Sampling Spreadsheet to help determine the Sample Size for Sampling Plans

Statistical Steven

Statistician
Staff member
Super Moderator
#11
Abhijeet said:
When setting up SPC system (eg I and MR chart )do we need to check the normality of the data.Since we use the standard deviation (Avg MR for I-MR) in setting up our limits, do we need the data to be normal?
You should have started a new thread to get the most feedback on your question.

To answer your question, the underlying assumption of SPC is that the data is normally distributed. You can calculate a movR of the data set, but if the data is not normally distributed that estimate is incorrect.
 
Elsmar Forum Sponsor

Tim Folkerts

Super Moderator
#13
cochranemurray said:
Go here for various sampling plans
www.sqconline.com
This link provides a very handy link to a calculator that allows you to choose the appropriate MIL-STD-105e (aka ASQ Z1.4) plan (as well as various other info). Thanks. smile-a1.gif


However, my initial problem is that 105E is not statistically based. After you tell the calculator the you want a lot of 1000, AQL=1, Normal, Level II, it will tell you to sample 80 and accept 2. That is fine, but now tell me what the odds are of accepting or rejecting lots at any particular defect level. That sort of information is not built into the 105E type plans. About all you can really say is that the sampling plan indicated by 105E is "appropriate" - based on the opinions of a few guys 60 years ago.

My spreadsheet was designed to produce a fresh sampling plan to exactly meet a set of statistical criteria that you decide on. Whether that is overkill or not - I guess you each have to decide.

Tim F
 

Mike S.

Happy to be Alive
Trusted Information Resource
#14
Tim Folkerts said:
That is fine, but now tell me what the odds are of accepting or rejecting lots at any particular defect level. That sort of information is not built into the 105E type plans. About all you can really say is that the sampling plan indicated by 105E is "appropriate" - based on the opinions of a few guys 60 years ago.

Tim F
Tim,

Aren't OC curves provided in MIL STD 105 to show this?
 

Tim Folkerts

Super Moderator
#15
The OC curves are in the back of ASQ Z1.4, and they do provide info about probability of accepting and rejecting lots, so perhaps I was a bit harsh in my criticism of the plan. embarrassed.gif

Still there are a couple of problems.
  1. It takes a fair amout of effort to work through the curves and tables to find alpha & beta for different defect levels. Most people don't bother, so most people have no idea how likely their plan is to accept or reject lots of varying quality.
  2. If you want to start with AQL, LTPD, alpha & beta, you have to dig through the tables and find a plan that approximates what you want. Then you are going to end up with Level III, reduced sampling for one product, Level S3, tightened for another product, etc. A nightmare to explain to anyone.
  3. Once you have worked through one plan, you can't assume that the results will work for another plan. There is no simple rule like "Normal Level II plans provide at least 95% chance of accepting lots at meet the AQL". If someone can summarize summarize in 1 sentence (or even 1 paragraph) a relationship between the effects of type & level of inspection on alpha and/or beta, I'd love to see it!
    Every time you change the AQL or lot size, you have a different chance of accepting lots of a specific quality.
Tim F
 

Mike S.

Happy to be Alive
Trusted Information Resource
#16
Tim,

In all I like your idea and I don't mean to be nitpicky. You obviously understand more about statistics and sampling than I do, and this thread and your program has already helped me learn. For that I am grateful.

If I were to be nitpicky, here are my nits:

I'd like to see an explanation attached to the program, like on an accompanying sheet, to explain how to use it, the basic principals/theory behind the calculations, etc. In order for people less stats savvy than you to use the program they may have to defend it, and to do so, they might have to do some work to understand it. An attachment might make that easier for the user.

A validation from another statistician saying he/she basically checked your work in detail and thinks everything is kosher would give potential users more of a warm fuzzy feeling. (Of course, that might happen here at the Cove.)

I don't doubt that your stuff is right, but I would at this time not be in too good of a position to defend its use to a customer who may want the assumed security of an "accepted" sampling plan like ASQ 1.4.

Does this make sense?
 

Tim Folkerts

Super Moderator
#17
Mike S. said:
Tim,
In all I like your idea and I don't mean to be nitpicky.
If I were to be nitpicky, here are my nits:
Actually, I appreciate the nitpicking. It also helps me clarify my thoughts.

A validation from another statistician saying he/she basically checked your work in detail and thinks everything is kosher would give potential users more of a warm fuzzy feeling. (Of course, that might happen here at the Cove.)
Anyone brave enough to dig through it???

I'd like to see an explanation attached to the program, like on an accompanying sheet, to explain how to use it, the basic principals/theory behind the calculations, etc. In order for people less stats savvy than you to use the program they may have to defend it, and to do so, they might have to do some work to understand it. An attachment might make that easier for the user.
A separate attachment would be a good idea, or a bit more explanation in the spread sheet. Let me provide at least some more rationale now.

The calculation are based on a binomial distribution, which assumes that the sample is small compared to the lot size (say the sample is 10% or less of the total lot). It also assumes a product is either defective or not - you can't have 2 or more defects on a single product. If these are not the case, then the calculations will be off.

In the calculation section at the bottom:
  • column A is the number of defects found in a lot; let's call it "k".
  • column B is a remnant from when I was setting up the spreadsheet. It is the theoretical odds of finding exactly k defects in the lot when the defect rate is = AQL. It is not actually used in any of the further calculations.
  • column C is the cumulative odds of finding no more than k defects when defect rate = AQL. The cells are green whenever the odds are less than 100%-alpha.
  • columns D & E are like 2 & 3, only using defect rate = LTPD. Column 5 is red whenever the cumulative odds are greater than beta.
  • column F checks to see if column C is green. The green cells mean the producer doesn't have to worry that too many good lots will be rejected.
  • column G checks to see if column E is red. The red cells mean the consumer is at risk of accepting too many bad lots.
When the bottom of the green bar matches the top of the red bar, then the plan is acceptable to both parties, indicated in cell B1. When the bars miss by 2 or more, then it is clear which way to adjust the sample size to improve the plan, which is the advice given in cell B2

The AC number is where the producer thinks it should be set. The RE number is where the consumer thinks it should be set. Clearly these should be 1 apart. The spreadsheet basically allows a rapid "negotiation" between the consumer and the producer as to what plans might be acceptable.


I don't doubt that your stuff is right, but I would at this time not be in too good of a position to defend its use to a customer who may want the assumed security of an "accepted" sampling plan like ASQ 1.4.
Frankly, I would be hesitant to promote this plan to a customer, either no.gif . At least until 1 or 2 other people looked carefully at the equations and the logic behind them yes.gif .

Tim F
 

Statistical Steven

Statistician
Staff member
Super Moderator
#18
Tim Folkerts said:
Anyone brave enough to dig through it???
Tim F
I will dig through it and try to help with some documentation. I think it is quite intuitive and the selling it to a customer is not much different than Z1.4. Give me a few days to get to it.
 
#19
Wow, very intresting thread on sampling, and nice spreadsheet. After reading all this information, I was thinking of applying it in my department of calibration, not to specific final product.

I currently sample 15% of my technician's work each month. I've been performing this type of audit on my techs for 2 years, and noticed that some techs have no errors, while others have some, while others even have more than just some. Could something like this be used so I spend more time on techs that have more errors than others that don't (i.e. increase my sample on those with more errors)?

My typical cal techs usually calibrates between 70 to 140 instruments each month. For their reviews, they are rated on the number of errors that I find on paperwork. Example:
tech1 - I sampled a total of 180 records for a 10 month period. Out of this 180 records, I found 2 errors. This comes out to be 98.8%.
99-100% - outstanding
95-99% - value
<95% - improvement required

Thoughts?
 

Tim Folkerts

Super Moderator
#20
Charles,

I have a few thoughts. Much of if comes down to the fact that random variation makes it hard to be sure on any results. Also, remember that this spreadsheet is based on a binomial distribution, which assumes that you are checking only a small part of the total "production" (i.e. calibration reports). Some of the later number suggest you might have to check a large proportion of the monthly reports to get adequate accuracy, which means a more accurate model would be needed.

As I see it, the goal of a sampling plan is to take products that can be categorized into three groups: "good" = better than AQL, "bad" = worse than LTPD, and "indifferent" = between AQL and LTPD, and try to sort them into two groups ("pass" and "fail").

Ideally, bad lots will never pass and good lots will never fail. Indifferent lots may pass or may fail. In reality, bad lots will sometimes pass, and good lots will sometimes fail.

In your case a lot is the monthly output of 1 tech. A good tech produces 1% or less defects. A bad tech produces 5% or more defects.

If alpha=beta=5%, then you need to test at least 124 samples from that month to get to this level of confidence. Note that indifferent techs could easily pass or fail. Perhaps any tech that fails 3 times in a row could be required to have extra training.


Going the other way, if you wanted to be 95% sure he really was outstanding, you would need to test at least 299 pieces and find no defects (set alpha = 95 in the spreadsheet). On the other hand, to be 95% sure he really "needs improvement", you would just need 1 of 7 bad.


You could also work backwards. Your typical sample size seems to be about 20. If AC = 0, then alpha ~ 18% (there is an 18% chance that a good tech could fail) and beta ~36% (there is a 36% chance that a bad tech could pass and be told he’s OK).


You might also consider a 2-proportion test to see if two results (for example, tech 1 vs tech 2, or tech 1 vs the overall average) are indeed different.


Finally, a control chart could be a valuable tool. See if there any of the techs go "out of control". A p chart should do the trick.


NOTE: I'm still waiting for confirmation from a second source for the accuracy of the spread sheet. Also, I didn't double-check the numbers above, so you ought to get a second opinion before blindly accepting them.

Tim F
 
Thread starter Similar threads Forum Replies Date
T Double-sided (USL, LSL) Variables sampling plan Z1.9 - Use in Excel spreadsheet? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
J IVD sampling sizes for buyer Reliability Analysis - Predictions, Testing and Standards 0
S Which Sampling Plan(s) Should I Use? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 7
C Sampling - ISO 16269-6 vs ISO 2859 Other ISO and International Standards and European Regulations 0
L Sampling Plan Risks AQL - Acceptable Quality Level 6
A Sampling plan for in-process QC (medical devices) Inspection, Prints (Drawings), Testing, Sampling and Related Topics 13
M Minitab Capability of the Population (no sampling) Using Minitab Software 11
W LTPD, AQL, Ppk and Cpk validation sampling plan table Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
Q Sampling method for Distributor verification activities EU Medical Device Regulations 1
E Change in control plan - Do I have to do sampling? IATF 16949 - Automotive Quality Systems Standard 1
S Is using ANSI/ASQ Z1.4-2008 the correct sampling plan to determine Pass/Fail of Apparel measurements? AQL - Acceptable Quality Level 4
N Sampling Plan for Internal Audits - ISO 2859 or 3951 - Or Neither? Internal Auditing 6
F Product audit sampling plans IATF 16949 - Automotive Quality Systems Standard 3
R Reduced sampling plan for sterial products APQP and PPAP 0
A ISO 2859-1 - 9.3.3.2 Switching score - Sampling Plans and PPM AQL - Acceptable Quality Level 0
R BS EN 12060:1998 - Zinc and zinc alloys Method of sampling Specifications Manufacturing and Related Processes 4
S High voltage testing - ISO 17025 - 7.2.2 Validation of methods and 7.3 Sampling ISO 17025 related Discussions 3
8 Activity Sampling Exercise Lean in Manufacturing and Service Industries 11
T Defining sampling plan for different AQL AQL - Acceptable Quality Level 3
B AS9100D Sampling Plan AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 2
R Design verification for interim design outputs - sampling rationale ISO 13485:2016 - Medical Device Quality Management Systems 2
Nicole Desouza Sampling plan for a customer who wants AQL 1.0 (per ANSI Z1.4) AQL - Acceptable Quality Level 5
V How to interpret AQL sampling tables AQL - Acceptable Quality Level 5
A AQL sampling bags of parts Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
C Applying Weibayes to Attribute sampling Reliability Analysis - Predictions, Testing and Standards 0
I Sampling processes - Who must define the AQL level? AQL - Acceptable Quality Level 9
E Sampling for capability studies for variables and attributes Capability, Accuracy and Stability - Processes, Machines, etc. 4
O Statistical justification of sampling size in V&V tests ISO 13485:2016 - Medical Device Quality Management Systems 5
M Sampling Plan for Alumin High Pressure Die Castings Manufacturing and Related Processes 0
E Sampling plan for orthopedic implant - Process Validation Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
S Inspection/sampling economics Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
S How to make a Sampling Plan - Conveyor belts Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
V Statistical basis and justification while comparing / changing sampling plans Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 11
J AQL for Effectiveness Check - What AQL tiers to use on this type of sampling? Nonconformance and Corrective Action 9
N The question asks about sampling plans and AQL Reliability Analysis - Predictions, Testing and Standards 5
S Help develop sampling plan for prototype samples (medical devices) Statistical Analysis Tools, Techniques and SPC 7
A ISO 2859 Single Sampling - Clarification regarding the sampling table Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
C Are zero defect sampling plans relevant to AS9120B Distributor AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 4
R DCMA Sampling of CSI Parts AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 4
D Sampling method that is representative of the devices supplied by that distributor EU Medical Device Regulations 5
T ISO 13485: 2016 Internal Audit - Is sampling on projects allowed? ISO 13485:2016 - Medical Device Quality Management Systems 6
M Zero Defect Sampling Plan Standards Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
L 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
M ISO / ASTM standards for Sampling Plans for Medical Devices Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
N Sampling for stability studies - Class II surgically invasive devices Other Medical Device and Orthopedic Related Topics 1
S Surveillance Sampling Test - Determining Sample Size Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
A AQL Sampling Plan SOP / WI - Medical Device Industry Inspection, Prints (Drawings), Testing, Sampling and Related Topics 14
B IATF 16949 Cl. 8.6.6 - Acceptance Criteria - Zero Defects Attribute Data Sampling IATF 16949 - Automotive Quality Systems Standard 2
C Sampling of Class IIb Implantables under EU MDR - Assessments to the EU MDR EU Medical Device Regulations 4

Similar threads

Top Bottom