Metalanguage the most essential terms below are

Metalanguage
The most essential terms below are defined for you to have a better understanding
of this section in the course.
1. Factorial experiment. A factorial experiment is defined as one in which
responses are observed for every combination of factor levels.
2.
Residual. The difference between the observed value of the dependent variable
(y) and the predicted value (ŷ)
3.
Interaction plots. An interaction plot displays the levels of one variable on the
X axis and has a separate line for the means of each level of the other variable.
The Y axis is the dependent variable.
4.
ANOVA. Analysis of variance (ANOVA) is an analysis tool used in statistics that
splits an observed aggregate variability found inside a data set into two parts:
systematic factors and random factors. The systematic factors have a statistical
influence on the given data set, while the random factors do not. Analysts use
the ANOVA test to determine the influence that independent variables have on
the dependent variable in a regression study.
5. F Distribution. A probability density function that is used especially in analysis
of variance and is a function of the ration of two independent random variables
each of which has a chi-square distribution and is divided by its number of
degrees of freedom.
Essential Knowledge
Introduction
A factorial experiment is a powerful technique for this type of problem.
Generally, in a factorial experimental design, experimental trials (or runs) are performed
at all combinations of factor levels. For example, if a chemical engineer is interested in
investigating the effects of reaction time and reaction temperature on the yield of a
process, and if two levels of time (1.0 and 1.5 hours) and two levels of temperature (125
and 150°F) are considered important, a factorial experiment would consist of making
experimental runs at each of the four possible combinations of these levels of reaction
time and reaction temperature.
Experimental design is an extremely important tool for engineers and scientists
who are interested in improving the performance of a manufacturing process. It also has
extensive application in the development of new processes and in new product design.
We now give some examples.

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Example (Process Characterization Experiment)
In an article in IEEE Transactions [“Electronics Packaging Manufacturing” (2001,
Vol. 24(4), pp. 249 – 254)], the authors discussed the change to lead-free solder in surface
mount technology (SMT). SMT is a process to assemble electronic components to a
printed circuit board. Solder paste is printed through a stencil onto the printed circuit
board. The stencil-printing machine has squeegees; the paste rolls in front of the
squeegee and fills the apertures in the stencil. The squeegee shears off the paste in the
apertures as it moves over the stencil. Once the print stroke is completed, the board is
separated mechanically from the stencil. Electronic components are placed on the