A third method is the scalar or expansion method. This method calculates the amount the uncertainty ellipses must be expanded or contracted (in cases where the ellipses overlap) in order to just meet. The separation factor is simply the factor by which the ellipses are expanded or contracted. The calculations required to generate the separation factor using the scalar method are best left to the computer.
In the example the green ellipses are 40% bigger than the originals so the separation factor would be 1.4. When the geometries line up correctly this method produces the same number as the alternative methods. The same safety rules developed for use with the older methods can still be used. But the scalar method has the advantage of never calculating optimistic or pessimistic separation factors no matter what the 3D geometry.
This method produces numbers which are very similar to the other two methods and can be used with the same safety rules but it is never optimistic or pessimistic in any geometry.
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