Suitability of Attribute Control Charts for ppm Level Control

D

dlockesf

#1
Hi, y'all. Here's my next question. Remember I'm writing material on SQC and SPC (and Six Sigma and Lean) for a non technical audience of people in purchasing. I've come to the section on attribute control charts, and I'm coming to the conclusion they don't work well at low defect levels (say 1000 ppm) when looking for a single specific defect. I've been looking at c, u, p, and np charts and they all seem to have problems with high probability of false alarms or requiring very large sample sizes for the control limit math to work.

They do seem to have a use for complex products where multiple defects are likely on a given unit but that would require a purchasing mindset that the supplier can ship defective units, which is what I'm trying to train them out of.

Any comments? Suggestions?
 
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Jim Wynne

Staff member
Admin
#2
I'd think you would be most interested in explaining what control charts are for (regardless of the type), how they're constructed and maintained, and not much more than that. Attributes charts, like other control charts, are used to provide ongoing assurance of statistical stability over time, and in the end don't have much at all to do with PPM levels. Control charts might help to make predictions about PPM levels, but not to weed out defects or defectives.
 
S

SPC_Newbie

#3
The term I think you could use for the situation described is 'rare events data'. It took me a while to discover that there was such a term so hopefully this will save you some time in finding reasonable ways to chart low defects.

Cheers!
 
D

dlockesf

#4
I'd think you would be most interested in explaining what control charts are for (regardless of the type), how they're constructed and maintained, and not much more than that. Attributes charts, like other control charts, are used to provide ongoing assurance of statistical stability over time, and in the end don't have much at all to do with PPM levels. Control charts might help to make predictions about PPM levels, but not to weed out defects or defectives.
I've done what you suggested for variable charts because I think they are useful even at the ppm level, but I don't want to spend the "students'" time on things that aren't useful. I've walked them through capability studies which show the supplier's capability on a good day but I firmly believe that the supplier has to consistently produce material at the desired quality level because inspecting quality in doesn't work.
 
D

dlockesf

#5
The term I think you could use for the situation described is 'rare events data'. It took me a while to discover that there was such a term so hopefully this will save you some time in finding reasonable ways to chart low defects.

Cheers!
Thanks, that was helpful. It led me to t-charts and g-charts, which I've never seen before.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#6
your target audience probably won't encounter the need for rare events charts, so it may be an acedemic excercise...

the reason that the 'traditional' p charts and c charts don't work is that they are based on the Normal Distribution approximation of the Binomial and the Poisson. The Normal Distribtuion approximation doesn't hold at low failure rates, for one fairly obvious reason. Namely that both the Binomial and Poisson deal with integer counts of events. So a 'rare event' is roughly one that has an upper control limit of 1 event or less. The only answer you can ever get is 0, 1, 2,...for rare events you get long strings of zero events and then when 1 event does occur it's at the upper limit. The other not so obvious reason is that rare events tend to 'cluster'. What this means is that they are not homogenously distributed; you will go for a 'long' period of time wihtout an even then you will see 2-4 in a relatively short period of time. Rare events (roughly) follow a Geometric distribution. I posted a document on this in the cove somewhere.

the file is SPC for Rare Events
 
D

dlockesf

#7
your target audience probably won't encounter the need for rare events charts, so it may be an acedemic excercise...

the reason that the 'traditional' p charts and c charts don't work is that they are based on the Normal Distribution approximation of the Binomial and the Poisson. The Normal Distribtuion approximation doesn't hold at low failure rates, for one fairly obvious reason. Namely that both the Binomial and Poisson deal with integer counts of events. So a 'rare event' is roughly one that has an upper control limit of 1 event or less. The only answer you can ever get is 0, 1, 2,...for rare events you get long strings of zero events and then when 1 event does occur it's at the upper limit. The other not so obvious reason is that rare events tend to 'cluster'. What this means is that they are not homogenously distributed; you will go for a 'long' period of time wihtout an even then you will see 2-4 in a relatively short period of time. Rare events (roughly) follow a Geometric distribution. I posted a document on this in the cove somewhere.

the file is SPC for Rare Events
Thanks, Bev. I like your paper. The term "silly" is exactly what I thought when I made a demonstative c-chart with hypothetical 500 or even 1000 ppm data.

Strictly academic? I hope not. I hope our seminar "attendees" will be out surveying suppliers who produce at the 1000 ppm range.
 
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