Sampling plan to detect defective units - Given N=6000, PPM=500

Statistical Steven

Statistician
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Super Moderator
#11
Bev D said:
yes the theoretical requirement for the Poisson is not met. This is a consistant problem with very low defect rates...but we must remember that both teh Poisson and the Binomial are only models and estimates. The real proof is if they are useful for need. (to paraphrase George Box). Other factors suchas how the samples are taken and how the defects may or may not cluster will add more 'inaccuracy' to the result thant the choice of distributional model. and as you point out the differences are slight anyway.
I choose to use the Poisson in most cases (not all) because it is easy to calculate

But of course the real point here is that with small defect rates we need to stop looking for proportional sampling plans and begin assessing alternatives sucha s poke yoke and continuous data plans. you simply cannot guarantee zero defects with proportional sampling plans adn this is where so much of industry is headed - an drightly so in my opinion.
I think we open a can of worms here. If our goal is to guarantee zero defects, then of course you need to 100% inspect (or Poke Yoke). If our goal is to ensure that the quality level is acceptable (understanding that defects happen), then proportional sampling is acceptable (no pun intended). Too often we get caught up in the 6S, zero defect world that we fail to realize the cost of failure can be less than the cost of inspection.
 
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Bev D

Heretical Statistician
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Super Moderator
#12
nielsmx said:
Sorry, I'm not a statistician, but if I see the number 5992 out of 6000, I get the feeling that we're talking about 100% inspection. "..."so if we did 100% inspection, what will be our confidence of delivering according to the spec?
yes, 5992 is close to 100% of a 6000 piece lot. but since the sampling plan is not dependent on lot size, the lot size could have been significantly more or less.

to answer your real question: you cannot guarantee any accuracy of inspection using humans with pass fail data. you can find formulas to estimate it - but they are simply mathematical exercises or models. the actual accuracy of any human inspection is dependent on training, environmental conditions, equipment measurement error and wear and calibration - including human calibration if using visual criteria, etc. These factors are more dominant than any statistical model and vary form inspection to inspectiona nd company to company and industry to industry.

You could estimate your accuracy emperically is you knew the results from the user - if you can trust their accuracy in detecting the defect.

again - for low defect rates inspection is not the answer.
 

Bev D

Heretical Statistician
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Super Moderator
#13
Statistical Steven said:
I think we open a can of worms here. If our goal is to guarantee zero defects, then of course you need to 100% inspect (or Poke Yoke). If our goal is to ensure that the quality level is acceptable (understanding that defects happen), then proportional sampling is acceptable (no pun intended). Too often we get caught up in the 6S, zero defect world that we fail to realize the cost of failure can be less than the cost of inspection.
True, many defects are minor and trivial and won't lead to a failure of the product or service. If these occur at a very low rate and we have solid process controls in place, they probably shouldn't be inspected for at all.

However, many are not trivial and some are catastrophic in their effect. These cannot be guaranteed with a proportional data sampling plan and need poke yokes. And many poke yokes are surprising cheap and easy once you get teh right people to get creative.

logic and business needs should drive our solutions.
 

Statistical Steven

Statistician
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Super Moderator
#14
Bev D said:
True, many defects are minor and trivial and won't lead to a failure of the product or service. If these occur at a very low rate and we have solid process controls in place, they probably shouldn't be inspected for at all.

However, many are not trivial and some are catastrophic in their effect. These cannot be guaranteed with a proportional data sampling plan and need poke yokes. And many poke yokes are surprising cheap and easy once you get teh right people to get creative.

logic and business needs should drive our solutions.
Correct me if I am wrong, but my understanding of Poke Yoke is just another word for 100% inspection of a characteristic that is indicative of quality for the product.
 

Bev D

Heretical Statistician
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Super Moderator
#15
Statistical Steven said:
Correct me if I am wrong, but my understanding of Poke Yoke is just another word for 100% inspection of a characteristic that is indicative of quality for the product.
well, I wouldn't say that you're wrong - that would be rude. but your description of a poke yoke doesn't do it justice. A poke yoke is a mistake proofing device or procedure that eliminates huamn error and detects or prevents all occurences of a specific defect type. they are highly effective at guaranteeign zero defects. not all defects or errors can be poke yoked but the great majority can.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#16
Bev D said:
well, I wouldn't say that you're wrong - that would be rude. but your description of a poke yoke doesn't do it justice. A poke yoke is a mistake proofing device or procedure that eliminates huamn error and detects or prevents all occurences of a specific defect type. they are highly effective at guaranteeign zero defects. not all defects or errors can be poke yoked but the great majority can.
There is no device that can prevent all human error, even automation will have some component of error. Let's agree to disagree on the finer points of 100% inspection versus a procedure or device that checks every part.
 

Tim Folkerts

Super Moderator
#17
One simple poke yoka approach is used in electrical outlets. In the US, one prong is wider than the other, preventing the plug from being put in backwards, which prevents certain kinds of hazards. Old plugs had both prongs the same.

As long as the plug was wired correctly in the first place, it is impossible to accidently plug it in backwards. That is the gist of poke yoka.

Tim F
 

Statistical Steven

Statistician
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Super Moderator
#18
Tim Folkerts said:
One simple poke yoka approach is used in electrical outlets. In the US, one prong is wider than the other, preventing the plug from being put in backwards, which prevents certain kinds of hazards. Old plugs had both prongs the same.

As long as the plug was wired correctly in the first place, it is impossible to accidently plug it in backwards. That is the gist of poke yoka.

Tim F
Who knew there was a backwards to a plug. For all this time I thought the bigger prong was just a design improvement.:) :D

Excellent example, so a poke yoke to fix the hazards of a backward plug, creates issues with older outlets that cannot accept the bigger prong. So people "jam" it in, and get those same hazards. Like I said, you can NEVER 100% idiot proof anything. That is why liability insurance is so high.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#19
Statistical Steven said:
Like I said, you can NEVER 100% idiot proof anything. That is why liability insurance is so high.
true you can't always completely idiot proof against an idiot or a determined saboteur - but what is your point here? Most manufcturing people are neither.

In my experience poke yokes have in fact significantly reduced or eliminated errors and defects and have been much more effective (in $ and accuracy) than classical human inspections when the defect rate is very low. (although for soem things I have used them when the defect rate is high, I was working on root cause and couldn't affford an escape or to stop shipment)

And that's where this thread was going - what to do when the defect rate is very low. proportional sampling can be onerous due to to it's large size. 100% human inspection is not very accurate. an alternative that is very effective is the poke yoke.
 

Tim Folkerts

Super Moderator
#20
Statistical Steven said:
Who knew there was a backwards to a plug. For all this time I thought the bigger prong was just a design improvement.:) :D
Yep. One side of the outlet is "neutral" i.e. connected to ground (that is the longer slot). If the house is wired properly (and please don't try this experiment at home!), you can stick a finger in that side without any danger, even if you are standing in the bathtub. If you stick a finger in the other side, you can get a nasty shock. :mg:



Excellent example, so a poke yoke to fix the hazards of a backward plug, creates issues with older outlets that cannot accept the bigger prong. So people "jam" it in, and get those same hazards. Like I said, you can NEVER 100% idiot proof anything. That is why liability insurance is so high.
The point isn't that you can't do it wrong, just that you have to go out of your way to do it wrong. As you rightly state, nothing is 100%, but a well-designed system makes it easy to do things right and hard to do things wrong.


Tim
 
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