A Sampling Story

The field is getting rather crowded, but I'll add one more for the month.

I wrote in the style of an article I really enjoyed in QP severl months ago (a fictionalized account of a quality engineer struggling to understand capability calculations, especially for mixtures of parts from different production lines). I tried my hand at a similar approach for sampling. The beginning is mostly dialog, but the second half has some calculations and charts. I'm not sure how well the mix of fiction and stats works, but I'm sure you guys will tell me. (And I need a catchier title, but I can't think of anything right off-hand.)

I also attached the Excel file I used to do the calculations, in case anyone was interested.


Tim F

Good Tim,


You have a well thought out article that is very heavy on data. I love data but I prefer it in terms I can understand. My problem is that I like to see multiple tables to learn, not in the body of the text. I'm not that technical that I can read between those lines.

I was very interested in the extrapolation of the multiplier 4 for acceptance and defect.

Good article, keep it up!

Al...

Al,

The challenge, as you pointed out, was to make the fiction interesting and believable, while addressing some moderatly challenging mathematics. I could have made it entirely a story and skipped the math, or I could have just explained the math and skipped the fiction. I was hoping to hit a happy balance, but that balance point depends a lot on how much one knows of sampling plans and how much one knows of pure statistics.

The article that originally inspired me was from the June 2003 Quality Progress, "My Supplier's Capability Is What?" which can be found at
http://www.asq.org/pub/qualityprogress/past/0503/qp0503pylipow.pdf

Shortly after that, a thread came up on the ASQ Discussion boards which basically asked the main question addressed in my paper. I knew enough stats to feel comfortable with the mathematical end, but I didn't know a lot about the jargon of the official standards. The paper partially chronicles my learning of the topic (like trying to figure out the oddly printed tables).

Tim F

As mentioned, keep up the good work!!!

Al...

Very interesting Tim

Tim,
Obviously your article took the most time to read and understand -. I had to refresh my knowledge on Acceptance sampling. I understand you found an acceptance number for a given sample with 3 ranges of possible process average of defects.

One thing that was not clear to me;
Arriving the reject level of 67. Was that by trial and error? In your article you are getting to this point too quick.
"Pete checked a one more option. A reject level of 67 gave approximately the same 1% chance of rejecting the good lot.".
This is one of the reason, I read few times. This plan is steeper as 87 but with better protection.(Combined advantage).Good choice.

In the Last Page:
"Dropping the acceptance number to 66 slightly increased the odds of rejecting a good lot, but enhanced the odds of rejecting a bad lot".
May I add, there is also better protection to consumer.

Here is my rationale
I used your data from the table and at 5% alpha and 10% beta
The 21 option:
5% probability of rejecting lots better than 30 defects and 10% probability of accepting lots worse than 57 defects.
The 66 option:
5% probability of rejecting lots better than 27 defects and 10% probability of accepting lots worse than 39 defects.
The 87 option:
5% probability of rejecting lots better than 37 defects and 10% probability of accepting lots worse than 50 defects.

Please correct me if my interpretation is not appropriate. Iam willing to learn.

I found this article very interesting as this provides insight into fundamentals of acceptance sampling. Many organizations unknowingly inspect either too many samples and increase their cost or inspect less sample and increase risk to their customers.
By knowing the process average, acceptable alpha, beta risks, sampling plans that are economical to both supplier and customer can be derived. For those organizations aiming for a quick cost saving, This is a low hanging fruit.

Thanks for the article Tim. This forced me to get back to my basics and CQE BOK.
Regards,
Govind.

Note: I just the completed the review of full round of all May article..

One thing that was not clear to me; Arriving the reject level of 67. Was that by trial and error? In your article you are getting to this point too quick.

Click to expand...

I'm flattered that I was able to write well enough that ther was just one thing that wasn't clear. ;-)

It’s sort of trial and error. The first worksheet in the spreadsheet allows the calculation of the odds of getting a specific number of defectives when the user inputs the defect rate and the sample size. Since the spreadsheet list basically all the possible number of defectives, one just has to look down the list to find the one where the cumulative odds are 0.95 or better. I inputted 200 for the lot size and .25 for the defect rate (the numbers used in the article), and found that 67 defectives was the magic number to achieve 0.95 cumulative odds.

In other words, with 200 samples and defective rate of 0.25 you would expect on average 200 * 0.25 = 50 defects. The odds of getting 67 or more are less than 1%, so such a sample is unlikely to come from a good lot.

So yes, it is a “brute force” method, but no, I didn’t have to type in lots of number until I found the right one (I just let Excel do that for me).

In the Last Page:
"Dropping the acceptance number to 66 slightly increased the odds of rejecting a good lot, but enhanced the odds of rejecting a bad lot".
May I add, there is also better protection to consumer.

Here is my rationale
I used your data from the table and at 5% alpha and 10% beta
The 21 option:
5% probability of rejecting lots better than 30 defects and 10% probability of accepting lots worse than 57 defects.
The 66 option:
5% probability of rejecting lots better than 27 defects and 10% probability of accepting lots worse than 39 defects.
The 87 option:
5% probability of rejecting lots better than 37 defects and 10% probability of accepting lots worse than 50 defects.

Please correct me if my interpretation is not appropriate. I am willing to learn.

Click to expand...

That sounds good, although to be more specifically, I would say “No more than 5% probability of rejecting lots better than 30 defects per hundred and no more than 10% probability of accepting lots worse than 57 defects per hundred,” etc.

I’m guessing that is what you meant but it was so obvious that you just didn’t bother to type the extra words. 30% defects is the cut-off level for rejecting 5% of the lots; 57% is the cut off for rejecting all but 10% of the lots.

Otherwise, I think your interpretation is perfectly sound. All three plans will almost always accept good lots. The second plan listed above has the best chance of rejecting bad lots, so as you pointed out, it gives the best protection to the consumer. The advantage of the first is that you are only testing 50 samples instead of 200 - you save on testing, but you run a larger risk of accepting a bad lot.

Tim F