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Sample Size Calculation

My current process is operating at a 0.01 defect frequency (e.g., 3 defects in last 300 units inspected).  If I make a process change that could potentially increase the defect frequency, how many units will need to be inspected post-change to determine if a statistically significant difference in defect frequency?

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Sample Size Calculation

Mark:

Here is a good formula for the AQL sample size  and the RQL sample size   The sample size, 947 or 948 is shown.

I would have sent you the JMP table but don't know how to post it here   9 REPLIES 9

Re: Sample Size Calculation

Mark:

With the current process at 1% defective you have to set a upper defective limit say 2%. Also, the risks have to be assigned, typically 10% for type I & II errors

The sample size is than the sample size and defect value which will accept a 1% or lower defect level 90% of the time while rejecting the product when the relect level is 2% or higher 90% of the time.

An OC curve is the best way to visualize the results

Re: Sample Size Calculation

You will also need to articulate 'delta'...or what is the minimum defect rate improvement that you are trying to detect.

Re: Sample Size Calculation

Mark:

My Excel based calculation says a sample of 948. If there are 13 or less defects, accept that there is no process shift, greater than 13 defects a shift has occurred, given the risks specified. Re: Sample Size Calculation

Hi,

Can you please send the table as attached file.

Thanks  Steven_Moore
Super User

Re: Sample Size Calculation

I suggest you use a Runs Chart and/or Process Behavior Chart (Control Chart),  With this type of "rare event" data, both work well.  Use "good units inspected between defective units" as your test variable.  When you make your process change, you will be able to detect a shift in performance, if there is one.  See my article in Quality Digest regarding OSHA Recordable Injuries (same type of data)...http://www.qualitydigest.com/inside/quality-insider-article/alleviating-tortured-data.html

Steve

Re: Sample Size Calculation

Mark:

Here is a good formula for the AQL sample size  and the RQL sample size   The sample size, 947 or 948 is shown.

I would have sent you the JMP table but don't know how to post it here   Highlighted

Re: Sample Size Calculation

FYI (and regarding 'but don't know how to post it here') - If you use the 'Advanced Editor': there's an 'Attach' link at the bottom right.

Re: Sample Size Calculation

Thanks for the tip ! !

Re: Sample Size Calculation

I am having trouble with this formula for low rejection rates, e.g. AQL 0.1% RQL 0.25% .  Any ideas?  Curious about the use of Chi sqaure quartile vs binomial, etc

@vinkane wrote:

Mark:

Here is a good formula for the AQL sample size  and the RQL sample size   The sample size, 947 or 948 is shown.

I would have sent you the JMP table but don't know how to post it here   