FieldsMetals and metallurgy
Experiments here usually have about 3 factors and 16 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 | 18 | 3 | 16 |
| Fractional factorial or screening | 9 | 5 | 16 |
| Central composite or Box-Behnken | 2 | 4 | 20.5 |
| Mixture | 2 | 3.5 | 9 |
| Other designs | 8 | 3 | 20 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- Defective springs: percent acceptable springs against oven temperature, carbon and quench temperature (2^3)NIST/SEMATECH e-Handbook of Statistical Methods (2020) · 3 factors, 8 runs
- Baked density of a carbon anode at two furnace positions and three firing temperatures, run three times (Problem 5.13)Montgomery (2013) · 2 factors, 18 runs
- Coded lengths of steel bars: three times of day, two heat treatments and four machines, four bars in each cell (Baten 1956) (Problem 9.23)Montgomery (2013) · 3 factors, 96 runs
- Crack length in a nickel-titanium alloy: pouring temperature, titanium content, heat treatment and grain refiner, a 2^4 run twice (Table P6.2) (Problem 6.15)Montgomery (2013) · 4 factors, 16 runs
- Density and surface area of silver powder: ammonium, stir rate and temperature, a 2^3 run twice (Problem 5.31)Montgomery (2013) · 3 factors, 16 runs
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- Fatigue crack growth rate at three loading frequencies in three environments (Problem 5.24)Montgomery (2013) · 2 factors, 36 runs
- Strength of aluminum alloy bars from three vendors, three heats from each, in three bar sizes, two specimens each (Problem 14.16)Montgomery (2013) · 3 factors, 54 runs
- Warping of copper plates at four temperatures and four copper contents, run twice (Problem 5.7)Montgomery (2013) · 2 factors, 32 runs
- Martensite start temperature against carbon, manganese and nickel, a 2^3 (Exercise 4.8)Box and Draper (2007) · 3 factors, 8 runs
- Nickel plating thickness: bath temperature and plating time in a 2^2 factorial, five products a runSchmidt and Launsby (2000) · 2 factors, 4 runs
- Plating thickness in the 3^3 of time, temperature and nickel (the L27 of Case II of 5.10)Schmidt and Launsby (2000) · 3 factors, 27 runs
- Shrinkage of cast turbine blades: mold temperature, metal temperature and pour speed in a 2^3, three readings a runSchmidt and Launsby (2000) · 3 factors, 8 runs
- Turbine blade thickness in a 2^4 of metal and mold temperature, pour time and vendor (Problem 2 of chapter 5)Schmidt and Launsby (2000) · 4 factors, 16 runs
- Breaking strength against nickel and manganese (Problem 1 of Part III)Box, Hunter and Hunter (1978) · 2 factors, 4 runs
- Metal recovered against temperature, concentration and time, a 2^3 in duplicate (Problem 15 of Part III)Box, Hunter and Hunter (1978) · 3 factors, 16 runs
- Ultimate tensile stress of welds against ambient temperature and wind velocity (Problem 13 of Part IV)Box, Hunter and Hunter (1978) · 2 factors, 4 runs
- Corrosion of aluminium alloys: nine alloys exposed at four sites, each plate scored by four observersDavies (1956) · 3 factors, 144 runs
- The follow-up 2^2 with a centre point around the springs optimum (X1, X3) = (1.5, 1.3)NIST/SEMATECH e-Handbook of Statistical Methods (2020) · 2 factors, 5 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- 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
- 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
- Thickness of the carbonized layer on gear teeth: furnace temperature, cycle time, carbon concentration and cycle durations in a 2^(6-2) (Problem 8.53)Montgomery (2013) · 6 factors, 16 runs
- Weight of packing material stuck to carbon anodes after baking: six factors in a 2^(6-3) with three replicates (Problem 8.27)Montgomery (2013) · 6 factors, 8 runs
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- Turbine blade thickness in a 2^(4-1) with ambient temperature in the outer array (Problem 6 of chapter 5)Schmidt and Launsby (2000) · 4 factors, 8 runs
- Tensile strength in an unreplicated 2^(9-5) of resolution III: Lenth's PSE, ME and SME, and the contrasts' alias chainsLenth (1989) · 9 factors, 16 runs
- Heat input for welding: five settings, a 2^(5-1) fraction with three responses (Problem 29 of Part III)Box, Hunter and Hunter (1978) · 5 factors, 16 runs
- A 16-run half fraction of the 2^5 factorial for the rolling mill, infeasible because each run's three thickness reductions must sum to 1Goos and Jones (2011) · 5 factors, 16 runs
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
- Plating thickness in a Box-Behnken design for time, temperature and nickel (Case II of 5.10)Schmidt and Launsby (2000) · 3 factors, 15 runs
- Plating thickness: a 2^(5-1) of time, temperature, nickel, pH and phosphorus, four centre runs, then axial runs in three factors (Case I of 5.10)Schmidt and Launsby (2000) · 5 factors, 26 runs
Mixture
The ingredients add up to the whole.
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Aluminum smelting cell voltage under four ratio control algorithms, in six time periods as blocks (Problem 4.13)Montgomery (2013) · 1 factor, 24 runs
- Grain size of a grain refiner at four stirring rates, in four furnaces as blocks (Problem 4.14)Montgomery (2013) · 1 factor, 16 runs
- Rockwell C hardness from four tips on four coupons as blocks, coded by subtracting 40 (Problem 4.7)Montgomery (2013) · 1 factor, 16 runs
- Strength of normalized steel at two oven temperatures and three heat-treatment times, four shifts: the temperature set for the oven, the times within it (Problem 14.19)Montgomery (2013) · 3 factors, 24 runs
- Plating thickness in a fourteen-run D-optimal design for the full quadratic in time, temperature and nickel (Case II of 5.10)Schmidt and Launsby (2000) · 3 factors, 14 runs
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- 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
- Annealing copper tubes: eight lots and a dummy factor in an 8 x 8 Graeco-Latin square on the annealing jigDavies (1956) · 4 factors, 64 runs
- Electroplating copper strips: a replicated 2^3 in current, temperature and concentration, run as split plotsNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 3 factors, 8 runs