Applied Statistics and Probability for Engineers

14-9 FRACTIONAL REPLICATION OF THE 2kDESIGN 555

Design Resolution

The concept of design resolution is a useful way to catalog fractional factorial designs ac-

cording to the alias patterns they produce. Designs of resolution III, IV, and V are particularly

important. The definitions of these terms and an example of each follow.

1. Resolution III Designs.These are designs in which no main effects are aliased with
   any other main effect, but main effects are aliased with two-factor interactions and
   some two-factor interactions may be aliased with each other. The 2^3 ^1 design with
   IABCis a resolution III design. We usually employ a Roman numeral subscript to
   indicate design resolution; thus, this one-half fraction is a design.


2. Resolution IV Designs.These are designs in which no main effect is aliased with
   any other main effect or two-factor interactions, but two-factor interactions are
   aliased with each other. The 2^4 ^1 design with I ABCDused in Example 14-7 is a
   resolution IV design ( ).


3. Resolution V Designs.These are designs in which no main effect or two-factor
   interaction is aliased with any other main effect or two-factor interaction, but two-
   factor interactions are aliased with three-factor interactions. The 2^5 ^1 design with
   IABCDEis a resolution V design ( ).
   Resolution III and IV designs are particularly useful in factor screening experiments. A reso-
   lution IV design provides good information about main effects and will provide some infor-
   mation about all two-factor interactions.

14-9.2 Smaller Fractions: The 2kpFractional Factorial

Although the 2k^1 design is valuable in reducing the number of runs required for an experi-

ment, we frequently find that smaller fractions will provide almost as much useful informa-

tion at even greater economy. In general, a 2kdesign may be run in a 1 2pfraction called a

2 kpfractional factorial design. Thus, a 14 fraction is called a 2k^2 design, a 18 fraction is

called a 2k^3 design, a 116 fraction a 2k^4 design, and so on.



(^2) V^5 ^1
(^2) IV^4 ^1
(^2) III^3 ^1
+1

• 1
  
  
  • 1 +1
  
  
  
  

(1052, 1075) (749, 729)

(650, 642)

(550, 601)

A (Gap)

D (Power)

Figure 14-32 The 2^2 design obtained by

dropping factors Band Cfrom the plasma

etch experiment in Example 14-7.

A

B

C

a

abc

b

c

Figure 14-31 Projection of a 2^3 ^1 design into

three 2^2 designs.

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