GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 317 of 500
Plan a response-surface design — central composite or Box–Behnken — with the rotatable axial distance and the run count, for finding the optimum of a food process.
Try sample values — fills the form with the worked example below.
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Total runs
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Axial distance α
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Factorial runs
Equation: CCD: total = 2ᵏ (factorial) + 2k (axial) + centre points. Rotatable α = 2^(k/4); face-centred α = 1. Box–Behnken: total = 2k(k − 1) + centre points.
Method: Response surface methodology per Box and Wilson (1951) and Montgomery, Design and Analysis of Experiments. The rotatable α makes the prediction variance the same at all points the same distance from the centre.
Assumptions: the factors are continuous and controllable over the chosen ranges; the response is smooth enough for a second-order (quadratic) model.
Limitations: a face-centred CCD cannot estimate pure quadratic terms as precisely as a rotatable one, and Box–Behnken has no corner runs, so it cannot explore the extremes of all factors at once. The planner counts runs; fit the quadratic model with Tool 312 extended to squared terms, or a statistics package.
Rounding: α to 4 decimal places; run counts are whole numbers; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Response surface methodology per Box and Wilson (1951) and Montgomery, Design and Analysis of Experiments. The rotatable α makes the prediction variance the same at all points the same distance from the centre.
Assumptions: the factors are continuous and controllable over the chosen ranges; the response is smooth enough for a second-order (quadratic) model.
Limitations: a face-centred CCD cannot estimate pure quadratic terms as precisely as a rotatable one, and Box–Behnken has no corner runs, so it cannot explore the extremes of all factors at once. The planner counts runs; fit the quadratic model with Tool 312 extended to squared terms, or a statistics package.
Rounding: α to 4 decimal places; run counts are whole numbers; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: 2 factors, CCD, 6 centre points, rotatable α: factorial 4, axial 4, total 14 runs, α = 1.4142.
Enter values above to see results.
Centre points are repeated so pure error can be estimated — use at least 3, and 5–6 is usual. Tool 317 of 500 — GIFSQ
