Statistical basis for 30 pieces for FAI

ScottK

Not out of the crisis
Staff member
Super Moderator
#1
Came up in a conversation today...

What is the statistical basis for a 30 piece sample when doing FAI on medical devices... it seems that is the standard across many of the large customers I've served in the past (Stryker, Medtronic, Zimmer/Biomet, J&J, BD, Cardinal, etc...)

Wondering where this came from. At some point in my distant past I was given the statistics behind this but that's long lost...
 
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optomist1

A Sea of Statistics
Super Moderator
#2
here's a bit of info re: sample size, this is independent of industry....there is much more to this...choosing sample size...type I/II errors...if you're using Minitab the tutorial re: "Power and Sample Size" is good. Thirty (30) pieces is used across many fields...

Sampling – the greater the sample size the better the probability of detecting differences in data groups means etc, this applies to anova, t-test and doe replication as well, replication increases the degrees of freedom, reduces beta errors and increases the ability to detect differences. Small sample size gives high beta errors and harder to detect differences.

This scratches the surface, hope it helps...optomist1
 

Miner

Forum Moderator
Staff member
Admin
#3
I agree this is somewhat independent of industry. When I first started in automotive quality (back in the 80s), the required sample size was 30. In the 90s, it became 50, then rapidly changed to 100.

See the attached graphs for an example of how the confidence limits for the mean and the standard deviation decrease with sample size. While 30 or 50 might be reasonable for the mean OR the standard deviation, when you combine them into the Cp/Cpk indices, the confidence limits for the index become very large until you reach a sample size of 100. The automotive industry learned this the hard way when suppliers reported good capability, but the actual performance was far worse.

The history behind most of these practices was an economic balance between the cost of collecting the data and the cost of being wrong.
 

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Bev D

Heretical Statistician
Staff member
Super Moderator
#4
And when I was in the aircraft engines business the sample size was 1. I always thought that was silly for various reasons. 30, 50, 100 are the base sample sizes for capability studies so I guess that’s the intent.
 

nozzle

Involved In Discussions
#5
The last company I worked for in the medical devices sector required a FAI on one piece and then measurements of CTQ dimensions on 32 pieces to determine the process capability.

The FDA accepted this approach as the CTQ dimensions were identified as the highest risk.
 

Jim Wynne

Staff member
Admin
#6
Came up in a conversation today...

What is the statistical basis for a 30 piece sample when doing FAI on medical devices... it seems that is the standard across many of the large customers I've served in the past (Stryker, Medtronic, Zimmer/Biomet, J&J, BD, Cardinal, etc...)

Wondering where this came from. At some point in my distant past I was given the statistics behind this but that's long lost...
The justification, as I originally heard it many years ago, was that after 30 pieces randomly selected, the difference between the population standard deviation and the sample standard deviation becomes insignificant for practical purposes. In other words, if the sample of 30 is truly random (which almost never happens) you will allegedly get roughly the same information as you would if the entire population were measured.
 

ScottK

Not out of the crisis
Staff member
Super Moderator
#7
The justification, as I originally heard it many years ago, was that after 30 pieces randomly selected, the difference between the population standard deviation and the sample standard deviation becomes insignificant for practical purposes. In other words, if the sample of 30 is truly random (which almost never happens) you will allegedly get roughly the same information as you would if the entire population were measured.
That's ringing a bell.

Funny thing most of the time I've done this the populations is very small... a typical order size would be 20 every 6 months, for example.
So the qualification lot would often be bigger than a normal order.
But I guess that comes from working much of my career in high variety, small lot size business.
 

dwperron

Trusted Information Resource
#8
I had always been taught that 30 was the dividing point for the sample size. Above 30 you could use z distribution, below 30 you used Student-t distribution.
Below 30 was considered a small sample size.
 
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