Noob question regarding sample size

#1
Hello everyone,

I am a newbie here and hoping someone can point me a direction regarding my questions.

I am a RA for a medical device manufacturer located in SEA. I am trying to figure out plans for several 510k submission, and not sure what to do with sample size. We have some consumables like sterile catheters, and some sterile media for lab. For local authorities, we use confidence/reliability based on RPN to decide sample size, it is usually 29 or 59 and we do 10 * 3lots or 20 * 3lots.

I am wondering if the same could be applied for 510ks, and if there is other ways to calculate the sample size. Some keywords and brief explanation would be much appreciated!

Thank you!
 
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Steve Prevette

Deming Disciple
Leader
Super Moderator
#2
There are lots of ways to calculate sample sizes and sample plans. The 29 and 59 numbers are very common and reflect the sizes for c=0 plans. That is I sample 59 items and if I get zero defective, I am 95% "confident" (or "sure") that no more than 5% of the population are defective. You see 59 called out a lot, especially by the EPA. If I sample 29 items and I get zero defective, I am 95% confident that no more than 10% of the population are defective.

A common document used for sample plans was MIL-STD 105E, which was free. But it got canceled and rolled into ANSI/ASQ Z1.4 which you have to pay for to get a copy ($159).

I am no expert on 510k so will have to pass on that part of the question. But yes, there are lots of various sampling plans out there, all based around balancing false negatives and false positives (like the "problems" with the COVID tests). You end up looking at OC curves to judge how good a plan is, and what risks it represents. Whole textbooks are out there on the subject,

ASQ has this intro about acceptance sampling - ANSI/ASQ Z1.4 & Z1.9 Sampling Plan Standards for Quality Control | ASQ
 
#3
There are lots of ways to calculate sample sizes and sample plans. The 29 and 59 numbers are very common and reflect the sizes for c=0 plans. That is I sample 59 items and if I get zero defective, I am 95% "confident" (or "sure") that no more than 5% of the population are defective. You see 59 called out a lot, especially by the EPA. If I sample 29 items and I get zero defective, I am 95% confident that no more than 10% of the population are defective.

A common document used for sample plans was MIL-STD 105E, which was free. But it got canceled and rolled into ANSI/ASQ Z1.4 which you have to pay for to get a copy ($159).

I am no expert on 510k so will have to pass on that part of the question. But yes, there are lots of various sampling plans out there, all based around balancing false negatives and false positives (like the "problems" with the COVID tests). You end up looking at OC curves to judge how good a plan is, and what risks it represents. Whole textbooks are out there on the subject,

ASQ has this intro about acceptance sampling - ANSI/ASQ Z1.4 & Z1.9 Sampling Plan Standards for Quality Control | ASQ
Thank you for the tips! It is very helpful!
 

rayhope

Starting to get Involved
#4
Dear Steve,
Please suggest any literature which is freely available for C=0 sampling plan. above discussion is very helpful. Thanks
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
#5
I ran the 29 and 59 numbers in Excel using Binomdist. If you wanted to know - how many do I need to sample to be 95% confident that no more than 5% are defective - you are solving for the number of samples:

=BINOMDIST(0,59,0.05,TRUE) gives you the result of 0.048 which is just a hair under the 5%. If you put in 60 instead of 59, you get a result higher than 59. Also you can calculate that from (1-0.05)^59. Binomdist does assume a very large population size, you can refine the result using the hypergeometric. Bottom line for a sample of 59 - if there is a 5% defect rate, I have a 95% chance of detecting one or more failed items. Pretty good assurance that we will detect it in just this one sample.

Zero Acceptance Number Sampling Plans, Fifth Edition | ASQ is an example result if you put "c=0 sampling plan" into Google.

IMPORTANT - there is a downside to c=0. Yes, it gives you the smallest possible sample size BUT is more susceptible to false detects than the MIL STD plans. For example, if the actual defect rate is 2% (not 5%), I have a 70% chance of getting a defective item in a sample of 59. By the way, this is how you develop the Operating Characteristic curve for an acceptance test. Also, MIL STD is based upon accumulating results across many sample runs.

As an alternative, I could choose to construct a c=2 plan (Accept on zero one or two defects). To get the 95% confident that no more than 5% are defective, I go with a sample size of 124. Double the sample size. BUT if my "true" defect rate was 2%, the chance of getting 3 or more defects drops to =1-BINOMDIST(2,124,0.02,TRUE) or 45%. Still pretty high, but better than 70% from the 59 sample size.

As you can see from this exercise, that is why go no-go sampling (versus inspection for variables) gives such high sample sizes. And when we talk detecting 1% or less defect rates, it requires very large sample sizes.
 
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