Explain why the 1/4-fractional-factorial and orthogonal array plans shown in Exh

Question

Explain why the 1/4-fractional-factorial and orthogonal array plans shown in Exhibit 15-4 are balanced.

2 Chper 15 1/2 Fractional Factorial Matrix A1 A2 Full-Faetorial Mstriz B2 81 C1 | C2 | C1-21 C11-C2 D1D2D1 D2 D1 D2 D1D2 D1 D2D1D2 82 B2 ipzy 02 01 626102 01 6201 02 D1 D2 D1D2 F2 F2 1/8 Fractional Factorial Matrix 1/4 Fractional Factorial Matrix A2 A1 A1 A2 B1 82 B1 B1 B2 B2 C1 C2 C1 C2 C1 C2 C1 D1D2D1 D2D1 D2 D1 D2 D1 D2 D1 D2D1D2 81 C1 C2 C1 C2 C1 C2 C1 C2 0102010201 02D1D2 01D2 D1 D2D1D2 D102 G1 G1 61 G1 G2 G1 G2 G1 G2 G1 L8 Orthogonal Array (1/16 Fractional Factorial Matrix) One Factor at a Time A1 A2 A2 B2 81 B2 B1 B2 B1 B2 B1 C1 C2 C1 C2 C1 C2C1 C2 D1D2D1D2D1 D2D1D2 D1D2D1D2D1D2D1 D2 C1 C2 C1 C2 C1C2 C1 C2 D1D2D1 D2D1 D2D1D2D1D2D1D2D1D2D102 F1 E1 G2 G1 G2 G1 G2 G1 E F2 G2 F1 G1 F2 G2 Source: Based on Fractional factorial layouts adapted from Ross, Phillip J., Taguchi Techniques for Quality Engineering, McGraw-Hill. New York 19 EXHIBIT 15-4 Several alternative experimental plans for seven factors (A, B, C, D, E. F, and G) at two l each. The full-factorial experiment contains 2 128 trials, while the L8 orthogonal array design contains only denoted by the is shown in conventional row/column format in Exhibit 15-5 marks in the matrices. The L8 orthogonal array plan is the one used for the seat belt periment and

Explanation / Answer

1/4 Factorial Design: This design uses only a small fraction of the combinations used in the full factorial design. In exchange for this efficiency, the ability to compute the magnitude of all the interaction effects is sacrificed. Instead the interactions are confounded with other interactions or with some of the main factor effects. Note that the fractions factorially layout still maintains balance within the experimental plan. This means that for the several trials at any given factor level, each of the other factors is tested at every level the same number of times

L8 Orthogonal Array: This design is the smallest fractional factorial plan that still allows the team to identify the main effects of each factor'. However, these main effects are confounded with many interaction effects. Nevertheless, orthogonal array layouts are widely utilized in technical investigations because they are extremely efficient. L8 orthogonal array experiment design because this plan would be an efficient way to explore seven factors at two levels each. Subsequent rounds of experimentation could later be used to explore additional levels of key parameters aswell as interaction effects if necessary

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.