Calculation of specification limits for manufacturing yield

[Bev D]

I’ve successfully used the I, MR chart for yield (and RTY) data for decades. The I, MR chart is quite robust and useful - Wheeler nicknamed it the Swiss Army knife of control charts. And having to truncate a control limit is a very small thing compared to using the wrong chart and chasing false alarms or missing real alarms. I typically supported literally 10s of thousands of real time charts from manufacturing yields and test data to warranty/Customer complaints to field product performance data. We used many different types of charts so we never used Minitab/JMP or any of the EXCEL based charting software - they really don’t support real time charting of streaming data nor do they scale for the number of charts we used. We used SAS. Control charts in the popular software packages tend to be more useable or useful for initial investigation or for troubleshooting (and they are a very weak analysis for troubleshooting compared to multi-vari charts)

I used to believe that the I, MR chart wouldn’t work for large changes in the subgroup sizes but my experience has been that you really have to try the chart(s) to see which works best. The generic guidance is just that, guidance. Like ‘the best subgroup size is 5 sequential pieces’…might have been in Shewhart's day and before calculators and software - and with many manual processes where piece to piece variation was the most common largest component of variation, but not today.

We used the Laney p’ and u’ charts when the defect or occurrence rate was very low compared to the ‘denominator’ or area of opportunity.
The I, MR chart is just fine for ‘attribute’ data, more frequently than the p chart which is limited to requirements of meeting the binomial distribution. See Dr. Donald Wheeler’s papers on this topic:
What About the p-Chart?
Individual Charts Done Right and Wrong (how does your software rate?)
What Makes the I, MR Chart Work
A History of the Chart for Individuals
And many others found at SPCPress.com

One of the least discussed, trained and understood aspects of SPC is how to select the correct chart and set up rational subgrouping…

In other words the right answer is “it depends”

 

[Angelo2Raffa2]

First of all, I would like to thank you for your support.
I’m working in pharma acoustical manufacturing and I have to calculate the limits for the yields of each step of manufacturing.
The calculation of limits yields for each manufacturing step is mandatory and required by FDA.
So my doubts are the following:
1) how much data I need to calculate the limits;
2) the statistical approach to apply;
3) if the limits required by FDA, are considered the classical Ctrl limits of the control chart or other.
Thank you very much for your support.

 

[Bev D]

Can you quote the section that requires this?

I suspect that you are dealing with ‘yield’ limits that are essential to understanding how much of the active ingredients were actually incorporated into the product. Too little and the things will not perform correctly and ‘too much’ might indicate either fraud or an over incorporation that would also affect performance. There should always be some loss as things get stuck in the equipment, etc. in the USDA world this is called ‘accountability’. For some things excessive loss can be dangerous (hazardous chemicals for example)

An I, MR chart still seems like the best way to understand the natural variation of your process. But it is not how you ensure that the correct amount of stuff was incorporated into your product, as this is done during development OR it can be that you made a few batches that worked and passed performance requirements in which case you are stuck with the limits from the development verification lots. These can be changed after regulatory approval with manufacturign yield data that is correlated to performance data but is a lot harder to do this after the fact.

Specification limits and control limits are completely different things and you haven’t successfully told us which one you actually need…so I have no idea what you are actually asking

There are some engineering/scientific calculations to determine the minimum and maximum yield that will guarantee performance that meets label claim.

Again perhaps this is a language issue, but without knowing the exact requirement and exactly what you are making we cannot give you reliable advice. So far you have not answered these questions…