When considering the concept of what gage resolution is appropriate for SPC, we can benchmark some of the work from the automotive industry found in AIAG MSA (Measurement System Analysis)
3rd edition. It refers to the "10:1 rule of thumb" on page 43-44. They state that it can be considered a starting point, but that it "does not include any other element of the measurement system's variability." ndc (number of distinct categories) uses the gage study to generate statistically significant "buckets" or true gage resolution versus the indicated gage resolution or "readability" or "discrimination" (number of graduations, digits, etc. on the gage).
On page 45, they claim that the ndc should be greater than 5. And that may be true for general measurement. But it is woefully inadequate for SPC!
The most key statement is "If the measurement system lacks discrimination (sensitivity or effective resolution), it may not be an appropriate system to identify the process variation or quantify individual part characteristic values. All parts in the same category will have the same value for a measured characteristic."
On page 45 through 46, they indicate the need for good resolution in order to have SPC be effective. They claim, again, 5 categories is sufficient for SPC, which, again, is woefully inadequate. You should have 5 categories on either side of the mean - if you are using X-bar-R charts or similar - to have enough resolution to utilize Western Electric rules (or similar). In fact, on page 46 they indicate "adequate resolution would be for the apparent resolution to be one tenth of the total process six sigma standard deviation." For SPC, I prefer the following:
ndc (for SPC) = ((UCL-LCL)*1.41)/(GRR) >10
This calculation assures 10 statistically significant categories within the control limits.
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Gage Resolution Required for SPC
Inadequate gage resolution will destroy your SPC efforts!