# 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
Staff member
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
Staff member
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
Staff member
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.

Thread starter Similar threads Forum Replies Date
Minimum sample size - Guidance and statistical rationale Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
Unrealistic Packaging Validation Sample Size 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 13
Control chart for huge sample size Statistical Analysis Tools, Techniques and SPC 9
Is there a standard for sample size during R&D phase Other ISO and International Standards and European Regulations 18
Sample size definition in an Automotive SMT pilot lot run Misc. Quality Assurance and Business Systems Related Topics 1
Correct way to certify hydrostatic testing when it is not 100% (and Sample Size) Various Other Specifications, Standards, and related Requirements 6
Determining sample size for device sterility Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
Determining of sample size for 'Operational Qualification' AQL - Acceptable Quality Level 5
Bayes Success run Theorem for sample size during OQ&PQ Qualification and Validation (including 21 CFR Part 11) 4
Device modifications - Clinical sample size rationale EU Medical Device Regulations 5
Sample size for creating a data base as a reference to a tested variable Other Medical Device and Orthopedic Related Topics 6
Sample Size for Design Validation Design and Development of Products and Processes 4
AS9138 Sample Size Determination AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 1
Acceptable maximum RSD (relative standard deviation) for an sample size Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
Sample size for design verification of variable in single use device Design and Development of Products and Processes 19
Sample size for clinical validation/investigation EU Medical Device Regulations 4
Process Validation sample size selection Statistical Analysis Tools, Techniques and SPC 0
Interesting Discussion Sample Size Determination for Medical Device Other Medical Device and Orthopedic Related Topics 9
Is it possible to make an educated decision using a very very small sample size? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
Sample Size for Biocompatibility Tests Other Medical Device Related Standards 4
Firmware Verification Testing & Sample Size Software Quality Assurance 1
Determining Sample Size for Medical Device Component Validation Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
Surveillance Sampling Test - Determining Sample Size Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
Sample Size Calculation (Confidence Interval and Reliability) - Medical Devices Reliability Analysis - Predictions, Testing and Standards 6
Cleaning and Disinfection Validation Sample Size of 3? Other Medical Device Related Standards 2
Sample Size Calculation for Image Analysis - Microscopy Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
G Sample Size, Significant Figures, Scale General Measurement Device and Calibration Topics 3
L Heated Sealed Packages - Sample Size for OQ (Operational Qualification) and PQ Inspection, Prints (Drawings), Testing, Sampling and Related Topics 11
P Frequency and Sample Size Requirements for an MSA Studies Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
When and How to apply the Bayes Success Run approach for Sample Size Determination Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
Sample Size Justification for Medical Device Shelf-Life Inspection, Prints (Drawings), Testing, Sampling and Related Topics 13
Process Qualification Sample size Document Control Systems, Procedures, Forms and Templates 6
Sample size for IEC 60601-1-11 environmental tests IEC 60601 - Medical Electrical Equipment Safety Standards Series 1
IEC 60601-1-2 Sample Size issue Other Medical Device Related Standards 1
A How to calculate Mean and standard deviation without sample size in Minitab Using Minitab Software 5
What is the minimum Sample Size for Weibull Analysis Reliability Analysis - Predictions, Testing and Standards 12
C Sample Size for Stability Testing Other Medical Device and Orthopedic Related Topics 2
M Calculating Cpk when sample size equals to 1 Capability, Accuracy and Stability - Processes, Machines, etc. 12
F Power and sample size for factorial design Using Minitab Software 4
S Sample Subgroup Size for NP/P chart - nPbar>=5 Statistical Analysis Tools, Techniques and SPC 4
F Sample Size to get Statistically Valid Data Measurement Uncertainty (MU) 6
S Low Sample Size for Gage R&R Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
SPC Card for One Sample Size - Customer requires for all critical dimensions Statistical Analysis Tools, Techniques and SPC 8
S Determining sample size for inspection to achieve x% confidence re defects Misc. Quality Assurance and Business Systems Related Topics 10
S Determining Sample Size - AQL & LQ AQL - Acceptable Quality Level 10
Bayes Success-Run on Attribute Data - Determining Sample Size Statistical Analysis Tools, Techniques and SPC 2
J Flammability: Testing Burn Rate with Improper Sample Size fmvss 302 Various Other Specifications, Standards, and related Requirements 1
H Factory Dictated Sample Size Justification Statistical Analysis Tools, Techniques and SPC 9
M Design Verification: "Difference" in Sample Size Calculations? Design and Development of Products and Processes 1
M Calculating Adequate Receiving Inspection Sample Size Statistical Analysis Tools, Techniques and SPC 2