Calculation of specification limits for manufacturing yield

[Angelo2Raffa2]

Dear expert, I need to understand how calculate the specification limits for manufacturing yield.
I have only four value as dataset. They are related to first batches manufactured to validate the manufacturing line.
The data are the following: 87% - 92% - 93% - 90%.
I don’t know the minimum dataset size needed to calculate the specification limits and the approach to apply.
Is there someone that help me?
Thank you very much!

 

[Bev D]

Is this some kind of homework assignment?

There are no specification limits for manufacturing yield.

If this is a PQ build or a ‘design’ requirement (related to the target profitability and availability usually set by the product owner/marketing) then the minimum yield is set PRIOR to manufacturing not from actual yields.

If you are trying to set control limits for yield you need to know both the numerator and denominator of the yields.
In any case, while there is no real precise sample size, 4 samples is too few.

So what are really trying to do?

 

[Angelo2Raffa2]

I need to create a control chart to monitor the parameter (filling yield). I have at the numerator the number of units filled and at the denominator the theoretical solution before of the filling step.
We are thinking to calculate the action/specification limits in order to consider them during of the manufacturing.
The batch size is not the same; it change.

 

[Bev D]

So words matter. Action limits, specification limits and control limits all have very different meanings. If you are creating a “control chart” then you will be calculating control limits. There are very specific formulas and rules for this. If you are trying to monitor your process to determine when you need to action because the process has changed then specification limits and the ill advised action limits are not appropriate.

Although I’m not sure you are calculating the yield correctly (it’s not the ways I would normally calculate fill yield) it might still work for your needs. I would probably recommend using a “Individuals, Moving Range chart” (aka I, MR or X, MR chart). Hte applicable formulas are readily available on the web. OR you can go to SPCPress.com to see Dr. Donald Wheeler’s papers on I, MR chart (I do recommend this)

You can start calculating limits at 10 batches (anything before that is probably too soon) and then adjust as you get to 20 batches…

Control charts are not easy. They are not a cut and paste thing. They are complex. Do your research.

 

[Angelo2Raffa2]

Thank you for your explanation.
We use the control chart to monitor shift/trend an we’ll use the individual chart.
We are thinking to have the specification limits and entered in the frame of working instruction to use during the manufacturing. While the control chart we cannot have the possibility to see them during
If I consider 10 batches to calculate the specification limits, please can you suggest me how calculltate them?
Thank you

 

[Bev D]

NO SPECIFICATION ONLY CONTROL LIMITS

 

[Bev D]

If you need a specification for the individual containers you have to set that not calculate from yield. For example a 12 ounce beer bottle has a min fill spec of 12 ounces. And a max that is less than an overfill

There can be no spec on yield. Maybe a goal or target. But again you set that. And it isn’t a control limit

 

[brionhurley]

You might also consider a p-chart to monitor yields (or defect rates), as the I-mR chart can signal more out of control conditions the closer it gets to 100% (nonnormal distribution).

 

[Bev D]

You might also consider a p-chart to monitor yields (or defect rates), as the I-mR chart can signal more out of control conditions the closer it gets to 100% (nonnormal distribution).

Actually it’s the other way around. The p chart is based on the estimation to the Normal (binomial distribution) AND that the defect rate is at least 5%. The closer it gets to 0 or 100% the further the binomial deviates from an approximation of the Normal. The I, MR chart is very robust for ANY distribution like other Shewhart charts.

 

[brionhurley]

Why I like that the p-chart is that it doesn't give lower control limits below zero, where I-mR can require the control limits to be manually adjusted (set UCL at 100% or LCL at 0%) since the software programs don't know it is binary data, and it can give limits above 100% and below 0%. I also don't like treating yield data equivalent to continuous data, but that could just be my bias.

What would be the best recommendation for P vs Laney P' vs I-mR when using pass/fail (binary) data?

• You can typically use the I-mR chart for pass/fail data except when there are dramatic changes in sample sizes in each subgroup (then p-chart might be better)
• You could also use a p-chart if % defective (p) is at least 5% (or success rate is less than 95%) and n*p or n*(1-p) is greater than or equal to 5 for each subgroup
  • If the p-chart identifies lots of outliers (due to more variation than assumed by the binomial), then consider Laney P' chart to handle overdispersion or underdispersion

Does this sound correct, or if not, what would you change?