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Capability calculations for True Position

VinniUSMC
Has anyone come across this as a means of calculating Cpk of a true position?

http://documentation.statsoft.com/ST...tionCapability

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.

Parents
  • 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. Sunglasses
  • in reply to vpt.se
    This was my interpretation as well. We were hoping that you, being Swedish, would have been born with intimate knowledge of all things Swede, including, but not limited to, Volvo standards, Ikea furniture assembly and surstromming eating. Slight smile

    With your interpretation (as mine), I have trouble squaring this with what I am calling the infinity paradox. As the slope of the line nears vertical, the points furthest from the center approach infinity in Y, which also means the dispersion and tolerance variaton approaches infinity. Then we would never reach a satisfactory Cp/Cpk.
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  • in reply to vpt.se
    This was my interpretation as well. We were hoping that you, being Swedish, would have been born with intimate knowledge of all things Swede, including, but not limited to, Volvo standards, Ikea furniture assembly and surstromming eating. Slight smile

    With your interpretation (as mine), I have trouble squaring this with what I am calling the infinity paradox. As the slope of the line nears vertical, the points furthest from the center approach infinity in Y, which also means the dispersion and tolerance variaton approaches infinity. Then we would never reach a satisfactory Cp/Cpk.
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