FieldsPlastics, rubber and polymers
Experiments here usually have about 3 factors and 15 runs. Fractional factorials and response surface designs 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 | 12 | 2 | 7 |
| Fractional factorial or screening | 16 | 7 | 12.5 |
| Central composite or Box-Behnken | 13 | 3 | 16 |
| Mixture | 3 | 3 | 11 |
| Other designs | 6 | 3.5 | 19 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- Jesus's blown-film machine: width A, cooling rate B and film thickness C, with the haze judged hazy or clearDunn (2015) · 3 factors, 8 runs
- Defects in aircraft interior panels: temperature, clamp time, resin flow and closing time in a single replicate of a 2^4, for location and dispersionMontgomery (2013) · 4 factors, 16 runs
- Molecular weight and viscosity of a polymer: temperature, catalyst concentration, time and pressure, a 2^4 with four centre runs (Table P6.8) (Problem 6.31)Montgomery (2013) · 4 factors, 20 runs
- Polymer elasticity: a 2^3 factorial around the best conditions so far shows large interactions, so the first-degree model failsBox and Draper (2007) · 3 factors, 8 runs
- Durometer hardness of a butadiene rubber: cure temperature and filler in a 3^2 factorial, three readings a runSchmidt and Launsby (2000) · 2 factors, 9 runs
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- Tensile strength against dwell time and cure temperature, a 2 x 3 factorial whose factors do not interactSchmidt and Launsby (2000) · 2 factors, 6 runs
- Evolutionary operation on a polymer latex unit, phase I: addition time and stirring rate against optical densityBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase IIBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase IIIBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase IVBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase VBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Wear resistance of vulcanised rubber: five fillers, three pretreatments and four raw rubbers, a 5 x 3 x 4 factorialDavies (1956) · 3 factors, 60 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- Shrinkage of injection-molded film: seven factors in eight runsDunn (2026) · 7 factors, 8 runs
- Defects in the finish of sheet-molded grill opening panels: nine factors in a 16-run resolution III fraction (Problem 8.51)Montgomery (2013) · 9 factors, 16 runs
- Defects on sheet-molded grill opening panels: least squares on Freeman and Tukey's square root against a Poisson generalized linear modelMontgomery (2013) · 9 factors, 16 runs
- Shrinkage of injection molded parts: mold temperature, screw speed, holding time, cycle time, gate size and holding pressure in a 2^(6-2)Montgomery (2013) · 6 factors, 16 runs
- Force to open the closure of a medical infusion bottle: seven molding variables in a 2_III^(7-4), three readings per run (Exercise 5.34)Box and Draper (2007) · 7 factors, 8 runs
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- Part shrinkage of an injection molder: seven factors in a 2^(7-2) run on two production lines as blocks (Problem 5-1)Anderson and Whitcomb (2007) · 7 factors, 32 runs
- Shrinkage of injection-molded parts: eight variables in a 2^(8-4) resolution IV design obtained by fold-over (Table 5.5)Box and Draper (2007) · 8 factors, 16 runs
- Williams's 28-run Plackett and Burman type design for 24 variables, with cross products and effects (Exercise 5.20, Table E5.20)Box and Draper (2007) · 24 factors, 28 runs
- Part shrinkage in injection molding: seven control factors in an L8 inner array, three noise factors in a four-run outer arraySchmidt and Launsby (2000) · 7 factors, 8 runs
- Rubber boots for constant velocity joints: seven formulation factors, seven interactions and a test block in an L16 (Quinas)Schmidt and Launsby (2000) · 7 factors, 16 runs
- Shrinkage of an injection molded part: six process settings in an L8, five lengths and five widths a runSchmidt and Launsby (2000) · 6 factors, 8 runs
- Width of an injection molded part: mold temperature, injection velocity, hold pressure and cooling time, B = DAE (Problem 4 of chapter 5)Schmidt and Launsby (2000) · 3 factors, 8 runs
- Injection molding: shrinkage against eight variables, a 2^(8-4) resolution IV fraction, then four runs to separate an interaction stringBox, Hunter and Hunter (1978) · 8 factors, 20 runs
- Pull-off force of an elastomeric connector on a nylon tube: a 3^(4−2) inner array crossed with a 2^3 outer array in three conditioning factors (Byrne and Taguchi 1987)Montgomery (2013) · 4 factors, 9 runs
- The outer array of the connector pull-off force experiment: a 2^3 in conditioning time, temperature and relative humidity, as printedMontgomery (2013) · 3 factors, 8 runs
- Cast films: a 2^(5-2) fraction (4 = 23, 5 = 123) whose six responses are yes-or-no judgementsBox, Hunter and Hunter (1978) · 5 factors, 8 runs
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
- Derringer and Suich's tire tread compound: four responses from a 20-run CCD in silica, silane and sulfurNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 3 factors, 20 runs
- Viscosity of a polymer in a Box-Behnken design in temperature, agitation rate and pressure (Problem 11.11)Montgomery (2013) · 3 factors, 15 runs
- Abrasion index, modulus, elongation and hardness of a tire tread compound against silica, silane and sulfur levels, a central composite design (Exercise 11.5)Box and Draper (2007) · 3 factors, 20 runs
- Exercise 12.10: NBS abrasion resistance of a rubber compound in a three-factor composite designBox and Draper (2007) · 3 factors, 15 runs
- Exercise 12.13: tensile strength, impact, gloss and izod of an easy flow Rovel grade against four injection molding variablesBox and Draper (2007) · 4 factors, 27 runs
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- Exercise 8.4: Mooney viscosities ML4 and MS4 of filled, plasticized NBR against silica and oil, a Box-Cox power for eachBox and Draper (2007) · 2 factors, 13 runs
- Exercise 8.5: Mooney viscosity ML4 against two silicas and a carbon black, choosing a Box-Cox power for a first-order modelBox and Draper (2007) · 3 factors, 12 runs
- Mooney viscosity of rubber compounds: silica filler, oil filler and shear rate, data set (a), for an incomplete cubic model (Exercise 7.19)Box and Draper (2007) · 2 factors, 13 runs
- Mooney viscosity of rubber compounds: silica filler, oil filler and shear rate, data set (b), for an incomplete cubic model (Exercise 7.19)Box and Draper (2007) · 2 factors, 14 runs
- Polymer elasticity: a central composite design in two orthogonal blocks, its fitted maximum and its residual degrees of freedom isolatedBox and Draper (2007) · 3 factors, 16 runs
- Tensile strength of a silica-filled rubber compound against five ingredients: a central composite design in three blocks (Exercise 11.20)Box and Draper (2007) · 5 factors, 34 runs
- Tire tread compound: abrasion index, modulus, elongation and hardness against silica, silane and sulfur, a 20-run central composite design optimised by desirabilityDerringer and Suich (1980) · 3 factors, 20 runs
- Radial runout of tires against postinflation time and pressure, cure temperature and rim size (Problem 35 of Part IV)Box, Hunter and Hunter (1978) · 4 factors, 25 runs
Mixture
The ingredients add up to the whole.
- Cornell's yarn elongation: a {3,2} simplex lattice in polyethylene, polystyrene and polypropylene, 15 runsNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 3 factors, 15 runs
- Glass transition temperature of pseudolatex films with three nonionic surfactants: path of minimum response (Exercise 19.7)Box and Draper (2007) · 3 factors, 11 runs
- Yarn elongation for blends of polyethylene, polystyrene and polypropylene in a {3, 2} simplex lattice (Cornell 2002)Montgomery (2013) · 3 factors, 6 runs
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Surface tension of polypropylene after a gas plasma treatment: an 18-run D-optimal design with three covariates chosen from samples in stockGoos and Jones (2011) · 7 factors, 18 runs
- Exercise 12.12: tensile strength of silica filled natural rubber in a third-order rotatable design in three blocksBox and Draper (2007) · 4 factors, 21 runs
- Abrasion resistance of rubber: five materials in five runs of the four-position wear tester, a Youden squareDavies (1956) · 2 factors, 20 runs
- Road tests on tyres: four tread compounds, three to a tyre, in a balanced incomplete block designDavies (1956) · 1 factor, 12 runs
- The 40 polypropylene samples in stock: their EPDM and ethylene proportions and whether they contain EVAGoos and Jones (2011) · 3 factors, 40 runs