# Statistics equation to determine the number of samples in a lot

C

#### CraigSutton

I have searched this forum and cannot find the answer to my question.

I have a lot of items "A" with a small possibility (<1%) of there being an item "B" in the lot. How do I determine the number samples needed to show there are zero items of type "B" in the lot to a 95% confidence level.

The lot sizes change but are typically never more than 400 items. The goal is always zero defects at 95% confidence. The time and cost of 100% sampling is prohibitive.

Is there an equation that can determine this or what other information is required to determine.

:

T

#### TheGoldenBlazer

If you did a study to see what the mean number of part B in the lot is (.1? .05? etc), you could use a poisson distribution and solve for k at 95% confidence.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
To put it simply, you can't.
you can calculate the upper confidence limit for various sample sizes that have zero defects in them.

I have attached a spreadsheet you can use for this. the example has the 95% upper confidence limit and I iterated the sample size until the UCL was at 1% defective. the sample sizes are quite large.

sample sizes for the detection of small defect rates get very large very fast.

#### Attachments

• 88.5 KB Views: 280

#### Miner

##### Forum Moderator
Staff member
Once your defect rate drops below a certain level you either inspect 100% or don't inspect at all because sampling plans no longer work.

C

#### CraigSutton

Thanks for the help. That is what I was suspecting from what I had gathered but was unsure and could not prove it to myself. Again I appreciate the help.

Craig

#### Bill McNeese

##### Involved In Discussions
I wonder how folks really think about the all or nothing rules for inspecting incoming material. Dr. Deming talked about it in his book Out of the Crisis and showed how it works under some basic assumptions, focusing on pbar, k1 and k2 costs.

Bill McNeese

#### Miner

##### Forum Moderator
Staff member
Deming was right. I completely phased out inspection at two locations because the defect rate was so low that we never found anything. I put the effort into process control and mistake proofing instead.

End result: our field performance improved.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Was Deming right or wrong? he was right, but many people misinterpret what he really said and they are wrong.

This is one of too many of Deming's discussions that has been simplified to the level of slogan. In the process of attempting to explain a complex concept in simple terms we have not just clarified his dense prose, but we have eliminated the nuances that truly layout the case.

First, given that the point of these discussions is whether or not sampling detects and screens out higher than desired defect rates, teh whole argument goes off the rails when the use AQL only plans. c=0 AQL plans are even worse. Plans for this type of discussion must involve RQLs; the defect rate you want to detect and reject. An AQL is the defect rate you will accept most of the time it is present.

The following scenarios have a foundational assumption of an RQL based plan:

When the defect rate is exceptionally low sampling is useless. Given that hte sample size will be dependent on the defect rate the sample size will be very large anyway. If the defect has a severe effect we must 100% inspect until the process is mistake proofed. If the defect isn't severe then inspection is a waste.

When the defect rate is at the level you want to reject sampling becomes silly. you will randomly fail to reject some lots and randomly reject others. You may improve the over all defect rate if you do 100% inspection but you will still be sending lots that have high defect rates. Again the all or nothing scenario can be invoked.

When the defect rate is above the level you want to reject sampling results in a foregone conclusion. You will reject almost every lot. And again the all or nothing scenario can be invoked.

BUT when you have a defect rate below the level you want to reject, sampling does provide protection against increases in the defect rate.

Of course Miner is correct, in the long run the best thing to do is to improve your processes and control them through various means available: SPC, mistake proofing, controlling inputs, etc.

Two interesting articles on this issue are:
?Mood?s theorem, Deming?s kp Rule and the Death of Acceptance Sampling? Steven Rigdon, Quality Engineering, 8(1), 129-136 (1995-96
?Acceptance Sampling? The Enterprise Strikes Back! AS9100 c=0 Plans; When Slogans Supplant Science? Quality Engineering, 18:237-236, 2006
Both are available through ASQ?s knowledge Center?

We must always remember that no single QC tool was ever meant to be the only tool. They all have their time and place?a hammer should never be used to drive a screw and a screw driver makes for a pretty lousy hammer?

slogans should never replace thought.

#### Bill McNeese

##### Involved In Discussions
Good post Bev. As I mentioned, Dr. Deming talked about the all or nothing rule under some basic assumptions. These were:

• We are dealing only with one part
• We will test/inspect the final product before leaving our area
• If the incoming part is defective, the final product will not pass test/inspection; if the incoming part is not defective, the final product will pass test/inspection
• A supply of parts exists to replace defective items

You should always be sure the assumptions are met. How often are these four met in reality? Probably not very often.

Last edited:
CQT Exam - Statistics Professional Certifications and Degrees 4
Simple statistics questions on labor data Statistical Analysis Tools, Techniques and SPC 2
Statistics and / or Forecasts on medical products exports from China Other Medical Device and Orthopedic Related Topics 1
What could go wrong with information: Ransomware statistics and facts (2018 to present) IEC 27001 - Information Security Management Systems (ISMS) 0
Good resources for learning statistics (quality engineering related) Statistical Analysis Tools, Techniques and SPC 10
Statistics - Where to start in ISO 9001? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 5
Visitor Statistics - How to see a poster's stats easily? Elsmar Xenforo Forum Software Instructions and Help 3
D How do you use statistics in your job Statistical Analysis Tools, Techniques and SPC 6
Excellent Resource on Statistics / Lean / Six Sigma Book, Video, Blog and Web Site Reviews and Recommendations 2
Accelerated Learning and Simulations / Scenarios - Statistics Statistical Analysis Tools, Techniques and SPC 0
P Where to find conformance statistics for ISO 15189 Other Medical Device Regulations World-Wide 1
Statistics - Designs - Differences between Orthogonality and Confounding Using Minitab Software 5
M Statistics Question - What percent falls above 105? Statistical Analysis Tools, Techniques and SPC 2
A Assessing a Preventive Maintenance Strategy - Reliability or Maintenance Statistics Reliability Analysis - Predictions, Testing and Standards 2
Statistics and Sampling - Accounting for Failed Tests Statistical Analysis Tools, Techniques and SPC 10
Metrics and Statistics for Improvement - Easy to implement Statistical Analysis Tools, Techniques and SPC 4
ASQ CQE statistics training in Australia? Training - Internal, External, Online and Distance Learning 2
E Online Degrees and Graduate Certificates in Statistics Training - Internal, External, Online and Distance Learning 1
Guide to Microsoft Excel for Calculations, Statistics, and Plotting Data Excel .xls Spreadsheet Templates and Tools 11
C Basic Statistics Template .xls Document Control Systems, Procedures, Forms and Templates 0
S Statistics in Check/Replicate Analysis - HPLC Assay (Sample Duplicates) Statistical Analysis Tools, Techniques and SPC 1
R Student Question - Help needed with statistics questions Statistical Analysis Tools, Techniques and SPC 6
M The Statistical Meaning of "Muddy Middle" - Statistics Terminology Statistical Analysis Tools, Techniques and SPC 6
B Descriptive Statistics where the Data Type is Text? Using Minitab Software 4
R Industry Statistics on the benefits of Quality Management Systems ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 8
xkcd on Statistics and Mainstream Media Funny Stuff - Jokes and Humour 2
A R using RExcel - Non GUI Statistics Program Statistical Analysis Tools, Techniques and SPC 1
Job recovery? or "statistics don't lie, people do" Career and Occupation Discussions 37
G Statistics Question from Production and Operations Management Course Statistical Analysis Tools, Techniques and SPC 3
O Information on the extent of Statistics in the Six Sigma Green Belt Exam Professional Certifications and Degrees 9
J Gage R&R Module for R (Statistics Program) Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
T Survey or Statistics on the use of OHSAS 18001 Worldwide Occupational Health & Safety Management Standards 66
T Survey or Statistics on the use of the AS 9100 Standard Worldwide AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 2
H Elsmar Cove Statistics Found Online Coffee Break and Water Cooler Discussions 2
Quotable Quotes - Statistics Funny Stuff - Jokes and Humour 10
S Statistics of Gage R&R & Boundary Specifications Statistical Analysis Tools, Techniques and SPC 15
K Sample Statistics on HR (Human Resources) Key Processes ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 3
FDA released guidance on use of Bayesian statistics in Clinical Studies 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 0
O Weighting Problems (Statistics) - Weight distribution for a machine setup Capability, Accuracy and Stability - Processes, Machines, etc. 5
S "Human Error" statistics Quality Manager and Management Related Issues 3
S ASQ CSSBB Exam & Knowledge of Statistics Professional Certifications and Degrees 3
Are there PPM statistics kept by Industry Manufacturing and Related Processes 4
Battery-Life Statistics After Work and Weekend Discussion Topics 4
F Error in Minitab (no statistics can be calculated with these data) Using Minitab Software 10
O The Basis of %GRR (% Gage R&R) and other Statistics - Minitab Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 21
V Management Review Meeting - Statistics for Customer Complaints and Non Conformances ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 2
T The use of Statistics at a Medical Device Manufacturer US Food and Drug Administration (FDA) 16
Y Statistics and MiniTab - Example Problems Using Minitab Software 4
Application of Statistics/ SPC tools in Oil Refineries Statistical Analysis Tools, Techniques and SPC 11
Q Specific requirements for Statistics in CQE exam Professional Certifications and Degrees 3