Determining the Appropriate Sample Size for Process Validation/Qualification

J

jameswalsh

#11
In my company we use 99% reliability with 95% confidence for high risk (patient safety), 95% reliability with 95% confidence for medium risk (functional defects) and 90% reliability with 90% confidence for low risk (cosmetic defects).
I found some very useful Beta tables in a book called Reliability Statistics by Robert A. Dovich. These tables allow you to calculate the reliability of a process (at a given confidence level) if you know the number of samples taken and the number of failures.
While these tables are very useful, I would love to know the mathematical formula behind them. Does anyone know it?
Regards,
James
 
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R

rangerboat72

#12
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.
Do you have any idea why Ford now requires their suppliers to do a 125 piece capability study?
 

Miner

Forum Moderator
Staff member
Admin
#13
Do you have any idea why Ford now requires their suppliers to do a 125 piece capability study?
It has to do with the level of confidence around the capability indices. When you take a sample, there is a confidence interval around both the mean and the standard deviation. A Cp or Cpk index uses BOTH the mean and the standard deviation with their associated confidence intervals. Therefore the capability index has even wider confidence intervals.

Increasing the sample size reduces the width of the confidence intervals.
 

Romvill2002

Involved In Discussions
#14
I have the same issue, Trying to validate a process change and came across on what sample size would fit the test(life cycle test). I found out that my monthly average production for the medical device averaging 61. Im trying to find formula that will link confidence and reliability and how it affect AQL and LTPD. I know there is link to these four parameters - need help share me the formula of each above parameters and i will just link them mathematically.
Formula for AQL, how we the 1.0, 1.5 ...
Formula for LTPD?
Formula for Confidence level ?
Formula for reliability level?

sample:
TypeParametersAQLLTPD0.1Singlen=15, a=00.34%15%Singlen=25, a=11.44%15%

How to derive these values?
 
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