Examples

Four designed experiments, worked through step by step

From the question through the choice of design, the design with its measurements, model and analysis of variance to the confirmed setting: four complete analyses as they come about in DoEStat. Every table and every chart comes out of the software — and every example ships with it as a project, to be run yourself.

Screening

Ten factors, 26 runs

Warpage in injection moulding: which of ten machine settings matter? A minimum-run resolution IV design finds four factors and one interaction — and the centre runs show that the surface is curved.

  • Four screening designs compared
  • Half-normal and Pareto plots
  • Interaction, curvature check, confirmation
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Response surface

Four factors, three responses

An API synthesis without constraints: yield, by-product and residual palladium pull in different directions. A central composite design with 30 runs and desirability find the compromise.

  • Model order and model reduction per response
  • Analysis of variance, contour and 3D plots
  • Multi-response optimisation with overlay and ramps
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Mixture

Five components, four kinds of limits

An emulsion paint: lower and upper bounds, a sum constraint and a ratio constraint leave a body with 28 vertices of the mixture space. An I-optimal design with 25 batches leads to the best feasible recipe for three responses.

  • The region from its constraints
  • Scheffé models in pseudo-components
  • Trace and ternary contour plots
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Sequential

From screening to a response surface

Tabletting in two campaigns: the six-factor screening ends with an optimum on the edge. The 19 runs are carried into a slightly shifted region of the three active factors and augmented by 15 — five responses, one window.

  • Screening for five responses in one table
  • Shifting the factor region, augmenting the design
  • Campaigns as a block, optimum in the interior
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About the data. The measurements of all four examples are simulated: from models we set ourselves, plus random scatter. That is deliberate — only then can the end of each example show what the analysis found and what it did not. The models are given in each section “Cross-check”. Examples with published measurements from the literature ship with DoEStat as well.

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