P chart sigma trade-offs (to monitor mis-labeled samples coming into our lab)

D

dsm_racing

I'm considering setting up a P chart to monitor mis-labeled samples coming into our lab. However, I'm not sure that I fully understand the tradeoffs involved when selecting a sigma. Could someone please tell me if this is right? If I choose a low sigma, then I am setting my UCL and LCL more narrow which will increase the probability that a point outside the limits is due to Type 1 error, however, if I set my sigma too high then I widen the limits and could be overlooking some assignable causes of variation?
 

Jim Wynne

Leader
Admin
Re: P chart sigma trade-offs

I'm considering setting up a P chart to monitor mis-labeled samples coming into our lab. However, I'm not sure that I fully understand the tradeoffs involved when selecting a sigma. Could someone please tell me if this is right? If I choose a low sigma, then I am setting my UCL and LCL more narrow which will increase the probability that a point outside the limits is due to Type 1 error, however, if I set my sigma too high then I widen the limits and could be overlooking some assignable causes of variation?

Welcome to the Cove. :D

I'm not sure what you mean by "selecting a sigma." "Sigma" is another way to say "standard deviation," and it's a calculated value, not one that you arbitrarily select. Have a look at the NIST Engineering Statistics Handbook explanation of Proportions Control Charts, and/or post back if I've misunderstood what you're looking for.
 

reynald

Quite Involved in Discussions
Re: P chart sigma trade-offs

Welcome to the Cove. :D

I'm not sure what you mean by "selecting a sigma." "Sigma" is another way to say "standard deviation," and it's a calculated value, not one that you arbitrarily select. Have a look at the NIST Engineering Statistics Handbook explanation of Proportions Control Charts, and/or post back if I've misunderstood what you're looking for.

I think dsm_racing is referring to where to set the control limits, +/-1 sigma limits, or +/-2 sigma limits, or any 'sigma' distance.

In that case the answer is use +/-3sigma or 3*"standard deviation". That strikes the balance between Type1 and Type2 errors.

Reynald
 
D

dsm_racing

Yes, reynald, that's what I'm wondering. If my thinking is right, by using the 3 sigma value, there is a chance that 26 samples out of 10000 will fall outside the limits due to Type I error. Those cannot be correctly assigned a cause of variation. I could reduce the Type I error by using a higher sigma to set the controls so most of the points that fall outside the limits will have assignable causes, but that would mean a lot fewer points will fall outside the limits so I would miss out on a lot of assignable variation.

Am I thinking about this right?
 
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Bev D

Heretical Statistician
Leader
Super Moderator
Yes, reynald, that's what I'm wondering. If my thinking is right, by using the 3 sigma value, there is a chance that 26 samples out of 10000 will fall outside the limits due to Type I error. Those cannot be correctly assigned a cause of variation. I could reduce the Type I error by using a higher sigma to set the controls so most of the points that fall outside the limits will have assignable causes, but that would mean a lot fewer points will fall outside the limits so I would miss out on a lot of assignable variation.

Am I thinking about this right?


yes and no.
you can play with the error rate if you want to but why would you? the "3sigma limits" have been proven over decades to strike the best balance. why do you feel the need to change that without even having tried the best practice method.

Also the 'error rate' or alpha risk if you will is NOT fixed tor control charts. nor are they intended to; control charts aren't hypothesis tests....
 
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