# Sample size to prove parts are good with 99.73% confidence

U

#### Uchiha

Hello all:

Thank you everyone for making this forum such a great place to exchange knowledge.

Today I have a question that is blocking me at work. It's about sampling statistics.

We receive some parts from our supplier. The supplier is supposed to have checked the parts 100% before shipping. The final objective is that we do not want to check again at our incoming inspection.

However, the issue is that we have no garantee that the parts are not damaged during transportation. So we would like to have that proof...

We received a batch of 150 parts and we checked all of them. We found 1 NG part.

We're about to receive more shipments (around 4000 parts each).

My question is: how to prove statistically that the received parts are good with a confidence of 99.73%?
To ask the question in a different way: knowing that we found 1/150 bad part, how many parts do we need to check and find GOOD to proove statistically, with a confidence of 99.73%, that all the parts received are good and that no damage occurred during trasnportation?

Please be aware that my question is about pure sample statistics. The reasoning behind considering such a decision (and not checking all the parts for example) is not subject to this discussion.

Thank you very much

#### Jen Kirley

##### Quality and Auditing Expert
Assuming you are dealing with attributes and pass/fail, I wondered if the thread titled Using ANSI/ASQ Z1.4 to Reduce Impact of Field Service Campaign would be of use to you. sjared supplied a link to an online calculator that shows margin of error when considering 1 fail out of 150-item batch with a 98% confidence level.

I hope this helps! Please also note that related threads are listed at the bottom of this page and the one I am referring you to.

#### Statistical Steven

##### Statistician
Super Moderator
100% inspection! Why you say? You found 1/150 defective (0.67% defective), which makes it nearly impossible to have such confidence of zero defectives.

Regardless, you would need to sample 1108 units and see no defectives to have 95% confidence of 99.73% reliability.

Hello all:

Thank you everyone for making this forum such a great place to exchange knowledge.

Today I have a question that is blocking me at work. It's about sampling statistics.

We receive some parts from our supplier. The supplier is supposed to have checked the parts 100% before shipping. The final objective is that we do not want to check again at our incoming inspection.

However, the issue is that we have no garantee that the parts are not damaged during transportation. So we would like to have that proof...

We received a batch of 150 parts and we checked all of them. We found 1 NG part.

We're about to receive more shipments (around 4000 parts each).

My question is: how to prove statistically that the received parts are good with a confidence of 99.73%?
To ask the question in a different way: knowing that we found 1/150 bad part, how many parts do we need to check and find GOOD to proove statistically, with a confidence of 99.73%, that all the parts received are good and that no damage occurred during trasnportation?

Please be aware that my question is about pure sample statistics. The reasoning behind considering such a decision (and not checking all the parts for example) is not subject to this discussion.

Thank you very much

#### Mike S.

##### Happy to be Alive
Trusted Information Resource
Without doing a single calculation I'm guessing SS is correct -- 99.73% is an insane confidence level and you might as well just default it to 100% inspection and hope you can inspect well enough, because even then, your inspection is likely to not be 99.73% accurate!

#### Bev D

##### Heretical Statistician
Super Moderator
for additional clarity: you can NEVER prove that all parts are 'good' with a sampling plan.

sample plan statistics simply don't work that way. I know we wish it were different, but its not. you can only say with some risk of being wrong that the lot is no worse than some defect rate > 0 defective.

When trying to understand if a lot has no defects you can use the upper exact binomial confidence interval on zero defect rate to determine the worst case defect rate that would result in zero defects found in a sample.

you also make sure that your sample is random for the statistics to have more meaning than a mathematical exercise.

if you are concerned about damage, it is better to understand how the damage occurs. are the damaged parts anywhere in the box? at the corners, edges or perhaps along any side?

The single best way to guarantee that the parts are not damaged is to understand how they got damaged and change the packaging to prevent the damage.

Sampling plans are really only intended to stop gaps and safety nets until we can fix the root cause of any problem.