Determining Sample Size needed for Operational Qualification (OQ)

Bev D

Heretical Statistician
Staff member
Super Moderator
#11
Thanks for all the replies. I ended up just using the Power and Sample Size for One-Way ANOVA tool from Mini-Tab. I entered a standard deviation, Power value and maximum difference b/t the means, and then MiniTab calculated the sample size.
be aware that MINITAB gave you the sample size for estimating the MEAN and in OQ or any other validation we also need to understand the variation of the INDIVIDUAL VALUES with relationship to the specifications. The intent of validation is to demonstrate that all material made meets spec - or in some cases that the generated defect rate is no worse than the previous process.
The sample size necessarry to estimate the variation of the individual values is tied to the standard deviation and not the mean...the sample size for good estimates of the standard deviation are larger than those for the mean... if you are submitting data for a regulated industry such as pharma or medical devices (which are the industries that typically reference IQ, OQ PQ for 'special process' validation) a good reviewer will question this choice.
 
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mipelamo

#12
Bev,

Let me give you a little bit more background information. In the past, I have always performed OQ at minium of 2 lots at worse case conditions with each lot having a minimum of 60 pieces. Since my accceptance criteria is usually measured in Cpk, I have always used the rule of thumb that at the minimum 25 pieces should be used to acess process capability. Hence, the 60 is more than double.

However, my customer doesnt want to pay for that many samples. He wants historical data to determine the sample size. Hence, my question to the forum. Are you recommending that I use a different tool than the Minitab Power and Sample size?
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#13
yeah - too many Customers want perfection but they're only willing to pay for "not quite good enough"...

I think what you want to play with (and yes its a trial and error or iteration process) is the confidence intervals for Cpk (or more correctly Ppk) to see what sample size is appropriate.

Look at Barbara's post and attachment here

and the formulas (from Minitab) are here
 
#16
Another style of spreadsheet to check out.
Good morning all, and particular thanks to Bev for posting the spreadsheet above.

Quick question if I may: Is this spreadsheet applicable for Ppk as well?

We have recently adopted a method for validation sample sizing which relies on the valid statistical techniques and incorporates risk, as discussed by Bev & others in many threads.

2nd question: When considering the Medical Device GMP, is incorporating a tool like this CPk Limits spreadsheet to establish 95% confidence of a true Ppk something that should typically be done in addition to the proper sample sizing? I'm looking for confirmation that doing both isn't overkill, but expected...

Thanks in advance for your help!
 

Statistical Steven

Statistician
Staff member
Super Moderator
#17
Here is a formula that I sometimes use to determine a sample size:


n= ln(1-C)/ln(R)

Where:
n= the required sample size
C = confidence level
R = reliability

For exaplme if you want to be 95% that you are 95% relaible you wood need 59 good (failure free parts).

Mark
This assumes an attribute (go/no-go).

As Bev stated, usually the hypothesis for an OQ is no difference in the response (output) when varying the process parameters (determining the operational window). You can use tolerance intervals, confidence intervals or the confidence interval on Cpk (I usually use this approach with the MSE from the ANOVA being my estimate of S).
 

Statistical Steven

Statistician
Staff member
Super Moderator
#18
Good morning all, and particular thanks to Bev for posting the spreadsheet above.

Quick question if I may: Is this spreadsheet applicable for Ppk as well?

We have recently adopted a method for validation sample sizing which relies on the valid statistical techniques and incorporates risk, as discussed by Bev & others in many threads.

2nd question: When considering the Medical Device GMP, is incorporating a tool like this CPk Limits spreadsheet to establish 95% confidence of a true Ppk something that should typically be done in addition to the proper sample sizing? I'm looking for confirmation that doing both isn't overkill, but expected...

Thanks in advance for your help!
You can use JUST Cpk (Ppk) limits to set sample size.
 
#19
Not sure I understand Steven, let me rephrase:

We currently use 95% confidence, a reliability requirement based on risk, a previously observed standard dev. and agree upon an acceptable difference of means to get the sample size, through a leading software. Say the output of this is 40.

Then say I use the attachment I mentioned to calculate that I need an observed Ppk of 1.65 for 40 samples to be 95% sure that my true Ppk is at least 1.33.

Are these 2 steps redundant, or both important?

Thanks again!
 

Statistical Steven

Statistician
Staff member
Super Moderator
#20
Not sure I understand Steven, let me rephrase:

We currently use 95% confidence, a reliability requirement based on risk, a previously observed standard dev. and agree upon an acceptable difference of means to get the sample size, through a leading software. Say the output of this is 40.

Then say I use the attachment I mentioned to calculate that I need an observed Ppk of 1.65 for 40 samples to be 95% sure that my true Ppk is at least 1.33.

Are these 2 steps redundant, or both important?

Thanks again!
It is redundant. Based on the risk, you determine the true Ppk you would need. Instead of selecting an arbitrary Ppk of 1.33, you select one that reflects the risk or amount of out of specfiication product that can be theoretically seen in a process (it is the same as the rationale you use for the difference in the means).
 
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