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Lecture notes, lecture Some disasters caused by numerical errors - Numerical analysis - math 685
Course: Numerical Analysis (MATH 685)
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University: George Mason University
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Some disasters caused by numerical errors
Patriot Missile Failure
Explosion of the Ariane 5
EURO page: Conversion Arithmetics
The Vancouver Stock Exchange
Rounding error changes Parliament makeup
The sinking of the Sleipner A offshore platform
Tacoma bridge failure (wrong design)
200 million dollar typing error (typing error)
Collection of Software Bugs
Patriot Missile Failure
On February 25, 1991, during the Gulf War, an American Patriot Missile battery in Dharan, Saudi Arabia, failed to
intercept an incoming Iraqi Scud missile. The Scud struck an American Army barracks and killed 28 soldiers. A
report of the General Accounting office, GAO/IMTEC-92-26, entitled Patriot Missile Defense: Software Problem
Led to System Failure at Dhahran, Saudi Arabia
reported on the cause of the failure. It turns out that the cause was an inaccurate calculation of the time since boot
due to computer arithmetic errors. Specifically, the time in tenths of second as measured by the system's internal
clock was multiplied by 1/10 to produce the time in seconds. This calculation was performed using a 24 bit fixed
point register. In particular, the value 1/10, which has a non-terminating binary expansion, was chopped at 24 bits
after the radix point. The small chopping error, when multiplied by the large number giving the time in tenths of a
second, lead to a significant error. Indeed, the Patriot battery had been up around 100 hours, and an easy calculation
shows that the resulting time error due to the magnified chopping error was about 0.34 seconds. (The number 1/10
equals 1/24+1/25+1/28+1/29+1/212+1/213+.... In other words, the binary expansion of 1/10 is
0.0001100110011001100110011001100.... Now the 24 bit register in the Patriot stored instead
0.00011001100110011001100 introducing an error of 0.0000000000000000 000000011001100... binary, or about
0.000000095 decimal. Multiplying by the number of tenths of a second in 100 hours gives
0.000000095×100×60×60×10=0.34.) A Scud travels at about 1,676 meters per second, and so travels more than half
a kilometer in this time. This was far enough that the incoming Scud was outside the "range gate" that the Patriot
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