Sigma is shorthand for Standard Deviation. In brief, standard deviation is how far off from the normal most items will be.

Automotive manufacturers implemented statistical quality assurance programs that built into both the design and manufacturing a whole range of practices to insure the final assembly of the subsystem would always be in specification.

In brief.
If a part is being made there is going to be variation. There will be an average (mean), a maximum and a minumum. If the item is measured and plotted and there are enough samples most of the measurements should fall in the middle. Here's an example I found on-line showing Tire Pressures for a motorcyle.


With enough samples, the histogram ends up being shaped like a bell, hence bell curve. Most of the results will be within one standard deviation of the average (mean).

Going out plus minus three standard deviations (ie 6 sigma) covers most of the results.


So six sigma helps insure minumum defects


But if we are making 100,000 parts or filling 500,000 tires we need to know whether its likely that every one will fall within the acceptable plus/minus limits of our product.
If we're planning on making a million cars, then statistically 12 sigma as shown below could still potentially have out of spec items. This is why I mentioned that 6 sigma is not enough on safety systems. So in addition to going beyond 6 sigma for safety systems, engineers have always added factors of safety to the design limits.