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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.

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  • As I understand the Volvo doc, here is my "translation" :


    Don't forget that I work essentialy on prototypes, so I'm not user of those tools Disappointed.

    I think 1 or 2 things might not be right (or I could be reading the Volvo standard wrong).

    When the points are projected onto the line, they should be projected perpendicular to X, not dependent on the angle of the projected line, shouldn't they? So, when the line is at 0 degrees, the farthest point in -X, and the farthest point in +X should have the same X coordinate no matter what angle the projection line is at. But, that would mean that when approaching 90 degrees, the Y coordinates would approach +/- infinity (which doesn't make sense, and is why I think I could also be wrong) and the distance to barycenter would also approach infinity. Which would also make the Cp never good.

    Also, I think the barycenter should not change while rotating. The projected line should rotate about the barycenter of the initial input. "By iteratively rotating the constructed plane through the point of balance in different directions" (page 28).
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  • As I understand the Volvo doc, here is my "translation" :


    Don't forget that I work essentialy on prototypes, so I'm not user of those tools Disappointed.

    I think 1 or 2 things might not be right (or I could be reading the Volvo standard wrong).

    When the points are projected onto the line, they should be projected perpendicular to X, not dependent on the angle of the projected line, shouldn't they? So, when the line is at 0 degrees, the farthest point in -X, and the farthest point in +X should have the same X coordinate no matter what angle the projection line is at. But, that would mean that when approaching 90 degrees, the Y coordinates would approach +/- infinity (which doesn't make sense, and is why I think I could also be wrong) and the distance to barycenter would also approach infinity. Which would also make the Cp never good.

    Also, I think the barycenter should not change while rotating. The projected line should rotate about the barycenter of the initial input. "By iteratively rotating the constructed plane through the point of balance in different directions" (page 28).
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