Energy, fuels and mining

Experiments here usually have about 4 factors and a dozen runs. Most are full factorials.

Plan one like these

Full factorial
Fractional factorial or screening
Central composite or Box-Behnken
Mixture

Show the numbers

The experiments of each kind, with their median size
Kind of design	Experiments	Factors	Runs
Full factorial	7	3	16
Fractional factorial or screening	2	4.5	8.5
Central composite or Box-Behnken	1	2	11
Mixture	2	3.5	9.5

Factors and runs are the medians of each kind.

Full factorial

Every combination of the factor levels.

Arif's summer electricity use: thermostat setting A and window blinds B, and two runs beyond the cubeDunn (2015) · 2 factors, 6 runs
Advance rate of a drill: load, flow rate, rotational speed and type of mud, a single replicate of a 2^4 analysed in ln y (Daniel 1976)Montgomery (2013) · 4 factors, 16 runs
Pressure drop across a turbine's expansion valve against gas temperature (fixed), operator and pressure gauge (random), two replicates: exact, approximate and synthesized tests and the variance componentsMontgomery (2013) · 3 factors, 72 runs
Rate of penetration of a drill against speed, thrust and drilling fluid flow rate (Exercises 4.9 and 4.12)Box and Draper (2007) · 3 factors, 16 runs
A solar water heater, modelled: four dimensionless groups and a centre point (Problem 16 of Part III)Box, Hunter and Hunter (1978) · 4 factors, 17 runs

Show the rest

Fractional factorial or screening

A planned part of the combinations, to find the factors that matter.

Central composite or Box-Behnken

Extra runs that fit curvature, to find an optimum.

Wind turbine power: rotor diameter D and tensile strength T in a central composite design, and its optimumDunn (2015) · 2 factors, 11 runs

Mixture

The ingredients add up to the whole.