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!