FieldsVehicles and engines
Experiments here usually have about 4 factors and 16 runs. Fractional factorials and full 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 | 3 | 3 | 12 |
| Fractional factorial or screening | 14 | 4 | 8.5 |
| Central composite or Box-Behnken | 3 | 4 | 18 |
| Mixture | 2 | 3 | 12 |
| Other designs | 8 | 3 | 22.5 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- A measure of tire performance against four variables, a 2^4 with four centre points (Exercise 4.20)Box and Draper (2007) · 4 factors, 20 runs
- Heat inside a parked car: window cover, direction and location in a 2^3 (Problem 3-2)Anderson and Whitcomb (2007) · 3 factors, 8 runs
- Noise of a prototype engine against three adjustable variables (Problem 26 of Part IV)Box, Hunter and Hunter (1978) · 3 factors, 12 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- A fictitious starter motor: inner 2^3 in turns, gauge and ferric content crossed with outer 2^2 in temperature and voltageNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 5 factors, 32 runs
- Robert's fuel economy: tire pressure A, air conditioning B, route C and cargo D, with D = ABCDunn (2015) · 4 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
- Free height of leaf springs: a 2^(4−1) inner array in the controllable factors crossed with quench oil temperature, the noise factor, and its mean and ln(s²) modelsMontgomery (2013) · 4 factors, 8 runs
Show the rest
- Free height of leaf springs: furnace temperature, heating time, transfer time, hold down time and quench oil temperature, a replicated 2^(5-1) (Problem 8.10)Montgomery (2013) · 5 factors, 16 runs
- Proportion of nondefective sand castings of engine intake manifolds: ten factors in a 16-run resolution III fraction (Problem 8.50)Montgomery (2013) · 10 factors, 16 runs
- Gas mileage: tire pressure, timing, oil and gas in a 2^(4-1) fraction, each run driven for three weeksSchmidt and Launsby (2000) · 4 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
- Unburned hydrocarbons from a carburetor: spring tension, air gap, aperture and gas flow (Problem 9 of Part III)Box, Hunter and Hunter (1978) · 4 factors, 8 runs
- Gatei's gas mileage: air conditioning A, road R, time of day T and oil E, with E = ARTDunn (2015) · 4 factors, 8 runs
- Jim's gas mileage: air conditioning A, road R and time of day T, with T = ARDunn (2015) · 3 factors, 4 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
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
- Door-closing effort in a randomized Draper-Lin small composite design for General Motors (Exercise 15.10)Box and Draper (2007) · 4 factors, 18 runs
- Peak gas temperature against compression ratio and cooling water temperature: check an engineer's fit (Problem 20 of Part IV)Box, Hunter and Hunter (1978) · 2 factors, 12 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.
- 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
- Miles per gallon of gasoline blends of three components in an augmented simplex lattice (Myers, Montgomery and Anderson-Cook 2009) (Problem 11.31)Montgomery (2013) · 3 factors, 10 runs
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Brake-specific fuel consumption with three lubricating oils, on five trucks as blocks (Problem 4.9)Montgomery (2013) · 1 factor, 15 runs
- Mileage with five gasoline additives in a balanced incomplete block design on five cars (Problem 4.40)Montgomery (2013) · 1 factor, 20 runs
- Drag, lift and efficiency of a race car in a wind tunnel: a 50-run I-optimal split-plot design in ten whole plots, two hard-to-change factorsGoos and Jones (2011) · 4 factors, 50 runs
- Push-out force of a ball welded over an air bag inflator's fill port: three setup factors in a 12-point D-optimal design (Morton International)Schmidt and Launsby (2000) · 3 factors, 25 runs
- Reduction in oxides of nitrogen: four additives tried by four drivers in four cars, a 4 x 4 Latin squareBox, Hunter and Hunter (1978) · 3 factors, 16 runs
Show the rest
- Road tests on tyres: four tread compounds, three to a tyre, in a balanced incomplete block designDavies (1956) · 1 factor, 12 runs
- Dr. Cavendish's first wind tunnel design: a 2^2 master design with its centre, each setting twice, crossed with the 2^2 and its centreGoos and Jones (2011) · 4 factors, 50 runs
- Dr. Cavendish's second wind tunnel design: a 3^2 master design with its centre twice, ten whole plots of five runsGoos and Jones (2011) · 4 factors, 50 runs