# Sampling Plan Risks

#### Leturc

##### Registered
Dear All,

I would like to thank you Elsmar community and wish to you all happy an safe new year 2021!

We have done visual inspection for one of our client before goods are shipped. Based on the result "Pass", our client allowed the shipment.

5 lots are concerned. Each inspection is done on various date. We inspected 200 samples (Level II) from 5 differents lots.

Our client came back to us telling they have discovered 1.48% defective rate on the shipment inspected by our team and statistically speaking there was only 5.07% of probability to accept the batch with this defect ratio.

We don inspection by attributes and have 3 types of defect classification :

Sampling size: Level II Normal
Critical: 0.065%
Major: 2.5%
Minor: 4.0%

If on a single piece we have multiple kind of defect, we will consider the most serious one as rejection reason: Critical > Major > Minor

Our client found as above around 1.48% of critical defective rate on the totality of pieces received: open seam
Our team didn't found this type of defect on inspected pieces. We assume they did the inspection properly as they have found other type of defects.
Our client is aware of the %P(a) of 5.07% of accepting a bad lot based on the OC Curve. But only for 1 inspection and says this is not normal to not having found at least 1 defect on the 5 different inspections.

I argued the same: probability but still don't agree.

Some will tell: if your client doesn't agree, he just switch to 100% inspection
Some will tell: this is the nature for the acceptance sampling and the risk "0" doesn't exist.

I tried to explain that for a lot of 4080 pieces we need to realise appr. 21 inspections of 200 pieces to inspect 100% of the lot. As we talk about probabilities, we can never know on which of 21 inspections we will detect these 2.06% defective units.

I tried to illustrate roughly the defected unit distribution and the risk involved to our client. But, still not conviced.

My questions are:

* How I can calculate the probability of falling on good / bad samplings among 21 inspections?
If there is only 1.56% of a probability to not detect at least 1 defect in the sample size of 200 pieces with c=0 and %p = 2.06% there should be also a way of calculating the probability of not fall on the sample size with at least 1 defect.

* Why the Lot size is not taken into account?

I would really appreciate your help,

#### Leturc

##### Registered
Hello,

is there any idea?

#### Tagin

Trusted Information Resource
Our client found as above around 1.48% of critical defective rate on the totality of pieces received: open seam
Our team didn't found this type of defect on inspected pieces. We assume they did the inspection properly as they have found other type of defects.

I don't see how that assumption is justified due to the facts of what the client found.

Could there be a calibration issue, where the criteria for what is an 'open seam' differs between your inspectors and the client's inspectors?

Can the 'open seam' defect rate be reduced by improvements in manufacturing, so that intense sampling is not required?

As for the statistics, I can't really speak to the numbers. I don't understand what you mean by '21 inspections of 200 pieces to inspect 100% of the lot.'

#### Leturc

##### Registered
Dear @Tagin ,

Client found 1.48% defective rate amont 100% of the lot but we just inspected 200 pieces from 4080 pieces (lot size). I think, due to the non uniform aspect of the lot this is probable to not found any defect within this particular sample size.

We cannot omit calibration issue but let say this we are well aligned.

Open seam need to be improved as this is considered as "critical defect".

For the last sentence, I wanted to say if we would inspect the whole lot of 4080 we should do around 21 sampling of 200 pieces.

#### Tagin

Trusted Information Resource
For the last sentence, I wanted to say if we would inspect the whole lot of 4080 we should do around 21 sampling of 200 pieces.

Oh, because 21x200 = 4200, which is greater than 4080? Ok, but 100% inspection is only if each piece is inspected; if each of the 21 inspections is sampling from the whole lot of 4080, then there is no guarantee of every piece being inspected, since some pieces may be in multiple samples and inspected repeatedly, which means that some pieces are never getting inspected, so not truly 100%.

Ah ok, that probably is why you ask: How I can calculate the probability of falling on good / bad samplings among 21 inspections?

I wish I knew statistics better; this sounds like a perfect place for using Bayesian methodology.

#### Johnny Quality

##### Quite Involved in Discussions
Leturc,

Has your organization seen the defects? Do you agree with the customer and the documented requirements that they are indeed defects?

#### Bev D

##### Heretical Statistician
Super Moderator
Dear @Tagin ,

Client found 1.48% defective rate amont 100% of the lot but we just inspected 200 pieces from 4080 pieces (lot size). I think, due to the non uniform aspect of the lot this is probable to not found any defect within this particular sample size.

We cannot omit calibration issue but let say this we are well aligned.

Open seam need to be improved as this is considered as "critical defect".

For the last sentence, I wanted to say if we would inspect the whole lot of 4080 we should do around 21 sampling of 200 pieces.

This non-homogeneity of the lot is exactly why sampling inspection is not an effective approach to shipping low defect rates to your Customer. even IF you actually do random sampling (as opposed to convenience sampling) you cannot overcome non-homogeneity. Customers and manufacturers too often refuse to acknowledge that sampling inspection means that defects will escape even when properly done. they refuse to remember that AQL means the Acceptable defect level - in other words you will ship the AQL defect level 95% of the time that it is present. The only way to guarantee low defect rates is to improve your process and use in-process controls. Tricks with statistics won't help you.