FieldsFood and beverages
Experiments here usually have about 3 factors and a dozen 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 | 15 | 3 | 8 |
| Fractional factorial or screening | 11 | 4 | 12 |
| Central composite or Box-Behnken | 8 | 3 | 19 |
| Mixture | 3 | 7 | 25 |
| Other designs | 5 | 4 | 24 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- Breaded chicken strips: cooking time, oven rack and preheating in a 2^3 factorialDunn (2026) · 3 factors, 8 runs
- Aditi's breaded chicken strips: cooking duration D, oven rack R and preheating PDunn (2015) · 3 factors, 8 runs
- Amir's yogurt: fat content of the starter yogurt F and fermentation time TDunn (2015) · 2 factors, 4 runs
- Baking temperature A and mixing time B: the direction in which taste improvesDunn (2015) · 2 factors, 4 runs
- Bread dough left to rise for an hour: type of sugar S and water temperature TDunn (2015) · 2 factors, 4 runs
Show the rest
- The popcorn: cooking time A and popcorn type B, yellow corn coded lowDunn (2015) · 2 factors, 4 runs
- Deviation from the target fill height of soft drink bottles: carbonation, operating pressure and line speed, a 3 x 2 x 2 factorial run twiceMontgomery (2013) · 3 factors, 24 runs
- Fill height deviation: carbonation, pressure and line speed at two levels each, a 2^3 run twice (Table P6.3) (Problem 6.20)Montgomery (2013) · 3 factors, 8 runs
- Scrumptiousness of brownies: pan material, stirring method and brand of mix, eight batches each rated by an eight-person panel (Problem 6.30)Montgomery (2013) · 3 factors, 8 runs
- Syrup loss from frothing when filling 5-gallon containers: three nozzles, filling speeds and pressures, a 3^3 factorial run twice (coded data)Montgomery (2013) · 3 factors, 54 runs
- Time to deliver 12-bottle cases: glass or plastic bottles, two workers, a 2^2 run four times (Problem 6.9)Montgomery (2013) · 2 factors, 4 runs
- Four responses of a 2^4 with six centre points (Chang, Kononenko and Franklin 1960; Exercise 4.16)Box and Draper (2007) · 4 factors, 17 runs
- Microwave popcorn: brand, time and power in a 2^3 factorial, with taste and the weight of unpopped kernelsAnderson and Whitcomb (2007) · 5 factors, 8 runs
- Yield of popcorn: brand, ratio of popcorn to oil and batch size, with four runs at the centre (Exercises 10.3, 10.6 and 10.9)Box, Hunter and Hunter (1978) · 3 factors, 12 runs
- Jennifer's cookies: duration D, temperature T and chips N, blocked on the mixing bowlDunn (2015) · 3 factors, 8 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- Breaded chicken: the 2^(3-1) half fraction with P = DRDunn (2026) · 3 factors, 4 runs
- Cake ovens: baking temperature A, baking time B and mixing speed C, the half fraction C = AB, and a step toward the optimumDunn (2015) · 3 factors, 6 runs
- Cake ovens: baking temperature A, mixing speed B and baking time C in four runs, with C = ABDunn (2015) · 3 factors, 4 runs
- Average taste-test rank of the 1987 Pinot Noir: seven factors, fermentation temperature at four levels as two two-level columns, in 16 runs (Problem 9.22)Montgomery (2013) · 8 factors, 16 runs
- Filling variability of dry soup mix packages: mixer ports, temperature, mixing time, batch weight and delay in a 2^(5-1) (Problem 8.54)Montgomery (2013) · 5 factors, 16 runs
Show the rest
- Ranks of 1985 Pinot Noir wines: clone, oak, barrel age, yeast/skin contact, stems, toast, whole cluster and fermentation temperature in a 2^(8-4) (Problem 8.30)Montgomery (2013) · 8 factors, 16 runs
- Yield of peanut oil from supercritical CO2 extraction: pressure, temperature, peanut moisture, flow rate and particle size in 16 runs (Problem 8.49)Montgomery (2013) · 5 factors, 16 runs
- Bread making: four ingredients in a 2_IV^(4-1) with three runs repeated, then four semifold runs (Exercise 5.35)Box and Draper (2007) · 4 factors, 12 runs
- Dancing raisins: seven factors in a 2^(7-4) and its complete fold-over in a second blockAnderson and Whitcomb (2007) · 7 factors, 16 runs
- The popcorn 2^3 cut to the half fraction ABC = +: a resolution III design and its aliasesAnderson and Whitcomb (2007) · 3 factors, 4 runs
- Parvin's yogurt: temperature T, sugar S and culture C in four runs, C = TSDunn (2015) · 3 factors, 4 runs
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
- Cake ovens near the optimum: baking temperature A from 357.5 to 370 °F and time B from 20 to 25 min, and the axial runs of a CCDDunn (2015) · 2 factors, 5 runs
- Nathan's beer: malt M and hops H in a 2^2 factorial with a centre point, then a central composite designDunn (2015) · 2 factors, 9 runs
- Tear and leakage of one-pound coffee bags against plastic viscosity, clamp pressure and plate gap in a central composite design (Quality Progress, 2011) (Problem 11.33)Montgomery (2013) · 3 factors, 19 runs
- Transglutaminase activity against four medium components in a central composite design (Electronic J. Biotechnology) (Problem 11.37)Montgomery (2013) · 4 factors, 27 runs
- Brookfield viscosity of a sterilized concentrated baby formula after 0, 3, 6 and 9 months: five additives in a 2^(5-1) plus axial and centre runs (Exercise 7.27)Box and Draper (2007) · 5 factors, 27 runs
Show the rest
- Exercise 12.11: viscosity of foliole puree of hearts of palm after cellulase and pectinase treatmentsBox and Draper (2007) · 3 factors, 19 runs
- Exercise 12.4: six properties of edible wheat gluten films against gluten, ethanol and pH in a central composite designBox and Draper (2007) · 3 factors, 19 runs
- Hardness, cohesiveness, springiness and compressible water of a whey protein gel against cysteine and calcium chloride, a central composite design with five centre runs (Exercise 11.25)Box and Draper (2007) · 2 factors, 13 runs
Mixture
The ingredients add up to the whole.
- A bread-making experiment in four blocks: a nearly D-optimal four-ingredient mixture design in orthogonal blocks, fitted in all four and in the first two ingredients (Draper, Prescott et al. 1993)Box and Draper (2007) · 7 factors, 36 runs
- Cake volume and top contour of cakes whose five ingredients are set by four ratios in a central composite design (Kissell and Marshall 1962)Box and Draper (2007) · 9 factors, 25 runs
- Taste of jelly candy blends of apple, cinnamon and lemon: a simplex centroid with replicatesAnderson and Whitcomb (2007) · 3 factors, 11 runs
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Bacteria growth in milk containers with three washing solutions, on four days as blocks (Problem 4.4)Montgomery (2013) · 1 factor, 12 runs
- Expansion of pastry dough: a 28-run D-optimal response surface design in seven blocks (days) of four runsGoos and Jones (2011) · 3 factors, 28 runs
- Peel strength of a hermetic package seal: temperature, pressure and speed, made robust to three suppliers of packaging materialGoos and Jones (2011) · 4 factors, 24 runs
- A 24-run D-optimal design for peel strength: a full quadratic in temperature, pressure and speed, with three suppliersGoos and Jones (2011) · 4 factors, 24 runs
- A 24-run I-optimal design for peel strength: a full quadratic in temperature, pressure and speed, with three suppliersGoos and Jones (2011) · 4 factors, 24 runs