PHOTO: Jeff Topping/The New York Times/Redux

31 March 2008—Modern nuclear reactors are designed to have a rate of failure, involving the release of significant radiation, of just 1 in 1 million per year per reactor. But what about that other potential source of lethal radiation—nuclear war? Martin E. Hellman, emeritus professor of electrical engineering at Stanford University and IEEE Fellow, applied engineering risk-analysis methods to the question of what the failure rate is for the strategy of nuclear deterrence. His conclusion? The failure rate of nuclear deterrence is a lot higher than you might think.

Hellman is probably best known for co-inventing public key cryptography, but he’s been working on the issue of nuclear deterrence since the 1980s. Nuclear deterrence could fail by a terrorist event, a command-and-control error, or a Cold War meltdown like the Cuban Missile Crisis of 1962, Hellman writes in the spring issue of The Bent of Tau Beta Pi, the magazine of the engineering honor society.

Leaving aside the former two scenarios, Hellman came up with a sort of equation for Armageddon: the annualized probability of a Cuban Missile Type Crisis (CMTC) resulting in World War III during the 50 years of the Cold War is equal to the annualized probability that an initiating event (such as the Berlin crisis of 1961) would lead to a CMTC (3 chances in the past 50 years, by Hellman’s count), times the conditional probability that the event becomes a CMTC (one event was the actual Cuban Missile Crisis, so that’s 1 in 3), times the conditional probability that the CMTC leads to the use of a nuclear weapon, times the conditional probability that the use of a nuclear weapon leads to full-scale nuclear war.

The stickiest points are the last two probabilities, because they have never happened. Hellman uses statements from participants in the Cuban crisis to come up with a lower bound of 10 percent and an upper one of 50 percent for the chance that nuclear weapons would be used. His estimate of the probability of nuclear weapon use leading to an all-out nuclear war is in the same range, based on statements by both the U.S. president at the time, John F. Kennedy, and his secretary of defense, Robert S. McNamara.

The result is a range from 2 chances in 10 000 per year to 5 chances in 1000 per year for just this one type of trigger mechanism. The values are valid only for the Cold War years, writes Hellman. But that doesn’t make them irrelevant at a time when relations between the United States and Russia are deteriorating; India and an unstable Pakistan have acquired atomic weaponry; and military planners from Washington, Tokyo, and Seoul worry about whether a nuclear-armed China would go to war to reclaim Taiwan.

Hellman’s method isn’t unfamiliar to those trying to gauge the risk of failure for complex systems, such as nuclear reactors. IEEE Spectrum asked J. Wesley Hines, a professor of nuclear engineering at the University of Tennessee, to examine Hellman’s methods, which were detailed in the appendix of the Bent article. “I only read the appendix but feel his argument is rational and also feel his methods are justified,” says Hines. “Some could argue with the numbers he used, but he does give logical reasons for using those numbers and admits that they have large uncertainties since the events have been rare in the past.”

Robert N. Charette, who runs the risk-management consultancy ITABHI and is a regular contributor to IEEE Spectrum, agrees with Hines. However, he says Hellman should have also turned the analysis on its head. “The other side of the risk equation is, suppose you get rid of nuclear weapons. Does that increase the probability of war? Pretending there aren’t any nukes, how many wars would we have had?”

Hellman thinks that’s definitely a question that must be answered. “Before adopting a different strategy, we need to compare the risk of our current nuclear posture with the risk of that alternative strategy,” he wrote in an e-mail to IEEE Spectrum. “There are many options other than just the status quo and complete nuclear disarmament.”

Hellman calls for prestigious scientific and engineering bodies, such as the U.S. National Academy of Engineering, to do a far more careful and nuanced analysis of nuclear deterrence and its alternatives than he has. “If the results are anywhere near my preliminary estimate, then the world needs to be 10 000 times safer,” he says.