# Proper Sample Size to Evaluate Defect Rate

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- This topic has 6 replies, 2 voices, and was last updated 1 year, 8 months ago by Robert Butler.

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- November 12, 2013 at 6:19 pm #54590

edwardParticipant@eisidor1974**Include @eisidor1974 in your post and this person will**

be notified via email.Hi. I have a process with a very large batch size (let’s say 2 million units for the sake of argument) and what seems to be an extremely low defect rate (i.e. <0.1%). That said, I have no real idea of what the exact defect rate is. Currently we only sample & evaluate ~10 units per batch, so it could be 0.00001% or it could be 1%. As you’ve probably already figured out, I think our sample size is totally inadequate.

I’d like to figure out what the true defect rate is with a reasonable level of confidence, so I would like to execute a study of a typical batch and take a much larger sample. The question is, I don’t know how to decide (scientifically) how big that sample should be. I’d like to be 95% sure that the sample reflects the total population within 0.01 percentage points. Can anyone guide me towards the proper math here?

I searched for some similar posts and couldn’t find anything that really answered the question.

0November 12, 2013 at 8:56 pm #196226

Fahd lahrechGuest@founder1**Include @founder1 in your post and this person will**

be notified via email.What you need is to use “power and sample size estimate” in minitab. You provide the software with the following: comparison rates, power values and the hypothesized rate, minitab will then give you the sample size. Take for example, comparison rate to be 0.01, power to be .95 or 95% and the hypothesized if 0.1 or less, minitab will calculate the sample size. In this case it will be 76. good luck and let me know if you have other questions.

0November 13, 2013 at 3:19 am #196230

Don StrayerGuest@Straydog**Include @Straydog in your post and this person will**

be notified via email.If you don’t have a Minitab license, you can find quite a few sample size calculators via web search. Many of them are free for use on-line or download. Unless they say otherwise, assume that these only use the basic formula which applies to attribute (integer) measurements. If your measurements are proportional or use decimal places… This Wikipedia post is a pretty good starting point. http://en.wikipedia.org/wiki/Sample_size_determination

0November 13, 2013 at 7:59 am #196234

edwardParticipant@eisidor1974**Include @eisidor1974 in your post and this person will**

be notified via email.Hi guys. First off, thanks for the fast responses. I do have minitab, so I’m looking to that first. There are many sub-options for “Power and Sample Size”, so any advice about which one to choose would be helpful. I haven’t found one with the exact parameters founder1 mentioned. As a note, this is definitely pass/fail attribute data that I’m looking for.

0November 13, 2013 at 8:01 pm #196235

Fahd lahrechGuest@founder1**Include @founder1 in your post and this person will**

be notified via email.In minitab go to “stat” and then “power and size estimate” then look for 1 poisson rate… You should be able to enter those parameters. Hope thaf helps!

0July 26, 2018 at 5:10 am #202856hi,

I had raised 30 defect events on 60k trials, can you any one tell how many trial in smaller sample size need to conduct to achieve the confidence after rectifying the problem.0July 26, 2018 at 7:05 am #202857

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.Your data says you have a defect rate of .05% If you want to be 95% confident that this is the actual defect rate then you will need 22,600 samples. Your defect rate is so small that one would wonder why it is of any concern.

As for detecting a change. At this percentage level any change you could possibly see would be very small and the sample size needed to check the before and after proportions would be huge. For example, if you are looking to see a 10% decrease in this defect rate you would need a sample of 5.9 million to be certain with an alpha of .05 and a power of 80%.

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