Sampling Size and Sampling Frequency

Hi All, i am Hazwan. In my semiconductor workplace we just wanted to implement moulding process.
We have a LSL and USL defined by customer. Now we have to establish Sampling Size and Sampling Frequency for SPC.
IATF auditor mentioned he wants a statistical analysis with justification for the sample size and frequency.
After browsing the internet for hours and hours i still have no idea how to calculate to find the best sample size and sample frequency.
I guess there is a Power and Sample Size 1-T Test in Minitab for Sample Size.
Here are my questions:
1. Can i use Power and Sample Size 1 tail test for my case to get estimate sample size?.
2. Let say after use Power and sample size i got sample size = 2. In my process i have 4 mould cavity, does this means i need to take 2 samples from each mould cavity which makes my total sample size = 8 or is it just 2 random samples from any of the 4 mould cavities?.
3. I have no clue at all how to calculate or "estimate" sampling frequency statistically?. Is it something to do with ARL?.

Your auditor is an idiot who knows absolutely nothing about SPC. He/She is wrong. period. Full stop.
1) NO power and 1 tail tests are for comparing one sample to a standard or 2 samples to each other they ARE NOT for time series data.
2) NO you need to understand "Rational Subgrouping" see references below.
3) NO sample frequency is determined by the physics of the process - how frequently can the process change?

you are sniffing down the wrong road...and the right road is a long one. SPC is not that simple nor is it that statistically complicated. I take 2-3 8 hour days to teach SPC and I'm only scratching the surface.

SPC is has nothing to do with statistical inference or enumeration or statistical descriptions. It is an empirical enumerative methodology for time series data.

Please start by reading these FREE (click on the links) articles then come back with your questions:

Wheeler, Donald J., Neave, Henry R., “Shewhart and the Probability Approach”, Quality Digest, November 2015 (broken link removed)

Wheeler, Donald J., “Myths About Shewhart’s Control Charts”, SPC Tool Kit column, Quality Digest, September, 1996 https://www.qualitydigest.com/sep96/spctool.html

Wheeler, Donald J., “Myths about Process Behavior Charts”, Quality Digest September, 2011 https://www.qualitydigest.com/insid...icle/myths-about-process-behavior-charts.html

Wheeler, Donald J., “The Empirical Rule”, Quality Digest, March 2018 (broken link removed)

Wheeler, Donald J., “Exact Answer to the Wrong Question, Why Statisticians Still Do Not Understand Shewhart”, Quality Digest, March 2012 www.spcpress.com/pdf/DJW240.pdf

Wheeler, Donald, “The Right and Wrong Ways of Computing Limits”, Quality Digest, January 2010 https://www.qualitydigest.com/inside/six-sigma-column/right-and-wrong-ways-computing-limits.html

Wheeler, Donald, “What is a Rational Subgroup?”, Quality Digest, October 1997 https://www.qualitydigest.com/oct97/html/spctool.html

Wheeler, Donald, “Rational Subgrouping”, Quality Digest, June 2015 (broken link removed)

Wheeler, Donald, “Rational Sampling”, Quality Digest, July 2015 https://www.qualitydigest.com/inside/statistics-column/rational-sampling-070115.html

Bev D said:

Your auditor is an idiot

Click to expand...

Ohhhhhhhhh, what you said! I would have been called out for being mean, nasty, crude, impolite and harsh. Love it!

hazwan2283 said:

IATF auditor mentioned he wants a statistical analysis with justification for the sample size and frequency.

Click to expand...

Why is the auditor an idiot for asking such a question?

Because SPC doesn’t use or rely on classical statistical analyses to determine sample size or sampling frequency. In fact you’d be hard pressed to retroactively provide statistical justification for any of the standard sample sizes, WE rules, limit calculations, subgrouping scheme, etc. the few relevant statistical formulas and factors were all derived and published decades ago. So no justification there either.

Plus there is no standard that requires statistical analysis and justification (statistical or otherwise) for control chart sample size or frequency.

Sample size subgrouping and sampling frequency are determined by the physics of the process.

The auditor clearly doesn’t understand anything real about SPC and is imposing their own biased view.

I suspect the auditor is basing their inquiry on something like the auto industry supply chain book on SPC

Here what you could try:
1. Use historic data and plot it as SPC chart. Use one SPC chart for each of the four moulds.
2. Check, if you it is often one specific mould, which causes problems. If so, this suggests that the sampling frequencies for the moulds should differ.
3. Check that your data is normally distributed. If not, try to transform your dataset.
4. Check, if the results for the four moulds are (positively) correlated. If so, this might decrease the sampling frequency for each mould and suggests that we try to analyse the mould not at once, but separated in time. I also like to calculate the within and between standard deviations.
5. Check, if your process is stable. If not, optimise your process, because SPC won't help you.
6. Generate a list (process FMEA) containing the expected failure modes and their expected time periods. E.g. if the failure mode is gradually build up over a longer time interval, we are able to counter act this failure mode using SPC. In contrast, if a failure mode is expected to happen instantaneously (without any prior indicator), we are unable to counter act using SPC.
7. Next, determine the sampling frequency by incorporating the cost of a bad product and the cost of the measurement. Consider skipping certain measurements and just performing them every second/third/... time.
8. Finally, cross-check that your result makes sense. Do you have a procedure to relax the sampling frequency, if you find out that your initial calculations were too conservative? If not, consider accepting a higher risk by choosing a smaller initial sampling frequency. Do you believe that your historic dataset is representative of all the future datasets?

Finally, note that SPC works best if you know your process very well and thus you plot the key input parameters in the chart. I assumed that this is not the case.

hazwan2283 said:

Hi All, i am Hazwan. In my semiconductor workplace we just wanted to implement moulding process.
We have a LSL and USL defined by customer. Now we have to establish Sampling Size and Sampling Frequency for SPC.
IATF auditor mentioned he wants a statistical analysis with justification for the sample size and frequency.

Click to expand...

Hmmm. In rereading this post I am wondering if you are talking about acceptance sampling and not control charts? @hazwan2283 can you clarify?

Plastic Injection Molding SPC



First we have to understand when and how the characteristic(s) of interest can be measured. May plastic parts need to ‘cool’ to achieve their final dimension. Some can only be measured in a QC lab (CMM or comparator or other instrument that is not readily available on the manufacturing floor). These 2 things can add substantial delay front eh manufacture time to the measurement time. This typically doesn’t create problems for lot acceptance but can create problems for effective and timely SPC.



It’s often possible to measure the characteristic in it’s ‘hot’ state at the press IF the change is stable. Remember this is for SPC and not lot acceptance.



Next I would measure a 1-3 parts from every mold every 2 hours or so for an entire run. If the run is quite large I might space out the subgroups to every 4 - 6 hours. Then I old plot the data for each cavity on a separate run chart. LOOK at the data.

• if you took 2-3 measurements per subgroup is the variation within the subgroups roughly equal to the variation between the subgroups? I might try plotting the data on an Xbar R chart to see if it stable Again 1 chart for each cavity.
• If you took 1 measurement a simile I, MR chart will suffice. Again one chart for each cavity.

You should also LOOK at the difference between each cavity. Typically there will be a substantial fixed difference between the cavities. This is caused by size differences in each cavity and to a much lesser extent can be caused by ‘plumbing’ differences (size, length of tubing, etc.) that affect pressure, temperature, flow rate etc. This fixed difference is not random and so combining the different cavities in a single subgroup is wrong. The SD will be artificially inflated by the fixed differences. This difference isn’t always large enough to matter, so you must first collect the data, plot it and LOOK at it. With a small number of cavities it is fairly simple to maintain a chart for each cavity. With a large number of cavities it is better to chart only the extremes. This is part of rational subgrouping and understanding homogeneity and ho control charts detect non-homogeneity. It is also rarely taught.

In general my experience is that a subgroup of 1 is sufficient. BUT this must be validated by taking the data, plotting it and thinking about what the actual situation is.

HOWEVER, I have typically found (dealing with thousands of plastic parts of various sizes and complex geometries) that the traditional ‘in-line’ control chart is useless for injection molding. A well controlled process will drift slowly over time as the tool(s) wear. So, IF you have a solid set-up ‘first piece’ approval process for the start of a run, following maintenance, resin material lot changes etc. and you have validated the stability of the process over time using the above approach you are better off putting the lot acceptance data on a multi-vari chart and plotting the lot average on an I, MR chart. See the figure in the attachment. Miner can help you understand how to plot a multi-vari in MINITAB. (I am - or was - a JMP user). There are exceptions to this so be careful. It is far better to take a larger amount of data in the beginning to ensure that you understand your process variation and have validated that the process is stable.

Hi @Bev D , thank you for your reply. Really appreciate them, we quickly realized from your first reply that there is no real way to so call "calculate/estimate" what is the best sample size etc prior running anything. We are somewhat collecting some proper data first and as you said we also going to check is there any underlying factors between cavities etc. We also going to assess the resources we have against each sampling plan (size and frequency) as well. As for your question Bev, yes i was asking for SPC and not for the acceptance test Bev.

@Semoi , we are almost using some of your inputs as well.
Thank you very very much all of you.