Example: Landing planes

One of the best ways I have seen the six sigma concepts introduced uses the example of landing planes.

Observing a pattern

Consider a run-way where planes are landing. If you would observe enough planes, you would see the following happening:

1. The bulk of all planes land in the safe ‘green zone‘ away from the borders of the runway.
2. Most planes actually do land closely to the middle of the runway (the mean), some of them a bit further away to the left or right from the middle, and only a few quite far away from the middle.

Plotting Results

If you would measure long enough the distance in centimeters from the exact middle where each plane touches the ground on the tarmac, you can see that the pattern observed in time forms a normal distribution. A pattern with a mean (the middle line) and a standard deviation (the extent to which planes land further away from the middle line.) This is called the Gaussian Bell Curve with on the vertical axis the number of planes landed and on the horizontal axis the number of centimeters from the middle.

Normal Distribution

All data is now subdivided in segments called standard deviations (sigma) both to the left and to the right of the mean. The bulk of the landings are within 1-sigma from the mean, in a normal distribution this is about 34% of landings to the right and 34% of landings to the left. Outside the 3-sigma borders we can find only a small remainder of landings representing 0.27% of all landings.

Failure Criteria

The actual width of the runway combined with the skills of the pilots determine a successful or failed landing. It is obvious that we will have more crashes on narrow runways and when dealing with inexperienced pilots. Now we have a choice. We can decide that we for example align the left 3-sigma border with the Lower Specification Limit (LSL), and the right 3-sigma border with the Upper Specification Limit (USL).

This is equivalent to accept only those pilots who have consistently proven to be able to land within the borders 99.73% of the time. Alternatively, we could make sure that the runway is wide enough to land planes safely 99.73% of the time. The question now is: is this really good enough?

In reality, the above measure corresponding to 3-sigma, simply means that we are prepared to let 2.7 planes, out of 1,000 planes crash. This is of course not acceptable and therefore, the so-called Six Sigma criterion has been established.

Six Sigma

By definition, Six Sigma means that only in 3.4 cases per million a crash may occur. Although statistically not completely correct (as 3.4 cases per million correspond to 4.5-sigma rather than to 6-sigma), this metric has been established as an acceptable measure for designing boundaries and optimizing processes.

Six Sigma is all about influencing the process or designing the boundaries in such a way that the variation can be controlled within given specifications.

If we have a runway that is 80 meters wide, we will have to train our pilots and trim our planes in such a way that only 3.4 out of 1.000.000 landings would slip or crash. We can turn this around of course, in our runway example, if we know that from 1 million landings, 3.4 of them will land outside 80 meter, we will design the runway 80 meters wide.

During our training events, we will focus on practical examples and implementations taking the business objectives as the starting point. These are the given boundaries, we need to measure and find ways to ensure the Six Sigma criterion can be met by the process that is target of the optimization project.