About StDev in MINITAB13

[Richard-jxb]

when I use MINITAB's Process Analysis(Betwwenn/Within), the results showed me:

StDev(Within)=
StDev(Betw)=
StDev(Total)=
StDev(Overall)=

But I don't know how to calculate the above.
Would you like to help me?

[Dave Strouse]

Richard -

I'm assumming you mean capability analysis, MINITAB does not have a process analysis to my knowledge. Their help is a bit deficient here. However, the help for the I-MR controol chart within and between is the same method I believe. From that dialog, box click on help button then on see also. I cut and pasted it here, but you might want to look at it in your MINITAB as some of the symbols may not come through correctly. here

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If you do not estimate parameters by historical groups, Minitab displays three standard deviations in the Session window. These are the standard deviations for the between component, the within component, and the total variation. These standard deviations can then be used as parameters in other analyses. For example, you might want to use the estimate for the total variation as the historical sigma in a normal capability analysis.
Here are the model assumptions used in estimating these three standard deviations. The model assumes that an observation, Xij, is the sum of an overall mean, m, a between component, Bi, and a within component, Wj(i), as shown below.

Xij = m + Bi + Wj(i)

i = 1, …, I; j = 1, …, J

The between components, Bi, are assumed to arise from a normal distribution with mean 0 and variance B. The within components, Wj(i), are assumed to be independent of the Bi and arise from a normal distribution with mean 0 and variance w. The total variance of the observation, Xij, T, is the sum of B and w.
The I Chart of the subgroup means gives an estimate, say V1, of Var(i), the variance of the subgroup means:

Var(i) = B + w / J

The Range Chart gives an estimate, say V2, for w. This is true because the Range Chart for the Xij is the same as the Range Chart for the (unobservable) Wj(i), the within component.
We can combine V1 and V2 to get estimates of B and w, as

estimate of B = max( 0, V1 - V2 / J )

and estimate of w = V1 + (J - 1) * V2 / J.

It is possible that the estimate for B is zero.

[Atul Khandekar]

Also see the following articles from Minitab Answers Database:
http://www.minitab.com/support/answe...er.aspx?ID=605
http://www.minitab.com/support/answe...er.aspx?ID=654

[Darius]

Excelent links Atul, specially the second ones.

Within Sample Stdev = Range_Average /d2 or Stdev_Average/c4
(wich method depends on the sample size, some say that Range is used with subgroup sizes less than 10, but is the ones that is used to chart SPC and capability index; cpk, cp, cpm, cpmk)

Between Sample Stdev = Excel Stdev on the averages of each group /c4

Total Variation Stdev = Excel Stdev on the data / c4
(the ones for performance index; ppk,pp)

c4 is used to change values from biased to unbiaded estimates.

Excel Stdev is the traditional way to calculate stdev.

And in some texts, Overall an total are the same.