Determining Sample Size - Filling a bag with three different types of candy

P

PerfettiFUN

#21
I recommend performing a Poisson capability study. This is typically used for defects (which are count data), but can be interpreted as you need. It will provide the percentage of a given color with the expected variation about that percentage.
I was trying to read up on it but wasn't really sure how I would go about performing that test? Do I need a Minitab type program to do it without a mile of equations? I can find plenty of places that describe it but none that really give a good explanation on how to use it on data like mine. I would assume I would treat the color like a "defect" type but not really sure.

Also here is my data for anyone that wanted to take a look. 48 Bags so far, just kinda threw it all into excel and planned on making it pretty later when I get a chance.

also what program would you all suggest for generating the theoretical data for if the placement of the bars was purely random? that is one of the important things i need to do i think because i want to be able to say whether we can improve the process by mixing the candy better before bagging or if we already mix enough and need to retool to something that will count individual colors in each bag.
 

Attachments

Last edited by a moderator:
Elsmar Forum Sponsor

Miner

Forum Moderator
Staff member
Admin
#22
I was trying to read up on it but wasn't really sure how I would go about performing that test? Do I need a Minitab type program to do it without a mile of equations? I can find plenty of places that describe it but none that really give a good explanation on how to use it on data like mine. I would assume I would treat the color like a "defect" type but not really sure.

Also here is my data for anyone that wanted to take a look. 48 Bags so far, just kinda threw it all into excel and planned on making it pretty later when I get a chance.

also what program would you all suggest for generating the theoretical data for if the placement of the bars was purely random? that is one of the important things i need to do i think because i want to be able to say whether we can improve the process by mixing the candy better before bagging or if we already mix enough and need to retool to something that will count individual colors in each bag.
Now that I have looked at your data, I am going to change my recommendation. I analyzed your data using a Wikipedia reference-linkc-chart, which is designed for Poisson or count data. There may be a shift in the mystery data, but the overall appearance is that the process is essentially in control. The c chart is not sensitive enough to tell whether a significant difference exists between the three means.

I recommend that you perform the Freeman Tukey transform for Poisson data, followed by either a 3-level, one-way ANOVA (see Wikipedia reference-linkAnalysis of variance) followed by a multiple comparison of means (see Wikipedia reference-linkPost-hoc analysis, or a 1-sample t-test (see Wikipedia reference-linkStudent's t-test on each color to test whether the mean = 10.

It appears that your problem is more related to bag to bag variation and the setting of the total count (< 30 pieces per bag) than it is to control.
 
Last edited:
P

PerfettiFUN

#23
Sorry, I forgot to mention it, but they were running valentines bags yesterday so they were actually 25 count bags (even though they were all 26 or 27).

Would i then do the same analysis steps to compare all the numbers i got compared to a random theoretical set? Because i also want to find out if our chances of getting less than 5 or whatever in a bag would be decreased if we mixed the colors together more or if we won't notice any difference from mixing them more than they are already being mixed.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#24
In thinking about this I think the theoretical distribution is not so much Poisson (since the quantity of each of the three different flavors are not independent of each other. This is more a combination problem.

It may make more sense to simply obtain the baseline (using the 30 count bags) and then perform your experiments with comparison to the baseline.

I would also not advise statistical comprisons of the means, but comparisons of the standard deviations. You have categorical data not continuous data and your pronlem is not with the mean but the variation (you said customers would complain about getting 'only two cherry candies') and in looking at the data you posted I can clearly see that you have a great deal of variation in the counts for all colors.

Why don't you get your baseline (50 randomly selected bags to start) and post that data. Then run your experiment (again with 50 bags) and post that data...then let's see what we can do.
 

Miner

Forum Moderator
Staff member
Admin
#25
In thinking about this I think the theoretical distribution is not so much Poisson (since the quantity of each of the three different flavors are not independent of each other. This is more a combination problem.
You may be correct. It would depend greatly on the OP's process and how they actually are controlling the feed and mix. I have seen processes where this would be a mixture problem and others where it would be an independent problem. We don't know enough about the process to be certain.
 
P

PerfettiFUN

#26
Did the test yesterday mixing the bars and this is the data i got. 25 count bags for both.

The left columns are our baseline of how it is currently running, the right columns are with pre-mixed candy put into the hoppers.

I also attached a picture of the packer in word document just to see what it is i am talking about.
 

Attachments

Last edited by a moderator:

Miner

Forum Moderator
Staff member
Admin
#27
I analyzed your data. Your process is in a state of statistical control. Your problem is in the capability of your mixing.

In rough numbers, your process average of each color is 33%, but each color may comprise anywhere from 5% to 60% of each bag.

Your typical customer would probably have a favorite color/flavor. If they received a bag where their favorite was 5%, you have an unhappy customer. On the other hand, if it was 33%, they would not be unhappy because they would understand before buying that it was a presumably equal mix.

If I interpret your photo correctly, your process is relying on 1) a steady feed rate from the hoppers, and 2) the vibrating chute to provide the mixing. The chute was probably designed more to provide start/stop transport than to actually mix, and to provide good mixing, the feed rates of the hoppers would have to be both steady and matched. This would be harder than getting three clocks to chime simultaneously for a month.

My guess is that the variation in flow rate from each hopper is the likely source of your capability issue.
 

howste

Thaumaturge
Super Moderator
#28
Maybe I'm being too simplistic again, but it seems like instead of trying to mix more, you'd want to mix less. If you can keep the ratio as close as possible to 1/3 just before it goes into the bags, you'll have less variation. Would it be possible to introduce three separate streams into the chute to the checkweighers? Possibly by having separate compartments in the elevator?

Candy Mix.png
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#30
Maybe I'm being too simplistic again, but it seems like instead of trying to mix more, you'd want to mix less. If you can keep the ratio as close as possible to 1/3 just before it goes into the bags, you'll have less variation. Would it be possible to introduce three separate streams into the chute to the checkweighers? Possibly by having separate compartments in the elevator?

View attachment 11466

yeah - that's where I would go. unfortunately the OP has stated that his organization doesn't want to "redo the machine". This could lead to a discussion about the impact on cost that long term and short term thinking have but the pooor guy is still an intern...

with any luck his 'manual mixing' won't work and they won't have any other choice and he can look like a hero...
 
Thread starter Similar threads Forum Replies Date
B Determining sample size for device sterility Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
D Determining of sample size for 'Operational Qualification' AQL - Acceptable Quality Level 5
R Determining Sample Size for Medical Device Component Validation Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
S Surveillance Sampling Test - Determining Sample Size Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
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
B Bayes Success-Run on Attribute Data - Determining Sample Size Statistical Analysis Tools, Techniques and SPC 2
A Determining Sample Size in Design V&V activities 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 44
G Determining Sample Size for Equipment Qualification Studies Qualification and Validation (including 21 CFR Part 11) 10
D Determining Sample Size for Capability in Six Sigma Project Six Sigma 5
H Determining the Correct Sample Size when AQL points to two Sample Sizes AQL - Acceptable Quality Level 7
L Determining Cpk based on a given Sample Size, Confidence Level, & Reliability Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
M Determining Sample Size needed for Operational Qualification (OQ) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 24
T Determining the appropriate Sample Size using an AQL Table Inspection, Prints (Drawings), Testing, Sampling and Related Topics 29
J Functional Test Sampling - Determining Sample Size to eliminate 100% Testing Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
W Sampling Plan problem - Determining Sample Size for both Attribute and Variables Data ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 2
S Determining the Total Sample Size using AQL - AQL Lot Quantity question AQL - Acceptable Quality Level 8
1 Determining AQL and Sample Plan - Batch size is from 1-500 AQL - Acceptable Quality Level 24
E Determining Sample Size for Design Verification and Design Validation Other Medical Device and Orthopedic Related Topics 20
N Auditing Proof of Delivery signed by the customer - Determining Sample Size General Auditing Discussions 6
Q Determining Sample Size for FDA Verification and Validation Activities Inspection, Prints (Drawings), Testing, Sampling and Related Topics 41
D Determining sample size required based on a 95% confidence level Reliability Analysis - Predictions, Testing and Standards 7
B Determining sample size for drop test and waterproof testing Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
T Determining Receiving Inspection Sample Size Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
N Determining Sample Size for Attribute Data Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
C Internal Audit Sampling Plans - Determining Internal Audit Sample Size Internal Auditing 45
Q Determining the Appropriate Sample Size for Process Validation/Qualification Inspection, Prints (Drawings), Testing, Sampling and Related Topics 13
T Using Cpk for the purpose of determining sample size/frequencies Capability, Accuracy and Stability - Processes, Machines, etc. 2
G Determining Sample Size and Frequency for Features on Control Plans FMEA and Control Plans 8
S Determining sample sizes for PQ Qualification and Validation (including 21 CFR Part 11) 4
R Determining Sample Sizes for Testing (Chemistry or Microbiology) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
B Selecting a Sample and Determining the Reference Value for a Bias Study Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
S Determining the requirements for the products and services ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 3
Q Determining Adverse Effects of Corrective/Preventive Actions ISO 13485:2016 - Medical Device Quality Management Systems 2
M Determining if an Insulin Pen Testing Machine is a Medical Device? EU Medical Device Regulations 4
M Determining a tolerance value for Measuring devices in-house inspection General Measurement Device and Calibration Topics 12
D Determining the the maximum number of reprocessing cycles of attachments CE Marking (Conformité Européene) / CB Scheme 2
R Determining Uncertainty from Gage R&R Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
A IATF 16949 4.3.1 - Determining the scope of the quality management system - supplemental IATF 16949 - Automotive Quality Systems Standard 9
D ISO 9001:2015 4.3 Determining the Scope of the QMS ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 3
J Determining SPC tolerance Statistical Analysis Tools, Techniques and SPC 21
B Determining SAT Offsets vs TUS Offsets per SAE AMS 2750E AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 0
R Question on determining defective units - I am not recording fixture to part rejected Statistical Analysis Tools, Techniques and SPC 5
S Clause 8.2.2 Determining the requirements for products and services ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 5
D Determining Calibration Frequency schedule for items used in production Manufacturing and Related Processes 2
C Determining if Maintenance Contractor is an External Service subject to ISO 9001 Clause 8.4 ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 43
S AS9100D PEAR - Examples for organization's method for determining process results? AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 5
I Determining Calibration Tolerance of a Measurement Device General Measurement Device and Calibration Topics 2
J ISO 17025 Documented Procedure for 6.2.5 - Determining competency ISO 17025 related Discussions 4
V Determining FDA 820 (registration) vs ISO 13485 - Supplier gives us the kit ISO 13485:2016 - Medical Device Quality Management Systems 1

Similar threads

Top Bottom