I think it should be possible, but I'm not sure if this is the answer or not. I was thinking about how something along the lines of the complex plane (or vectors/trig) could be used to identify grouping of a positional tolerance based on its quadrant within a unit circle, and then could be used to calculate Cpk. It's not unheard of. The
normal distribution of a multivariate system is calculable, so why wouldn't a statistic that is related to the normal distribution in 1 variable work for higher dimensions?
I'm thinking that there must be a way to calculate the variance of position based on the the quadrant it falls in. Whether it's a trigonometric function, or a complex function.
Anyone have any input as I dive into this blackhole?
Curiosity killed the cat, hopefully I'm not a cat.
Projection line parallel to X-axis (removing the Y-coordinate completely from the calculation).
During the rotation of the plane/line intersecting the centre of gravity, the points X-coord never changes - only the Y-position of them (X-coord is constant).
Find the rotation/angle where the dispersion of points (width) is at it's largest - this is the base for Cp calculation (perpendicular to the line/plane).
Find the rotation/angle where the tolerance violation is at it's greatest - this is the base for Cpk calculation (perpendicular to the line/plane).
This is over my head though, but you already knew that. I just looked at the pictures.