Variance Component Analysis

[#1]

I want to make Var Comp Analysis 

The random factors are

Operator, Day, Plate, Replicate

Balanced Nested Design

I want to make displays of how Variance can occupy within the Total Variance (It is the principle of Var Comp Analysis, Right?)

So I made the figure top of this post.

1. sigma operator makes O1 and O2 scatter

2. When O1 and O2 are fixed, they respectively has their Day distribution,

3. When D1,2 and D3,4 are fixed, they  respectively has their Plate distribution,

4...

Is my understanding good? (I know in the figure it is not proper to display sigma, maybe it is proper to substitute it to sigma (mean of operator), or something else, but out of point.)

Can uppermost distribution be assumed as equal to Total Distribution??

Please help me.

I have tried to search referable figure in the net by entering <nested design, distribution, split-plot, var comp, etc.> but I couldn't.

[#2]

I'm sorry I don't know what you are asking?  Are you asking how to do a nested or hierarchical study?  or, how to determine the relationships between variance components?  or, If you have 4 nested components of variation, how to do the math?

The way your diagram depicts the components appears to be Replicates within Plate, within Day, within Operator.  I typically visualize the components as a tree diagram.  For example (using your names):

 

What is Replicate?  What do you mean by "fixed"? I'm not sure I would agree with this hierarchy?  Are you sure the layers are nested and not crossed (or is there a mix)?

Variance in the study = Sum of the Variances at each layer of the tree.

[#3]

Thx for interest

What I am asking is, 

The graphical result of,

<Distribution of Total, With each component distribution of (operator, days, etc.)>

If Variance in the study = Sum of the Variances at each layer of the tree.,

Then, Distribution of the study can be divided into distribution of respective each layers.

However there is no example of this figure on the net.

Could you give me some ideas?

[#4]

I think that you are saying that you want to visualise the different variance components as distribution plots. Is that correct?

[#5]

Yes it is!

Hard to visualize it...

[#6]

I don't have a solution, just a comment: I think that it will be difficult for the viewer to quantify the magnitude of each variance component from looking at distribution plots. @XanGregg has some great presentations about visualisation and how accurately we can quantify information from different types of plots. Bar charts can be read with much greater accuracy than other chart types, which is why you get bar charts of the variance components in the MSA platforms in JMP.

[#7]

For nested studies, I prefer to use control charts to show the variation at each layer.  IMHO, without a time series, the summary plots are not very useful as they are potentially misleading (and they can be greatly affected by "special cause" data).