Calculating Cp and Cpk on a Non-Normal Distribution

bobdoering

Stop X-bar/R Madness!!
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#11
Hello Mr. Atul,

The readings taken were from a machining operation on multi-spindle screw machine and the measuring instrument used was 0.001 Micrometer. The dia 6.75 / 6.45 is maintained by a roughing using dovetail form tool and finishing using circular size tool. We suspect that the sizing operation contributes to this non-normal distribution but the advantage of using this tool is that we can get a very good consistency in the job.

You had mentioned about some "transform" that could be used to solve this problem. Can you please elaborate and also tell me what effect it has on the formula used to calculate the control limits, Cp and Cpk. Please also note that the readings are not stable when X-R chart is plotted.Can you advice me what to do?
Your machining operation should be non-normal. For a screw machine, it is absolutely imperative to collect and chart the data from each spindle separately, and keep the data from each spindle together. I am not sure if the data you provided was in that specific order. From that follow

SPC for Diameters - Parts not Perfectly round so charts are useless

Use the X-Hi/Lo chart for each spindle, and you will have a clearer idea of capability. If the data collected in this manner is found to be "normal", your process is out of control (bad spindle bearings, etc.) For the uniform distribution the results should form the sawtooth curve, and its capability = UCL-LCL/USL-LCL.
 
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#12
The output from a screw machine is rarely normal. The screw machine cuts to a hard stop. This results in a characterically skewed distribution since it is not possible to machine past the stop, but is possible to machine short of the stop.

If you have access to Minitab, you can either transform the data or fit a non-normal distribution to the data and determine capability using the fitted distribution.
 

bobdoering

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#13
Transformations may be OK for those people that cannot understand anything that is not in normal "format", but Shewhart said: "The total information is given by the observed distribution.” I will agree with that. Transformations can mask valuable information, which is clear when attempting to transform uniform distribution data to normal distribution. It's like teaching a pig to sing. I suggest using the X hi/lo-R chart described above, and analyze the distribution directly.:cool:
 
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bobdoering

Stop X-bar/R Madness!!
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#14
There is a reason why the data is non-normal: tool wear. If it is precision machining, most of the variation seen is likely to be from measurement error - not the process. The biggest problem is the process was not likely controlled correctly. If it was, transformations would not be required - it would be a uniform distribution.
 
E

Erik Alburg - 2009

#15
There are other distributions that can handle conditions where there is a barrier condition at the zero position, such as the Weibull and LogNormal distribution.

Time based data is typically Lognormal in nature but I see people all the time trying to force fit a normal distribution to the situation.

The bottom line is use the right distribution for the job. We don't try to fit a straight line to data that looks like a parabola.

It is pretty well documented how to analyze process capability using data that is normal, here is a link to a video that explains how to analyze data that is lognormal.

Admin note: The videos are on the posters web site. Please visit the poster's Profile for a link to his web site and other information.
 
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