Friday, April 29, 2011

Epsilon in $

"In the aluminum can industry, the thickness of the top of the pop-top cans has some physical limitations. It must be (say) not be thicker than 0.4mm, or else the poptop mechanism
may not work (many of us knows this from first hand experience). It must not be thinner than 0.3mm, or else the internal pressure may cause spontaneous explosion. Hence, we might tolerance this thickness as 0.35 ± 0.05mm. Now, if manufacturing processes were more reliable, and our ability to assess tolerance were more accurate, we might be able to tolerance this thickness as 0.32 ± 0.02mm. Such a change would save the aluminum can industry multi-millions of dollars in material cost each year".

"On 4 June 1996, the maiden flight of the 8 Ariane 5 launcher in French Guiana ended in self-destruction. About 40 seconds after initiation of the flight sequence, at an altitude of about 3700 m, the launcher veered off its flight path, broke up and exploded. A report from the Inquiry Board located the critical events: “At approximately 30 seconds after lift-off, the computer within the back-up inertial reference system, which was working on stand-by for guidance and attitude control, became inoperative. This was caused by an internal variable related to the horizontal velocity of the launcher exceeding a limit which existed in the software
of this computer. Approximately 0.05 seconds later the active inertial reference system, identical to the back-up system in hardware and software, failed for the same reason. Since the back-up inertial system was already inoperative, correct guidance and attitude information could no longer be obtained and loss of the mission was inevitable.”
The software error began with an overflow problem: “The internal SRI software exception was caused during execution of a data conversion from 64-bit floating point to 16-bit signed integer value. The floating point number which was converted had a value greater than what could be represented by a 16-bit signed integer. This resulted in an Operand Error. The data conversion instructions (in Ada code) were not protected from causing an Operand Error, although other conversions of comparable variables in the same place in the code were protected.”