Chapter 8. Two-Level Fractional Factorial Designs

Chapter 8. Two-Level Fractional Factorial Designs

Example 1. Five factors for an IC were investigated for improving the process yield.

: aperture setting (small, large)

exposure time ( below nominal, above nominal)

development time (s, s)

mask dimension (small, large)

etch time ( min, min)

(i)Create factorial designusing a design with .

(ii)Suppose that the experiment is performed in the run order so as to obtain the following data.

(iii)Fit a full model.

(iv)Fit a reduced model.

(v)Plot the interaction between A and B.

When B= -1, there is not much difference between the effect of A. However, if B=1, then A=1 has a much higher yield than A=-1. To get the maximum yield, we would use A=1 and B=1.

From the main effect plot, C=1 gives a higher yield than C=-1.

(vi)Provide the contour plot.

Example 2. A quality improvement team uses a designed experiment to study the injection molding process so that shrinkage can be reduced.Six factors are considered:

mold temperature

screw speed

cycle time

gate size

holding pressure

(i)Create factorial designusing a .

(ii)Suppose that you get the following data after experiments. Enter the data in column C11

(iii)Test hypotheses

(iv)Find the reduced model.

Example 3.DesignwithI=ACE and I=BDE.

Example 4.A human performance analyst is conducting an experiment to study eye focus time and has built an apparatus in which several factors can be controlled during the test.

: sharpness of vision

: distance from target to eye

: target shape

: illumination level

: target size

: target density

: subject

(i)Design

(ii)Suppose that you get the following data after experiments. Enter the data in column C12

(iii)Test hypotheses

Plot shows that A, B, D effects are significant. However, is aliased with is aliased with and is aliased with . Therefore, it is not known if A,D, AD are significant or if A,B,D are significant.

(iv)To separate the main effects and the two-factor interactions, we use the full fold over design

Case 1. Adjust the current design.

Suppose that we do not consider the block effect in the model.

Case 2. A new design is used.

(i)Suppose that you get the following data after experiments. Enter the data in column C12

(ii)Test hypotheses

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