Books

Jones and Nachtsheim · 2013

Definitive Screening Designs with Added Two-Level Categorical Factors

Factorial gives the paper's answers. Where they differ, this page says why: some are misprints in the paper.

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Examples

Each example, and how closely Factorial gives its answers.

Misprints

Misprints found in the paper, by page. Each shows what the paper prints and what its own data give.

  1. Information matrix: X'X row 2 (x1)p. 123

    The printed Figure 1a design gives the row 0 10 0 0 0 2 2: the printed X'X is that of the design with z2's runs 11 and 12 reversed in x6

  2. Information matrix: X'X row 3 (x2)p. 123

    The printed Figure 1a design gives the row 0 0 10 0 0 −2 2: the printed X'X is that of the design with z2's runs 11 and 12 reversed in x6

  3. Information matrix: X'X row 4 (x3)p. 123

    The printed Figure 1a design gives the row 0 0 0 10 0 −2 −2: the printed X'X is that of the design with z2's runs 11 and 12 reversed in x6

  4. Information matrix: X'X row 5 (x4)p. 123

    The printed Figure 1a design gives the row 0 0 0 0 10 2 −2: the printed X'X is that of the design with z2's runs 11 and 12 reversed in x6

  5. Information matrix: X'X row 6 (x5)p. 123

    The printed Figure 1a design gives the row 0 2 −2 −2 2 14 6: the printed X'X is that of the design with z2's runs 11 and 12 reversed in x6

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  1. Information matrix: X'X row 7 (x6)p. 123

    The printed Figure 1a design gives the row 0 2 2 −2 −2 6 14: the printed X'X is that of the design with z2's runs 11 and 12 reversed in x6

  2. Inner product: a_i'a_jp. 123

    As printed, x5'x6 = 6, the case the paper says is usually eliminated; equation (2) has +2 or -2

  3. Alias: β₀ row, β₁₆ columnp. 124

    Book −0.1429Data 0.142857

    The printed Figure 1a c = 2 design gives +0.1429. Table 3 is the alias matrix of the design with z2 reversed (rows 11 and 12 of x6 swapped), which reproduces every entry, as does equation (2)'s X'X

  4. Alias: β₀ row, β₂₆ columnp. 124

    Book −0.1429Data 0.142857

    The printed Figure 1a c = 2 design gives +0.1429. Table 3 is the alias matrix of the design with z2 reversed (rows 11 and 12 of x6 swapped), which reproduces every entry, as does equation (2)'s X'X

  5. Alias: β₀ row, β₃₆ columnp. 124

    Book 0.1429Data -0.1429

    The printed Figure 1a c = 2 design gives -0.1429. Table 3 is the alias matrix of the design with z2 reversed (rows 11 and 12 of x6 swapped), which reproduces every entry, as does equation (2)'s X'X

  6. Alias: β₀ row, β₄₆ columnp. 124

    Book 0.1429Data -0.1429

    The printed Figure 1a c = 2 design gives -0.1429. Table 3 is the alias matrix of the design with z2 reversed (rows 11 and 12 of x6 swapped), which reproduces every entry, as does equation (2)'s X'X

  7. Alias: β₀ row, β₅₆ columnp. 124

    Book 0.1429Data 0.4286

    The printed Figure 1a c = 2 design gives 0.4286 (x5'x6/14 = 6/14). Table 3 is the alias matrix of the design with z2 reversed (rows 11 and 12 of x6 swapped), which reproduces every entry, as does equation (2)'s X'X

  8. Alias max abs: intercept rowp. 125

    Book 0.1429Data 0.4286

    The printed Figure 1a design gives 0.4286 (6/14, the intercept's alias with x5:x6, since x5'x6 = 6). Table 4 and Table 3 fit the design with z2 reversed (rows 11 and 12 of x6 swapped), for which every intercept-row entry is 2/14 = 0.1429; generate_design(design_type='dsd') with 4 continuous and 2 categorical factors also gives 0.1429

  9. Information matrix: X'X diagonal, continuousp. 127

    Book 16 - 4Data 10

    These 16 runs give 10, n - 6: each continuous column is 0 in the two conference-matrix runs and the four centre runs. n - 4 holds for the 14-run DSD-augment design of the same size, two centre runs fewer

  10. Information matrix: X'X diagonal, continuousp. 127

    Book 16 - 4Data 10

    These 16 runs give 10, n - 6: each continuous column is 0 in the two conference-matrix runs and the four centre runs. n - 4 holds for the 14-run DSD-augment design of the same size, two centre runs fewer

  11. Information matrix: X'X diagonal, continuousp. 127

    Book 16 - 4Data 10

    These 16 runs give 10, n - 6: each continuous column is 0 in the two conference-matrix runs and the four centre runs. n - 4 holds for the 14-run DSD-augment design of the same size, two centre runs fewer

  12. Information matrix: X'X diagonal, continuousp. 127

    Book 16 - 4Data 10

    These 16 runs give 10, n - 6: each continuous column is 0 in the two conference-matrix runs and the four centre runs. n - 4 holds for the 14-run DSD-augment design of the same size, two centre runs fewer