# SPC Control Limit Calculation

S

#### Stevenli

Folks,

I am still confusion about the SPC control limit calculation. Let's take traditional Xbar-R chart as an example, in the SPC manual it's stated as control limit is Xbar+/-A2*Rbar. However in many six sigma material it's expressed as Xbar+/-3Sigma. So I know I am confused by how to estimated the variation in different situation.

Any explanations would be helpful. Thanks.

Steven

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Those who state that the control limits are calculated directly from the total standard deviation are simply wrong. The limits are referred to as 'three sigma limits' but the fundamental way control charts work is that the variation limits for the subgroup average are calculated using the within subgroup standard deviation. for an Xbar R chart this is done using the average range.

my recommendation is to invest in a GOOD book on SPC. Anything by Donald Wheeler will be good. the book "innovative control charting" by Steven Wise and Douglas Fair is excellent and covers many different types of processes....

D

#### Darius

control limit is Xbar+/-A2*Rbar expressed as Xbar+/-3Sigma
Xbar+/-A2*Rbar = Xbar+/-3Sigma_within_variation_estimate

Because Sigma (in your equation) or Sigma_within_variation_estimate = Rbar/d2

A2= 3/d2

As Donald Wheeler said in "Advanced topics on SPC" (more or less), there are several variation estimates wich can be applied in it's specific field of application.

This variation estimate, as Bev said is not total variation estimate (the traditional sigma), but the variation within a subgroup of samples,and try to capture or show the variation without special causes, the minimal variation.

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