# The Future of the U.S.-Soviet Nuclear Relationship(1991)

## Chapter: Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors

« Previous: Appendix B: Target Allocation Issues
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Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
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## The Sensitivity of Strike Results to Preattack Planning Factors 1

This appendix is based on work done for the committee by Paul Chrzanowski of the Lawrence Livermore National Laboratory; it will appear in an extended form in an LLNL report now in preparation. We very much appreciate his assistance.

The outcome of a strike against a set of targets depends not only on the capability of the weapons but also on the allocation of weapons to targets, which, in turn, depends on preattack planning factors. These factors include variables such as the reliability of weapons and delivery systems, the effectiveness of defenses in preventing weapons from reaching the target area, and the probability of damage to a target given that the weapon arrives in the target area. These factors can be combined into a single quantity Ps, which represents the survivability of a target if a single weapon is assigned to attack it. The “single-shot probability of kill” (SSPK) is 1 − Ps. The purpose of this appendix is to explore the sensitivity of strike results to prestrike assumptions about Ps.

A simple model is used to demonstrate that strike results are not very sensitive to misassumptions about attack planning factors. A specific case is considered in this appendix, where it is possible to derive analytic formulas for the optimal attack tactics, the value damaged, and the variance in value damaged. The case is one where values can be assigned to targets and the distribution of target value obeys a simple power law: Vcum = (x/T)Î±, where Vcum is the cumulative value of the targets, T is the total number of targets, x is target number with installations ranked in order of decreasing value, and Î± is in the range 0 < Î± < 1.

Page 60
Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
×

Page 60

For example, if one has Î± = 0.3, half of the value of the target base resides in the most valuable 10 percent of the targets [Vcum = 1/2 = (0.1)0.3]. Sample results for this value of Î± are plotted in Figure C-1 and Figure C-2. In the figures, Qs is the anticipated value of the single-shot probability of target survival, whereas Ps is the actual value. For various values of Qs, attack efficiency is shown as a function of Ps in Figure C-1. Figure C-2 shows the damage extracted as a function of attack size with perfect planning (Qs = Ps). Notice that the total target damage depends strongly on Ps (how well weapons perform) but that for a given value of Ps the results are fairly insensitive to Qs (the preattack assumption about Ps). In short, accurate attack planning assumptions (Qs = Ps) are important for understanding how well the strike will succeed but do not help one to devise a much more effective plan.

Page 61
Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
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Page 61

### NOTE

1. For a set of 1,000 targets with cumulative value growing as the 0.3 power of target number, and with perfectly planned allocation of weapons to targets (but without bomb-damage assessment or shoot-look-shoot), the fraction destroyed of total target set value may be calculated exactly:

 Case SSPK Weapons used Fractional value destroyed 1 0.90 187 0.556 1a 0.20* 18 0.171 2 0.20 187 0.299 3 0.90 1,075 0.942 3a 0.20* 1,075 0.294 4 0.90 22 0.294

Case 1a is the allocation of Case 1, but with the single-shot probability of kill degraded to the equivalent of 0.20 by random destruction before launch, for example. Case 2 shows the potential benefit over 1a of statistical reassignment (factor 1.75 increase in damage realized). Case 3a illustrates the much larger initial force required (without statistical reassignment) to provide damage comparable with the statistical reassignment Case 2. For comparison, Case 4 shows that the ability to reallocate specific surviving weapons to the most valuable 21 targets would enable damage to be maintained with 22 surviving weapons rather than the 40+ of Cases 1a or 2 or the 220+ of Case 3a.

Page 62
Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
×

Page 62

Page 59
Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
×
Page 60
Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
×
Page 61
Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
×
Page 62
Suggested Citation:"Appendix C: The Sensitivity of Strike Results to Preattack Planning Factors." National Academy of Sciences. 1991. The Future of the U.S.-Soviet Nuclear Relationship. Washington, DC: The National Academies Press. doi: 10.17226/1846.
×
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The United States and the Soviet Union could drastically reduce their nuclear arsenals below the levels prescribed by the new Strategic Arms Reduction Treaty (START). The end of the Cold War and the transformation of international security now under way present the United States with opportunities to develop new policies based on greater international cooperation with the Soviet Union and other major powers.

This new book describes two lower levels of nuclear forces that could be achieved, as well as other related measures to improve international security.

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