Capability Brain Teaser - Which distribution do you expect to see

bobdoering

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#1
Attached is a sketch of the cross-section of a connector. There is a dimension identified from the end of the connector to the tip of the terminal.

Brain teaser question: Which distribution (normal, etc.) do you expect to see for the variation associated with this dimension?
 

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Jim Wynne

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#2
Attached is a sketch of the cross-section of a connector. There is a dimension identified from the end of the connector to the tip of the terminal.

Brain teaser question: Which distribution (normal, etc.) do you expect to see for the variation associated with this dimension?
There are as many as three manufacturing processes associated with the part: the pin is probably stamped, the connector shell is probably molded plastic, and the process of inserting the pin into the shell (although overmolding is possible). Because of the interplay of the variables associated with these different processes, I would guess at a normal distribution, but I'd need to do some measuring before I was satisfied with the decision.
 

bobdoering

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There are as many as three manufacturing processes associated with the part: the pin is probably stamped, the connector shell is probably molded plastic, and the process of inserting the pin into the shell (although overmolding is possible). Because of the interplay of the variables associated with these different processes, I would guess at a normal distribution, but I'd need to do some measuring before I was satisfied with the decision.
You came pretty close to nailing the whole answer. The rest of the answer (and probably the most intriguing) falls in the overmolding approach
 
F

falconer65

#4
My first thought was "A normal distribution?" Assuming three processes. Further assumptions being the pin process has a normal distribution, the molding process has a normal distribution, and the assembly process has a normal distribution. Thus the variation of three processes is combined the dimension has a normal distribution? That is possible, though I would not be surprised to see a tri-modal bell curve.

Second thought was assume the assembly of the insertion of the pin and the molded part had stops. Each part may have normal distributions, but are irrelevant to the assembly process. They hit against their stops and the distribution would be non-normal, along the lines of a one sided bell curve.

Overmolding: assuming the pin hits a stop and has a half-curve, and the plastic has a normal distribution for shrinkage, then an overlay of the two distributions.

I prefer the EDA method, not classical, so in the end I would let the raw data show me.

Nice teaser.:applause:

:2cents:
Erik Sikora
 

bobdoering

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#5
My first thought was "A normal distribution?" Assuming three processes. Further assumptions being the pin process has a normal distribution, the molding process has a normal distribution, and the assembly process has a normal distribution. Thus the variation of three processes is combined the dimension has a normal distribution? That is possible, though I would not be surprised to see a tri-modal bell curve.
These are very good thoughts - and the thought process is what I use as a basis of developing the of the total variance equation. You might have a tri-modal distribution (which would no longer be normal) if all of the effects were of the same magnitude. Most likely the overwhelming variation will be the size of the hole in the terminal stamping that the molded tab drops into - and the ending location after the locking tab holds the assembly in place. Most likely distribution will be normal or possibly a "U" distribution if it ends up being truncated. Now you can look at the data and see if it supports the expected results.

Overmolding: assuming the pin hits a stop and has a half-curve, and the plastic has a normal distribution for shrinkage, then an overlay of the two distributions.
Very close, you are correct in that the locating stops for the terminals in the mold create a physical limit, and all of the variation will lie from that point out. However, it would not be technically a "half curve", but there will be non-normal distributions that will "best fit" the resulting data, such as beta distribution, etc. Use of a best fit distribution analysis would be a good tool for this process. Adding the plastic shrinkage, etc. are very good factors to add to the total variance equation for this process, but you will likely find the size of that effect will be much smaller that the location of the terminals in the mold prior to molding. Again, it is always an estimate until evaluated on a case by case analysis.

The data should support a theory, not be the theory.

Bottom line of this brain teaser is this - just because you have a dimension that is bilateral, does not mean the distribution you should expect is "normal". You need to find out what the process is that generates the variation. Here, there are at least two possible processes, with very different distributions. Also, it shows that rubber stamping "Cpks" on a print is equally a rudimentary use of statistics. There is no way looking at the print if Cpk is going to be statistically correct. In this case, for the overmolded approach, it holds no value.

Good work, Jim and Erik!
 
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