Let's use an example of a square block with a hole drilled into it. For simplicity, I am using only the X & Y coordinates. One corner of the block is the 0, 0 datum, and the hole is drilled at coordinates 1, 1. This is a [Link Removed]. This is the system in which a CMM operates and usually reports data in an x, y, z format.
Therefore, the hole location has an x coordinate and a y coordinate. It may vary less than 1 or greater than one. If you were to analyze the x or the y results individually, chances are good that you would see a normal distribution in each axis.
However, Position results convert the separate x, y coordinates into part of a quasi [link removed]. A true Polar coordinate system would provide both a radial distance and a polar angle for each measurement. Position results consider only the diametrical distance regardless of the angle. Therefore, a hole at (0.9, 0), (1.1, 0), (0, 0.9), or (0, 1.1) are all considered to have the same Position despite the fact that they are off location in four different directions. This usually results in a right skewed distribution.
Not only do you have to either perform a non-normal capability analysis, or transform the data to normal (not recommended), but you do not have the necessary information to improve the capability. To get that information, you have to study the x and y results separately in order to move the hole onto target.
Therefore, the hole location has an x coordinate and a y coordinate. It may vary less than 1 or greater than one. If you were to analyze the x or the y results individually, chances are good that you would see a normal distribution in each axis.
However, Position results convert the separate x, y coordinates into part of a quasi [link removed]. A true Polar coordinate system would provide both a radial distance and a polar angle for each measurement. Position results consider only the diametrical distance regardless of the angle. Therefore, a hole at (0.9, 0), (1.1, 0), (0, 0.9), or (0, 1.1) are all considered to have the same Position despite the fact that they are off location in four different directions. This usually results in a right skewed distribution.
Not only do you have to either perform a non-normal capability analysis, or transform the data to normal (not recommended), but you do not have the necessary information to improve the capability. To get that information, you have to study the x and y results separately in order to move the hole onto target.
Agreed.
It might not be 100% accurate but I think you could then take your capability on X and Y then plug them into the true position formula. To be clear, you would need to determine the range for whatever capability you are looking for. If your target is 4 sigma (1.25 cp) then take sigma and multiply by 4 to determine your expected range on each axis. Plug these values into the true position formula to determine what your 4 sigma t.p. value is.
I suspect that the actual capability on position would be a little better than you would obtain using this method but I can't prove it.
One thing is clear though:
If 99.999% of the parts are within +/-.005 on the X and 99.999% of the parts are withing +/- .005 on the Y then 99.999% (or more) of the parts will be within .014 true position.
MMC complicates things but you could use the minimum expected amount of mmc available based on the appropriate capability requirements and come up with a worst case scenario.
Alternately, you could convert a .014 true position to a +/- .005 per axis and report the capability on each axis. Again, not right but it may give you some useful information.