3.
Production
Process Characterization
3.2.
Assumptions / Prerequisites
3.2.3.
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Analysis of Variance Models (ANOVA)
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| ANOVA allows us to compare the effects
of multiple levels of multiple factors |
One of the most common analysis activities in PPC is the
comparison of things. We often compare the performance similar tools or
processes. We also compare the effect of different treatments such as recipe
settings. When we compare two things, such as two tools running the same
operation, we use comparison techniques.
When we want to compare multiple things, like multiple tools running the
same operation or multiple tools with multiple operators running the same
operation, we turn to ANOVA techniques to perform the analysis. |
| ANOVA splits the data into components |
The easiest way to understand ANOVA is through a
concept known as value splitting. ANOVA really just splits the observed
data values into components that are attributable to the different levels
of the factors. Value splitting is best explained by example. |
| Example: |
The simplest example of value splitting is when we just
have one level of one factor. Suppose we have a turning operation in a
machine shop where we are turning rods to .125 +/- .005 inches. Throughout
the course of a day we take five samples of rods and get the following
measurements: .125, .127, .124, .126, .128. |
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We can split these data values into a common value (mean) and residuals
(whats left over) as follows:
=
+
| -.001 |
.001 |
-.002 |
.000 |
.002 |
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From these tables, also called overlays,
we can easily calculate the location and spread of the data as follows:
mean = .126
std. deviation = .0016
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This is really all that the Shewart control chart model does. |
| other layouts |
While the above example is a trivial
structural layout, it illustrates how we can split data values into its
components. In the next sections, we will look at more complicated structural
layouts for the data. In particular we will look at multiple levels of
one factor ( One-Way ANOVA ) and multiple levels
of two factors (Two-Way ANOVA where the factors are crossed
and nested . |
