Count by weight statistical analysis

smryan

Perspective.
#1
I do not have a strong statistics background and am hoping someone here can help.

For our smaller parts we stock and ship counts figured by weight. With some newly subcontracted parts there is quite the difference in count results. I've just taken 8 samples of 50 each - the low is 112.99g and the high is 116.52g. Depending on which sample I happened to grab I would get considerably different results. My 68kg box labeled 30,000 would either come up 91 pieces over or 821 pieces short.

How does one determine an appropriate sample size to ensure 99.7% accuracy? (+/- 3 sigma)

I know some of you quality geniuses will have this easily. :D

Why don't they ever ask me about Newton's Laws? :rolleyes::lmao:
 
Elsmar Forum Sponsor

Jen Kirley

Quality and Auditing Expert
Staff member
Admin
#2
Based on your description, I can't think of any way to bring statistical confidence to your sampling except to count them out.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#3
in order to help you I would need to know a few more things: to start off, what exactly do you need to know? the count? if so, what amount of allowable variation can you have in the count? (regardless of whether or not you use weight or actual counting. Even counting can be inaccurate particularly with large numbers of things.
 

smryan

Perspective.
#4
in order to help you I would need to know a few more things: to start off, what exactly do you need to know? the count? if so, what amount of allowable variation can you have in the count? (regardless of whether or not you use weight or actual counting. Even counting can be inaccurate particularly with large numbers of things.
Yes, the count is the goal. Customers order by quantity, not by weight. There is no machine to do the counting, so hand counting is out of the question. Shipping uses a conversion scale - counts out a sample, inputs the count and weighs it - then piles on till the count (based on weight) reads the target amount.

Most of our parts have little variation within a 'run'. The problem parts are running higher variation. (sub-contracted)

Acceptable margin of error.... well, we would rather err on the side of more (would not want a customer to think we were shorting them ever) but not too far, as we really can't afford to give product away. Not a great answer - sorry.:mg:
 
Last edited:

Statistical Steven

Statistician
Staff member
Super Moderator
#5
This is how I would approach the problem. I would weigh out 30 individual parts, calculate a mean and standard deviation for the individuals. Then use simulation to simulate 1000 samples for a given sample size (n=50 for example). This will now give you distribution for the means (you can of course just use the the SD of individuals/sqrt(n) to get the estimate of the the variation if simulation is not your thing). Based on the 1000 samples I can set the specifications to control the percent of samples that will be on the low side and the percent on the high side. In other words, you do not want +/- 3S, what you really want is probably -0.5S/+3S to ensure you minimize under fulfillment while not rejecting too many that are overfilled.

I hope that makes sense.
 

smryan

Perspective.
#6
This is how I would approach the problem. I would weigh out 30 individual parts, calculate a mean and standard deviation for the individuals. Then use simulation to simulate 1000 samples for a given sample size (n=50 for example). This will now give you distribution for the means (you can of course just use the the SD of individuals/sqrt(n) to get the estimate of the the variation if simulation is not your thing). Based on the 1000 samples I can set the specifications to control the percent of samples that will be on the low side and the percent on the high side. In other words, you do not want +/- 3S, what you really want is probably -0.5S/+3S to ensure you minimize under fulfillment while not rejecting too many that are overfilled.

I hope that makes sense.
Nearly.
I had 8 groups of 50 each.
Of those I massed all 50 individuals of 3 groups (the hi, the low and a middle). The SD isn't the same on these 3 data sets - so how could I trust the info I was getting from just a single sample of 30?

How would one simulate 1000 samples from this? I'd like to try it.

At least the -0.5S/+3S makes perfect sense.:biglaugh:Thank you!
 

Miner

Forum Moderator
Staff member
Admin
#7
Statistical Steven's approach makes a lot of sense.

To answer your question on the standard deviation, calculate the confidence interval for the standard deviations, then use the upper 95% (or greater) confidence limit for the standard deviation.

You could extend Statistical Steven's suggestion a bit further to calculate a sample size such that the 3 standard deviations of the average is less than the weight of a single part. This may result in a prohibitively large sample size, so you may have to compromise at 2 standard deviations or aim slightly high on count.
 

Jen Kirley

Quality and Auditing Expert
Staff member
Admin
#8
Look at these great answers. There are times when the best I can do is make a post so as to bring the question back to the top of the list, where better expertise can take a crack at it. It appears to be working...:applause:
 

Statistical Steven

Statistician
Staff member
Super Moderator
#9
Nearly.
I had 8 groups of 50 each.
Of those I massed all 50 individuals of 3 groups (the hi, the low and a middle). The SD isn't the same on these 3 data sets - so how could I trust the info I was getting from just a single sample of 30?

How would one simulate 1000 samples from this? I'd like to try it.

At least the -0.5S/+3S makes perfect sense.:biglaugh:Thank you!

I use software like SAS, though you can do it in Excel too. You will need to actually do the simulation twice, first to simulate 1000 groups of 50 parts, then another simulation to look at groups of the 8 means from the 1000 means. This is not a trivial problem, as the question you are asking is to set specifications for weights of 400 parts (8 groups of 50) that come from a population of individuals. The means of the 50 parts should be consistent, but as you saw, the variation wihtin the sample of 50 can vary considerable.
 

smryan

Perspective.
#10
Statistical Steven's approach makes a lot of sense.

To answer your question on the standard deviation, calculate the confidence interval for the standard deviations, then use the upper 95% (or greater) confidence limit for the standard deviation.
OK - lets give this a shot.... using an online tool (as I have zero experience of my own with this :eek:) I came up with the following table... could someone who understands this better than I please tell me if its anywhere near accurate? THANKS!
 

Attachments

Last edited by a moderator:
Thread starter Similar threads Forum Replies Date
G Count By Weight Scale - Calibration within specification, but not linear General Measurement Device and Calibration Topics 8
P ISO Class 8 particle count (annual certification vs monitoring) ISO 13485:2016 - Medical Device Quality Management Systems 4
A AQL - How to count samples with defects for each defect class AQL - Acceptable Quality Level 17
M Viable count Measurement ISO Standard Other Medical Device Related Standards 1
supadrai How does the FDA count violations of, for example, misbranding? (Medical Devices) Other US Medical Device Regulations 1
M How to count the number of employees? Other Medical Device and Orthopedic Related Topics 4
M ISO 14644 Airborne Particle Count Testing Requirements Miscellaneous Environmental Standards and EMS Related Discussions 6
A Difference between Discrimination and Least Count IATF 16949 - Automotive Quality Systems Standard 2
W Legality of selling parts by count - Counting Scales Quality Manager and Management Related Issues 6
C Do Emails count as a Document/Record Document Control Systems, Procedures, Forms and Templates 6
S Head Count for Employees and Contract Workers Misc. Quality Assurance and Business Systems Related Topics 6
C What is an acceptable bioburden level or count when working in cleanroom ISO class7 ISO 13485:2016 - Medical Device Quality Management Systems 1
R Count NDC from Graphik Sample Range vs R chart Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 9
F Excel I want to use the count I get in another formula Excel .xls Spreadsheet Templates and Tools 13
N Requirements for the Classification of Cleanrooms other than the Particle Count Other ISO and International Standards and European Regulations 5
D Pls hlep me understand the "Total Anaerobic Plate Count" Food Safety - ISO 22000, HACCP (21 CFR 120) 1
T Significance Test for Count Data Statistical Analysis Tools, Techniques and SPC 8
M Setting Solid Dose Drug Fill Count Ranges Pharmaceuticals (21 CFR Part 210, 21 CFR Part 211 and related Regulations) 8
S Do Medical Sterile Drapes count as MOPP? IEC 60601 - Medical Electrical Equipment Safety Standards Series 2
I Bioburden Count Question - Bioburden is above the alert limit >1 CFU/component avg. 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 1
L GB15980-2003 Bioburden Count Trend on Operator Hands Other ISO and International Standards and European Regulations 1
S Count (Bolts and Nuts) Scale - Class of Calibration Weights Calibration and Metrology Software and Hardware 3
K Preventing Shortage of Product Quantity - Hand Count and Scale Count Manufacturing and Related Processes 13
D 510K Approval Guidelines and Marketing in the US - CD4 Count Reagent 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 1
R While Measuring Filter Face, Why We Count From Dead Area? HEPA Filter Related Manufacturing and Related Processes 3
Y Environmental Monitoring - Setting for Particulate Count ISO 13485:2016 - Medical Device Quality Management Systems 3
L Labeling and Count/Part Reconciliation Manufacturing and Related Processes 8
B Does this count as a 510(k) Medical Device Modification 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 14
M Devices with Measuring Function - Do rulers and calipers count? EU Medical Device Regulations 7
B Minitab Gage R&R using Defect Count per Unit Area Using Minitab Software 1
L Do "Informal" Internal Audits count? Internal Auditing 18
S How to count the number of NCs in an Internal Audit? General Auditing Discussions 18
C Do Newsletter articles count towards recertification? Professional Certifications and Degrees 1
T Does a years worth of prototype manufacturing "count" for TS 16949? IATF 16949 - Automotive Quality Systems Standard 6
A Class 8 100,00 Cleanroom - Airborne Microbial Count ISO 13485:2016 - Medical Device Quality Management Systems 6
Q Latest count of ISO 9001 Registration Certificates world wide ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 22
S The Logic behind Tolerance vs. Least Count 1/10 Ratio General Measurement Device and Calibration Topics 11
N Auditing Inventory Levels - Computer Count vs. Physical Inventory ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 40
B R&R Study in Microbiological Testing - Aerobic Plate Count, Coliform, and Salmonella Food Safety - ISO 22000, HACCP (21 CFR 120) 4
Jim Wynne Vista Deathwatch - Is the new Microsoft OS down for the count? World News 30
Jen Kirley How to count two criteria at once in Excel Excel .xls Spreadsheet Templates and Tools 17
Manix MTTF Prediction for Customer Requirements - Parts-count MTTF prediction for the part Reliability Analysis - Predictions, Testing and Standards 2
V Minitab Pareto - Trying to plot a relation of Count and Cycle Time Using Minitab Software 5
J Cumulative Count of Conforming Control Chart (CCC) - Calculating UCL and LCL Statistical Analysis Tools, Techniques and SPC 8
S Attribute GRR - Cross tab - Kappa - What does "Expected Count" mean? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
M Can multiple procedures count as one? Different aspects of document control system Document Control Systems, Procedures, Forms and Templates 6
T 3rd party audit time - Does working lunch count as audit time? General Auditing Discussions 66
Wes Bucey At the end of the day, only votes count! World News 5
D Gage R&R on a delta measurement - Particle measurement count tool Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
C Least count thumb rule - Stone walling SPC Statistical Analysis Tools, Techniques and SPC 7

Similar threads

Top Bottom