Page 483 - Design for Six Sigma a Roadmap for Product Development

442 Chapter Twelve

TABLE 12.14 2 6 2 Design
Factors
Run
number A B C D E ABC F BCD

1 1 1 1 1 1 1
2 1 1 1 1 1 1
3 1 1 1 1 1 1
4 1 1 1 1 1 1
5 1 1 1 1 1 1
6 1 1 1 1 1 1
7 1 1 1 1 1 1
8 1 1 1 1 1 1
9 1 1 1 1 1 1
10 1 1 1 1 1 1
11 1 1 1 1 1 1
12 1 1 1 1 1 1
13 1 1 1 1 1 1
14 1 1 1 1 1 1
15 1 1 1 1 1 1
16 1 1 1 1 1 1

The first k 2 4 factors are A,B,C,D. We will lay out the first four
columns with A,B,C,D in standard order (see Table 12.14).
Step 3: Use the defining relation to create the last two columns. In the
2 6 2 example, if we use I ABCE as the defining relation, then
E ABC, and I BCDF, then F BCD.

Example 12.7. A fractional factorial design The manager of a manufac-
turing company is concerned about the large number of errors in invoices.
An investigation is conducted to determine the major sources of error.
Historical data are retrieved from a company database that contains
information on customers, type of product, size of shipment, and other
variables.
The investigation group identified four factors relating to the shipment
of product and defined two levels for each factor (see Table 12.15).

TABLE 12.15 Factors and Levels for Example 12.7

Factor Level
Customer C Minor ( 1) Major ( 1)
Customer location L Foreign ( 1) Domestic ( )
Type of product T Commodity ( 1) Specialty ( )
Size of shipment S Small ( ) Large ( )