# Number of Distinct Categories" or NDC Calculation in MSA Studies

#### bobdoering

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Thank you for sharing. I will be working through these in detail but I can see he has come to the same conclusion as many of us: NDC is a flawed, essentially worthless calculation.

Unfortunately, we need a valid ndc calculation. Hopefully somebody can come up with it. We need to know the true "resolution" of a gage, with its error considered. For example, you have a steel rule with a 100th of a inch resolution. But, you never get that resolution measuring with it because of its various errors. So...what resolution can you count on...based on valid statistics? Most gages have the same issue.

#### bobdoering

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@bobdoering You may be looking for Dr. Wheeler's Relative Probable Error or the Effective Measurement Increment (in same article).
Looks close to what I am thinking. Sure looks handy for bilateral measurements or processes (not dimensions - measurements or processes), but might need transformed for unilateral measurements or processes, since their error cannot be normal (unless you are really far from the physical limit).

#### Welshwizard

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If we need a valid ndc calculation we need to be absolutely clear what we are asking for. The two most useful properties of a measurement process are, can I sort between good and bad parts according to a specification and can the measurement process monitor and improve as necessary the underlying process for the production process?

To answer the first one, we could start talking about bias and uncertainties but stripped bare you will always revert to the estimated standard deviation. The cousin of this is effectively the scaled standard deviation (Probable Error) which is what's referred to in Dr Wheeler's paper referenced above by Miner and is the effective resolution of the measurement process.

If you want to answer the second question you need to read manuscript 222 on www.spcpress.com and subsequently start using the Intraclass Correlation Coefficient (ICC).

If you have a customer who insists that you need to perform ndc calculations and reach the prescribed scores, respectfully outline what the ndc really does as I have pointed out here and compute the ICC also, if there is a dispute refer to the ICC and always try to get the most representative product variation sample you can. You will find that in using ICC your measurement process is far more useful than you ever dreamt it was for this property.

Whatever you do please be careful of what you wish for particularly for ndc which is not all its dressed to be unless you want to be a part sorter at the end of a production line. We don't need ndc but we do need effective resolution and ICC which are both easily determined from within the structure of a measurement study.

#### bobdoering

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...and can the measurement process monitor and improve as necessary the underlying process for the production process?
.

This is the key question I am concerned about. In order to make accurate decisions for SPC, for example, you need to have adequate statistical resolution (not gage resolution) to be certain you are "seeing" process change, and not gage error and thinking it is process error - common mistake. That resolution should be 10 "statistically significant buckets" for a Shewhart chart - 5 above and 5 below the target value. So, now we need to look back to Dr. Wheeler's approach and see if we can discern that.

#### bobdoering

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...and always try to get the most representative product variation sample you can.

As I stated originally, and my most significant point, what we know for sure is either historical data or an estimate of historical data from expected capability will make this calculation valid. It will never be even close to valid from the sample from a MSA study - especially on a new process. It is virtually impossible for that sample to represent the lifetime variance of the process. This would apply to ICC also.

#### Welshwizard

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With your "10 statistically significant buckets" I think you are maybe mixing up resolution and the notion of the increments versus tolerance against the way natural variation works, this is maybe due to what the ndc is portrayed to be against what it really is. Every observation you plot on a process behaviour chart has multiple sources of variation. In the context of the chart all we are interested in is can we pick up them shifts and patterns with whatever selection of western rules we choose.

Measurement error interacts with part variation in a process behaviour chart setting but we are only looking to pick up the patters and shifts so the notion of splitting out or dividing measurement error on its own isn't useful or required. In fact, if you do this for this purpose you will most likely condemn perfectly good measurement systems.

Of course, this doesn't mean that because we have an adequate ICC that these systems are adequate for sentencing good from bad parts, that's a different question. The aim, eventually is to harmonise adequacy for SPC vs adequacy for sentencing parts by working to get that elbow room in the production process.

ICC is not immune from inadequate estimates of part variation, no, its just a statistic and like all statistics it relies on its inputs. My significant point is that as a statistic the ICC is empirically proven to be an approach to portraying usefulness of the measurement process as opposed to the ndc.