# 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,

#### 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
Staff member
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.

Which Sampling Plan(s) Should I Use? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 7
Sampling plan for in-process QC (medical devices) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 13
LTPD, AQL, Ppk and Cpk validation sampling plan table Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
Change in control plan - Do I have to do sampling? IATF 16949 - Automotive Quality Systems Standard 1
Is using ANSI/ASQ Z1.4-2008 the correct sampling plan to determine Pass/Fail of Apparel measurements? AQL - Acceptable Quality Level 4
Sampling Plan for Internal Audits - ISO 2859 or 3951 - Or Neither? Internal Auditing 6
Reduced sampling plan for sterial products APQP and PPAP 0
Defining sampling plan for different AQL AQL - Acceptable Quality Level 3
AS9100D Sampling Plan AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 2
Sampling plan for a customer who wants AQL 1.0 (per ANSI Z1.4) AQL - Acceptable Quality Level 5
Sampling Plan for Alumin High Pressure Die Castings Manufacturing and Related Processes 0
Sampling plan for orthopedic implant - Process Validation Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
S How to make a Sampling Plan - Conveyor belts Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
Help develop sampling plan for prototype samples (medical devices) Statistical Analysis Tools, Techniques and SPC 7
Zero Defect Sampling Plan Standards Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
ISO 2859-2 LQL sampling plan linked to %confidence/%reliability Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
K Sampling Plan for transparent tubular plastic parts from 32 different cavities Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
A AQL Sampling Plan SOP / WI - Medical Device Industry Inspection, Prints (Drawings), Testing, Sampling and Related Topics 14
Sampling Plan Questions from the CQE Practice Exam Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
M Sampling Plan for for Chemical Analysis Testing of Medical Devices EU Medical Device Regulations 3
Sampling Plan for Destructive Testing Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
Can ANSI Z1.4 sampling plan be used for sampling alone without the Acc/Rej criteria? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
C Sampling plan for destructive tests on small lots ISO 13485:2016 - Medical Device Quality Management Systems 20
B Designing a Sampling Plan - AQL AQL - Acceptable Quality Level 19
N Use of arrows in ISO 2859-1 Table 1 and 2-A sampling plan Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
S AS9100 Sampling Plan Requirements - 8.2.4 AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 5
Military Sampling Plan 105E vs. ISO 2859-1 AQL - Acceptable Quality Level 2
Acceptance Sampling Plan for Variables - Product Performance Testing Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
Manufacturing Process Validation Destructive Testing Sampling Plan Advice Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
S Where could I get reference to an OQA Sampling Plan of 1 per 1000 ? Quality Manager and Management Related Issues 4
R What to Report when Using C=0 Sampling Plan Supplier Quality Assurance and other Supplier Issues 15
Results: Monte Carlo Simulation of Acceptance Sampling Plan AQL - Acceptable Quality Level 3
G Sampling Plan according to SAE ARP9013 C=0 Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
G Sampling Plan for Inspection of Metal Parts after CNC Machining Inspection, Prints (Drawings), Testing, Sampling and Related Topics 34
S Class III Sampling Plan - Explain AQL vs. 95%C & 90%R Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
G Sampling Plan for a Performance Qualification of an Inflation System Qualification and Validation (including 21 CFR Part 11) 2
How to establish a Sampling Plan from the Rework percentage? AQL - Acceptable Quality Level 6
Sampling Plan for Paper and Tape Industry Inspection, Prints (Drawings), Testing, Sampling and Related Topics 7
C Medical Device Tracking Sampling Plan using MIL-STD-105E Other US Medical Device Regulations 4
P Lot Acceptance Plan that specifies BS 6001 Double Sampling Plans, general inspection Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
A Destructive Testing Failure Mode Sampling Plan Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
Best Attribute Data Sampling Plan - Early Production Containment Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
B In-Process Sampling Plan for a Secondary Package Adjustment Process Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
Making a simple Sampling Plan by Variables Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
E How to determine the Lot Size for the OQ Sampling Plan Inspection, Prints (Drawings), Testing, Sampling and Related Topics 11
L Electrical Cable Harness Quality Control - Sampling Plan for Pull Test Manufacturing and Related Processes 4
G Sampling Plan - Sample Size Justification for a Bottling Cleaning Process Validation Qualification and Validation (including 21 CFR Part 11) 2
Alpha and Beta in the Sampling Plan for ISO 2859 & ISO 3951 Inspection, Prints (Drawings), Testing, Sampling and Related Topics 13
V Sampling Plan for Final Inspection and Process Verification Inspection, Prints (Drawings), Testing, Sampling and Related Topics 21
M Sampling Inspection at QA - Inputs on the following sampling plan Statistical Analysis Tools, Techniques and SPC 3