An integer linear programing approach to find trend-robust run orders of experimental designs

Examples

Each example, and how closely Factorial gives its answers.

• Face-centred CCD in two factors with one centre point, in standard order, with a linear time trendDesign · pp. 37-38Matches
• Face-centred CCD in two factors with one centre point, in a run order robust to a linear time trendDesign · p. 38Matches
• Run counts of the response surface designs for which trend-robust run orders were foundDesign · pp. 39, 46-48Matches
• The 3^3 factorial in standard order, with its coded cubic time trendDesign · pp. 43-44Misprint found
• The 3^3 factorial in run order 1, robust for a main-effects modelDesign · pp. 43-44Matches
• The 3^3 factorial in run order 2, robust for a full quadratic modelDesign · pp. 43-45Matches
• Face-centred CCD in three factors with one centre point, run order 1Design · pp. 45-46Matches
• Face-centred CCD in three factors with one centre point, run order 2Design · pp. 45-46Very close
• Box-Behnken design in three factors with one centre point, in its best trend-robust run orderDesign · pp. 46-47Matches
• Three columns of an eight-factor definitive screening design (17 runs), run order 1Design · p. 47Matches
• Three columns of an eight-factor definitive screening design (17 runs), run order 2Design · p. 47Matches

Misprints

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

1. Absolute correlation: ME, L, Maxp. 44

   Book 0.934Data 0.943

   The text restates the largest absolute cosine of a main effect with the linear trend as 0.934; the paper's own Table 6 prints 0.943, and the printed runs give 0.9435: the text transposes two digits

Not yet

Answers the paper prints that Factorial cannot compute yet, by what it lacks.

• The least number of centre runs for which the paper's integer program finds a run order with the main effects orthogonal to the linear and quadratic trends, which proves that fewer admit none; the library's trend_robust_run_order is a heuristic search, which cannot prove that; the size, 17 runs, is in Figure 3p. 46