Control chart for huge sample size

#1
I have to design a control chart based on an article of samples with size 500 each (generated from random observations with mean=0 and std=1). My main issue is that I'm unable to obtain the desired ARL out of control for different mean shifts (0.2,0.4,0.6,0.8...) because my standard deviation is so small (about 0.003). My out of control ARL for a 0.2 mean shift is 1 instead of about 180 in the article. I designed both an I-MR, xbar-R and also xbar-S for the same samples but the outcome is the same. Can someone give me a hint of what could probably be wrong in my design please? thanks
[Moderator note: A copyrighted attachment was removed.}
 
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Jim Wynne

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#2
Welcome to the Cove. :bigwave: I removed your attachment because it's copyright-protected. We don't share copyrighted materials here. Also, I moved your post to a more appropriate forum so that it will get better focus and attention.
 

Miner

Forum Moderator
Staff member
Admin
#4
Is this a class assignment, or for theoretical understanding? From a practical perspective, why would you want to create such a chart? There is an adage that goes: Just because you can, doesn't mean you should.
 

Miner

Forum Moderator
Staff member
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#8
We have to adapt it to a practical situation and provide improvement measures
From a practical perspective, why would you want to create such a chart? There is an adage that goes: Just because you can, doesn't mean you should.
Again, why would you want to do this? Shewhart control charts were designed and intended to gain the maximum information on the process stability from small subgroup sizes. By using "huge" subgroup sizes, you are throwing away most of the advantages of the tool.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#9
We have to adapt it to a practical situation and provide improvement measures
You still have not answered the question. SPC works because it is an empirical methodology, as stated by Dr. Shewhard and Dr. Deming and others. Neither fretted about ARL. And ARL only deals with alpha error - false alarms. The failure to detect beta error gets left in the dust. Thus you may be trying to control the false alarm rate and inadvertently end up removing the ability to detect a trend. Rather like pulling the batteries from your household smoke detector in order to eliminate false alarms.

I will agree with Miner that you are losing a lot of information by taking groups of 500, but if it is important to do so in order to trend such an average, there is no reason the control chart would not work. It is just highly likely that you can have individual results in the 500 that are unusual and will be missed on the Xbar chart and likely the Range (though it the individual result is far enough out, it should pick it up).
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#10
On a separate note, you state that you created random data set with mean of 0 and and a standard deviation of 1. Then you say you your SD is .003, can you explain that?

Also, a randomly generated distribution will b eperfectly homogenous and so it doesn’t match the example from the paper you originally posted...
 
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