FieldsMeasurement and laboratory testing
Experiments here usually have about 3 factors and 20 runs. Full factorials and fractional factorials are the most common.
- Full factorial
- Fractional factorial or screening
- Central composite or Box-Behnken
- Other designs
Show the numbers
| Kind of design | Experiments | Factors | Runs |
|---|---|---|---|
| Full factorial | 6 | 2 | 66 |
| Fractional factorial or screening | 6 | 3.5 | 24.5 |
| Central composite or Box-Behnken | 1 | 3 | 20 |
| Other designs | 10 | 5 | 15.5 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- Eddy current probe sensitivity: impedance against wire turns, winding distance and wire gauge (2^3)NIST/SEMATECH e-Handbook of Statistical Methods (2020) · 3 factors, 8 runs
- A gauge capability study: twenty parts measured twice by each of three operators, analysed with parts and operators random, and with operators fixedMontgomery (2013) · 2 factors, 120 runs
- A measurement system: ten parts, each measured three times by two operators (Problem 13.1)Montgomery (2013) · 2 factors, 60 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
- Thermal impedance of a power module: ten parts, each tested three times by three inspectors (Hoof and Berman 1988) (Problem 13.2)Montgomery (2013) · 2 factors, 90 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- Resolution and sensitivity of a supercritical Hantzsch reaction for formaldehyde: pressure, temperature, static and dynamic times and volume in a 2^(5-1) with a centre run (Problem 8.35)Montgomery (2013) · 5 factors, 17 runs
- Measurement device repeatability: five gaging factors in an L8 (Kurt Manufacturing)Schmidt and Launsby (2000) · 5 factors, 8 runs
- Moisture titrated from a freeze-dried product: methanol, chloroform, formamide and shake time in a duplicated half fractionSchmidt and Launsby (2000) · 4 factors, 8 runs
- Bulk density of precipitated chalk: 11 laboratories, 2 chalks, 3 repeat testsDavies (1956) · 2 factors, 66 runs
- Sampling and analysis of a fertiliser: 8 batches, 2 samples a batch, each analysed by 2 methodsDavies (1956) · 3 factors, 32 runs
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Rockwell C hardness from four tips on four coupons as blocks, coded by subtracting 40 (Problem 4.7)Montgomery (2013) · 1 factor, 16 runs
- Performance of three brands in four laboratories (Exercises 7.1 and 7.2, data set (b))Box, Hunter and Hunter (1978) · 1 factor, 12 runs
- Pollutant levels by three methods and two technicians (Exercises 7.1 and 7.2, data set (a))Box, Hunter and Hunter (1978) · 1 factor, 6 runs
- Soil nitrogen by five operators on three days, a sample each day split among them (Problem 9 of Part II)Box, Hunter and Hunter (1978) · 1 factor, 15 runs
- Case-study 60-run design augmented with a four-run block of new compound G (resolution-III fraction in co-solvent, pH, temperature)Dunn (2026) · 5 factors, 4 runs
Show the rest
- Case-study 60-run design augmented with an eight-run 2^3 full-factorial block of new compound GDunn (2026) · 5 factors, 8 runs
- D-optimal split-plot, 48 runs (quadratic model), compared against the I-optimal designDunn (2026) · 5 factors, 48 runs
- D-optimal split-plot, 60 runs (quadratic model), compared against the I-optimal designDunn (2026) · 5 factors, 60 runs
- I-optimal split-plot, 48 runs (quadratic model), compared against the chosen 60-run designDunn (2026) · 5 factors, 48 runs
- Six chromogens x four continuous factors: 60-run split-plot I-optimal design with a ten-point colour-development curve (simulated), analysed by ANOVA on the peak, PLS on the curve, and model inversionDunn (2026) · 5 factors, 60 runs