Statistical Details for Variability Charts

This section contains statistical details for variance components and the discrimination ratio.

Statistical Details for Variance Components

The exact model type that you choose depends on how the data was collected. For example, are the operators measuring the same parts (in which case you have a crossed design) or are they measuring different parts (in which case you have a nested design)? To illustrate, in a model where B is nested within A, multiple measurements are nested within both B and A, and there are na•nb•nw measurements, as follows:

•	na random effects are due to A

•	na•nb random effects due to each nb B levels within A

•	na•nb•nw random effects due to each nw levels within B within A:

The Zs are the random effects for each level of the classification. Each Z is assumed to have a mean of zero and to be independent from all other random terms. The variance of the response y is the sum of the variances due to each z component:

Models Supported by the Variability Charts Platform shows the supported models and what the effects in the model would be.

Models Supported by the Variability Charts Platform
Model	Factors	Effects in the model
Main Effects	1 2 unlimited	A A, B and so on, for more factors
Crossed	1 2 3 4 unlimited	A A, B, AB A, B, AB, C, AC, BC, ABC A, B, AB, C, AC, BC, ABC, D, AD, BD, ABD, CD, ACD, BCD, ABC*D, and so on, for more factors
Nested	1 2 3 4 unlimited	A A, B(A) A, B(A), C(A,B) A, B(A), C(A,B), D(A,B,C) and so on, for more factors
Crossed then Nested	3	A, B, A*B, C(A,B)
Nested then Crossed	3	A, B(A), C, AC, CB(A)

Statistical Details for the Discrimination Ratio

The discrimination ratio compares the total variance of the measurement, M, with the variance of the measurement error, E. The discrimination ratio is computed for all main effects, including nested main effects. The discrimination ratio, D, is computed as follows:

where:

P = estimated variance for a factor

T = estimated total variance