### TABLE III FRACTIONAL FACTORIAL 29 5

### Table 5: 33?1 fractional factorial design with C = ?AB

"... In PAGE 18: ... Consequently, any pair of AB interaction components can be added into the model. Table5 shows another 33?1 fractional factorial design in which C = A2B2 = ?AB. This design is considered isomorphic to the design C = AB in the combinatorial sense.... ..."

### Table 2 One-half fractional factorial design with 25 design

"... In PAGE 3: ... The factors and levels studied in this experiment were: two font types (Ming and Li), two character sizes (10 pt and 14 pt), two column effects (single and double), two line spacings (single and double), and two display polarities (positive and negative). Table2 shows the one-half fractional factorial design with 25 design. Each subject needed to perform 16 experimental conditions in which 16 different passages ... ..."

### Table 2: Comparison of CSB-X and Fractional Factorial Design

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### Table 2: Contrast Matrix of 34?2 fractional factorial design

### Table 3: 26?2 fractional factorial design

### Table 1: 34?2 fractional factorial design A B C D

"... In PAGE 2: ... In this paper, I propose a new framework for studying aliasing structures of multi-level factorial designs. Consider a 34?2 fractional factorial design listed in Table1 . It has four factors and is generated by de ning relations C = AB and D = AB2.... In PAGE 9: ...x1 x2 x3 x4 x5 x6 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1 -1 -1 -1 -1 -1 -1 under lexicographic order: fx6 ? x1x2x3; x5 + x2x3; x4 + x1x2; x2 3 ? 1; x2 2 ? 1; x2 1 ? 1g: One can easily observe that three polynomials in this Grobner basis are the de ning relations of the 26?2 design: x4 = ?x1x2; x5 = ?x2x3; x6 = x1x2x3: Pistone and Wynn (1996) also compute the Grobner basis of the 34?2 fraction factorial design given in Table1 . They set the three levels f0; 1; 2g to be f?1; 0; 1g.... In PAGE 17: ...1 33?1 Fractional Factorial Design In Chapter 5, Wu and Hamada (2000) studies a 33?1 fractional factorial design in which C = AB. This design is the rst three columns of the design in Table1 and its Grobner basis consists of the rst eight polynomials in Table 4. Besides the six main contrasts, two interaction terms are allowed to be added in the model.... ..."

### TABLE 1 2K-P Fractional Factorial Designs (adapted from Montgomery [1997])

### Table 3. For a detailed description of fractional factorial design, the reader is referred to references [2] and [4]. The use of fractional factorial designs has started to receive a lot of attention of late, and Taguchi techniques that use the so- called orthogonal arrays are based on essentially the same concept. 6. Reporting Guidelines: When reporting the results of an experimental study we recommend that the following details be included:

"... In PAGE 15: ... Full Factorial Design for Evaluating the effect of 5 elements of tool signature on cutting force (Fc). Table3 . One half fractional factorial design for evaluating theeffect of 5 elements of tool signature on cutting force (Fc).... ..."