Determining the Appropriate Sample Size for Process Validation/Qualification

Q

quality_ab

#1
What should be the rationale behind deciding the appropriate sample size for any process validation/qualification.

In fact even for capability studies a sample size of 30 seems to be the norm. How does one justify the sample size.

Thanks in advance.
 
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Marc

Hunkered Down for the Duration with a Mask on...
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#2
Any takers on this one? I don't know how the sample size of 30 was determined as 'standard'.
 
W

wmarhel

#3
quality_ab said:
What should be the rationale behind deciding the appropriate sample size for any process validation/qualification.

In fact even for capability studies a sample size of 30 seems to be the norm. How does one justify the sample size.

Thanks in advance.
I believe the norm of 30 comes from the Central Limit Theorem, but its Monday morning and the brain may not be fully awake. If I recall correctly, as the sample number approaches 30 the distribution begins to look normal.

Somebody let me know if I goofed that up..... :bonk:
 
D

Darius

#4
wmarhel said:
I believe the norm of 30 comes from the Central Limit Theorem, but its Monday morning and the brain may not be fully awake. If I recall correctly, as the sample number approaches 30 the distribution begins to look normal.

Somebody let me know if I goofed that up..... :bonk:
Agree, But it's not the same thing?, because of the central limit theorem the distribution looks Gausian :)mad: I hate the "normal" term, many tink that "non-normal distributions" are weir or not common), and the statistics so become more or less stable. :rolleyes:

But remember as I say, the statistics are just estimates, so IMHO you should see the confidence interval for the estimate (the lesser the sample size the bigger the confidence interval, or Uncertainty). :bonk:
 
Q

quality_ab

#5
Thanks to everyone for replying. I would now like to rephrase my earlier question.

Is there a good way to decide the appropriate sample size for process and equipment validation / qualification.

AB
 
A

Arvind

#6
Sample size 30 is decided from normality . Maynot be adeqate for capability

Magic number of 30 samples is derived from nomality point of view. This number may not be adequate if you need tighter confidence interval on capability.

Please take a look at confidence interval on Cpk which changes with sample size. The confidence intervals are calculated from Chi square tables.
Sample size---------- Tolerance on Cpk
10 ------------- +/- 45 %
30 ------------- +/- 25 %
100 ------------- +/- 14 %

In view of above, it doesnot serve much purpose to calculate Cpk on small sample size.

Arvind
 
J

Juan Dude

#7
Thanks to everyone for replying. I would now like to rephrase my earlier question.

Is there a good way to decide the appropriate sample size for process and equipment validation / qualification.

AB
Does anyone have any good suggestions?
 
M

M Komarmy - 2012

#8
The purpose of a machine acceptance study is to have confidence that the process can produce product at an acceptable quality level. Any short term study that you perform, whether it is 30 parts or 300 parts, will see variation in the results (Ppk) when replicated many times. There will be an upper and lower 95% or 99% confidence interval for the result. In the automotive industry, the PPAP process defaults to an initial process study comprising of 100 parts from a 300 piece production run (unless a different amount is agreed to by the customer). A typical OEM requirement is 1.67 Ppk with a 100 part study. The lower 99% confidence boundary is approximately 1.40 Ppk. If this is set as the minimum for acceptance, then as your sample size decreases, the acceptance limit will increase. For example, if you choose a sample size of 30 parts, to insure an equivalent capability of 1.67 Ppk with a sample size of 100 parts, the 30 part sample must achieve a 2.07 Ppk or higher. I have attached a chart taken from the Ford machine acceptance specification to show this in more detail.
 

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Miner

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#9
In the early 1980's the sample size required for a capability study was initially 30 pieces. This was because the confidence interval for the mean rapidly shrinks in size to about n = 30 then shrinks at a much slower rate.

However, the Cp/Cpk indices are calculated not only with the mean, but with the standard deviation, which also has a confidence interval associated with it. This confidence interval requires a larger number of samples. The minimum sample size was raised to 50 in the mid 80's to address this.

To make it worse, divide one number with uncertainty by a second number with uncertainty and you have a capability index with even greater uncertainty. As shown on the graph that M Komarmy provided, it takes ~ n = 100 before this confidence interval reaches an acceptable level. The automotive industry finally realized this and increased the sample size to 100. Unfortunately, they did not communicate the rationale for the change to the supply base, so people did not understand why they needed the additional samples.
 
B

badgary

#10
The answer to your question is this:

First: determine the risk level associated with the process. This can come from a process FMEA or similar activity. Many organizations keep things simple and categorize risk in to groups like low, medium, and high.

Second: Make a connection from the risk level to an appropriate confidence level and/or uncertainty level for use in statistics. Many organizations have internal procedures where they give guidance. For example... If HIGH risk, then sample size must satisfy a 99/99 confidence/reliability. If MEDIUM risk, then sample size must satisfy a 95/95 confidence/reliability. If LOW risk, then sample size must satisfy a 95/90 conf/reliab. The numbers should be agreed on across your organization so that there is continuity among all the validations.

Third: Choose from a number of statistical methods to calculate sample size, given the known variables that were determined from your associated risk level.

This answer is vague, but correct when it comes to validation. So a sample size of 30 may or may not be appropriate for validation. Its really only useful in that most data starts to look 'normal' shaped and it may eliminate the need to test for normality in some applications. If in doubt about the sample size to use, start with a RISK ANALYSIS.

-Gary
 
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