**R = The Reliability of the weapon.**
The reliability of the weapon is the probability that the weapon will
work.

If the weapon is *perfectly reliable* (i.e., R = 1.0), the chances
of a weapon with yield **Y** destroying a target of hardness **H** is

**Pk** = 1 - .5^{((LR/CEP)2)}

**Pk** is called the kill probability of the warhead.

If the reliability of the warhead is less than 1.0, then the probability
of the warhead destroying the target must take this into account. The
probability of the warhead destroying the target is:

**(R)(Pk)**

If the resulting probability of destroying the target is not high
enough for you, then you may aim more than one warhead against the
target. But there are very difficult issues of timing involved. If
one warhead arrives somewhat earlier than another, the effects of the
first explosion (the release of neutrons, the blast, the debris)
may disable the next warheads or "push" them away from the target.
The destruction of following warheads by those that arrive earlier
is called fratricide. It is commonly assumed that two -- but no more
than two -- warheads can be detonated close enough in time so that
fratricide can be avoided.

The KP program will calculate two different versions of the probability
that 2 warheads will destroy the target. One value for Pk2 assumes that
both warheads aimed at the target come from the same missile. The other
value assumes that each of the pair of warheads comes from a different
missile. This is known as cross-targeting. Cross-targeting is
better because if both warheads come from the same missile, and that
missile fails, the target will not be destroyed. If the warheads come
from different missiles, and one missile fails, there is still a chance
that the other warhead will work and destroy the target. The
two values will differ, but at some times the difference is so small
that is does not show up in the calculations.

## Additional Reading

If you want more information on these calculations, I suggest you read
the following:
Davis, Lynn and Warner Schilling. 1973. All You Ever Wanted to Know About
MIRV and ICBM Calculations But Were Not Cleared To Ask. *Journal of
Conflict Resolution* 17: 207-242.

Speed, Roger D. 1979. *Strategic Deterrence in the 1980's*.
Stanford, CA. Hoover Institution Press.

Steinbruner, John D., and Thomas M. Garwin. 1976. Strategic Vulnerability: The Balance between Prudence and Paranoia.
*International Security* 1,1: 138-181.

Tsipis, Kosta. 1983. *Arsenal: Understanding Weapons in the Nuclear
Age*. New York: Simon and Schuster.

Last updated - 2/17/10