FieldsFormulated chemical products
Experiments here usually have about 3 factors and 15 runs. Full factorials and fractional factorials are the most common.
- Full factorial
- Fractional factorial or screening
- Central composite or Box-Behnken
- Mixture
- Other designs
Show the numbers
| Kind of design | Experiments | Factors | Runs |
|---|---|---|---|
| Full factorial | 7 | 3 | 12 |
| Fractional factorial or screening | 3 | 4 | 8 |
| Central composite or Box-Behnken | 1 | 4 | 27 |
| Mixture | 3 | 3 | 14 |
| Other designs | 4 | 3 | 36 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- Wood polish formulation: three yes/no quality attributes from a 2^3 factorialDunn (2026) · 3 factors, 8 runs
- Shear strength of an adhesive at four pressures and three temperatures, one observation per cell (Problem 5.16)Montgomery (2013) · 2 factors, 12 runs
- Stain shade after washing: formulation, number of washings and detergent booster, run twice (Problem 5.28)Montgomery (2013) · 3 factors, 16 runs
- Exercise 8.6: washing performance against detergent, sodium carbonate and carboxymethyl cellulose (3^3, Feuell and Wagg 1949)Box and Draper (2007) · 3 factors, 27 runs
- Washing performance of a detergent: detergent level, sodium carbonate and sodium carboxymethyl cellulose in a 3^3 factorial (Exercise 7.8)Box and Draper (2007) · 3 factors, 27 runs
Show the rest
- Finish imperfections against relative humidity, ambient temperature and a pump (Problem 14 of Part III)Box, Hunter and Hunter (1978) · 3 factors, 8 runs
- Activity of a chemical mixture in three active ingredients and a diluent: the path of steepest ascent from a 2^3 factorial, turned along the constraint A + B + C ≤ 100Box and Draper (2007) · 3 factors, 8 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- Dry strip-shear strength of plywood glued with a sucrose-modified phenolic resin: six variables in a 2_IV^(6-2) (Exercise 5.22)Box and Draper (2007) · 6 factors, 16 runs
- Aircraft paint thickness: thinner, fluid pressure, temperature and vendor in a 2^(4-1) fraction, four readings a runSchmidt and Launsby (2000) · 4 factors, 8 runs
- Stability of a new household product: acid, catalyst, temperature and monomer in a 2^(4-1) fractionBox, Hunter and Hunter (1978) · 4 factors, 8 runs
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
Mixture
The ingredients add up to the whole.
- Knoop hardness and percent solids of an automotive clear coat: a 14-run D-optimal design over the constrained mixture of monomer, crosslinker and resinMontgomery (2013) · 3 factors, 14 runs
- Viscosity and clear point of detergent formulations of water, alcohol and urea: second-order fits in pseudocomponents (Exercise 17.5, Table E17.5, Narcy and Renaud 1972)Box and Draper (2007) · 3 factors, 15 runs
- A 3^2 factorial in two ratios of three resins for the weathering of a synthetic enamel (Kenworthy 1963)Box and Draper (2007) · 5 factors, 9 runs
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Product stability against monomer, acid, catalyst and temperature: eight runs so farDunn (2026) · 4 factors, 8 runs
- Reflectance of pigment in paint: four mixes, each applied by brushing, spraying and rolling, on three days (Problem 14.20)Montgomery (2013) · 2 factors, 36 runs
- Persistence of insecticide dusts: seven methods of mixing, forms of active ingredient and diluents in a 7 x 7 Latin squareDavies (1956) · 3 factors, 49 runs
- Three twelve-run designs for a second-order model in the adhesive's constrained region −1.5 ≤ x1 + x2 ≤ 1: an inscribed CCD, a D-optimal design and the D-optimal design with two runs moved to its centreMontgomery (2013) · 3 factors, 36 runs