceptors against a single target.

This figure shows that for a “well in the high 90s” overall effectiveness  (about 97.5%) with four interceptors launched per target would require an individual interceptor effectiveness of only about 60%.  This leaves plenty of room for assumed improvement, specifically to an individual interceptor effectiveness level of about 85%, which give about the same overall effectiveness with a salvo of only two interceptors.

However, General O’Reilly’s “high 90s” assessment was in response to a question about a single ICBM.  Suppose instead we asked how effective each interceptor would have to be if the requirement was that no warheads from a medium-sized attack (here assumed to be seven missiles) get through.

The figure below shows the result, again for both salvos of four and two interceptors:

Now we see that for the same high 90s overall effectiveness (97.5%) the individual kill probabilities of each interceptor must be 75% for the four-interceptor salvo and 93% for the two-interceptor salvo. 

Compare to the current intercept test success rate (in a very limited sample of five tests so far)  of operationally-configured  interceptors of between 40% and 60% (depending on whether one counts killed warheads or “successful intercepts”).