# Control limits

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• #31572

Andhale
Participant

Why do we generally choose to keep the control limits as 3 sigma for control charts?

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#83321

Chen
Participant

Hey Doctor Shewhart would be rolling in his grave if he heard this. Actually it gives a balance between type 1 and type 2 error. The gain to go to 4 sigma on control limits is so little it would not be apprecable. to go to 2 it would make for a lot of wild goose chases.

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#83330

Zilgo
Member

One of the assumptions for control charts is normality.  Plus/Minus three sigma from the mean of a normal distribution means that 99.73% percent of the data will be within the control limits.  So anything outside those control limits would be pretty rare, and therefore something out of control with your process.

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#83366

Andhale
Participant

Thank you Zilgo for your response.
If that is the only reason for 3 sigma limits then why not 4 sigma limits, or is it based on statistical experiance.

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#83369

Hemanth
Participant

Hi
Refer to the previous reply, Dr Shewhart identified 3 sigma as control limits because at this level, the chances of making an error is minimal. Lets assume that the control limits be 4 sigma wide, what would happen you are widening your control band so the control charts would become lesser and lesser sensitive to any change. So even if your process has changed you wont get the signals. (Type 1 error).
If you make it tighter that is 2 sigma wide, then you are being too strict, and in many cases you would start investigating the common cause, which you shouldnt be doing. (Type 2 error)
In statistical term Schewarht said at 3 sigma level the chances of making type 1 and type 2 error in judgement is minimal and hence the limits.(there is a valid statistical proof for that)

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#83373

Andhale
Participant

Thank you Hemanth

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