FieldsChemical reactions and processes
Experiments here usually have about 3 factors and 15 runs. Most are full factorials.
- Full factorial
- Fractional factorial or screening
- Central composite or Box-Behnken
- Other designs
Show the numbers
| Kind of design | Experiments | Factors | Runs |
|---|---|---|---|
| Full factorial | 80 | 3 | 9 |
| Fractional factorial or screening | 13 | 5 | 16 |
| Central composite or Box-Behnken | 21 | 3 | 17 |
| Other designs | 12 | 2.5 | 16 |
Factors and runs are the medians of each kind.
Full factorial
Every combination of the factor levels.
- Conversion of a chemical reaction: temperature, pH and agitation rate in a 2^3 factorialDunn (2026) · 3 factors, 8 runs
- Side product formed: temperature and surfactant, 2^2 with two centre points over two daysDunn (2026) · 2 factors, 6 runs
- Chemical process yield: a 2^2 in temperature and time with five centre runs, around 200 C and 200 minutesNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 2 factors, 9 runs
- Chemical process yield: a new 2^2 with five centre runs around 189.5 C and 350 minutesNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 2 factors, 9 runs
- Emil's reactor: feed F, jacket temperature T and agitator speed S, and its two half fractionsDunn (2015) · 3 factors, 8 runs
Show the rest
- Reactor yield: jacket temperature T and amount of additive D, and their interactionDunn (2015) · 2 factors, 4 runs
- Density of photographic plate film at three developer strengths and three development times, a 3^2 run four times (Problem 9.1)Montgomery (2013) · 2 factors, 36 runs
- Evolutionary operation of a chemical process: three cycles of a 2^2 with a centre point in temperature and pressureMontgomery (2013) · 3 factors, 15 runs
- Filtration rate in a pilot plant: temperature, pressure, formaldehyde concentration and stirring rate, a single replicate of a 2^4Montgomery (2013) · 4 factors, 16 runs
- Impurity of a chemical product at three temperatures and five pressures, one observation per cellMontgomery (2013) · 2 factors, 15 runs
- Molecular weight and viscosity of a polymer: temperature, catalyst concentration, time and pressure, a 2^4 with four centre runs (Table P6.8) (Problem 6.31)Montgomery (2013) · 4 factors, 20 runs
- Purity of oxygen from a liquid air plant against the condenser temperature and the pressure ratio of its columns: a 2^2 with four centre runs (Problem 11.1)Montgomery (2013) · 2 factors, 8 runs
- The chemical process 2^2 of Section 6.2 with each replicate run on its own batch of raw material: three blocksMontgomery (2013) · 2 factors, 12 runs
- The filtration 2^4 of Example 6.2 as a combined array: temperature a noise factor, its response, mean and variance modelsMontgomery (2013) · 4 factors, 16 runs
- The filtration 2^4 of Example 6.2 in two blocks of eight, ABCD confounded, with every response of the poorer batch 20 lowerMontgomery (2013) · 4 factors, 16 runs
- The filtration 2^4 of Example 6.2 run unblocked, the first eight runs in time 20 lower (Table 7.8)Montgomery (2013) · 4 factors, 16 runs
- The filtration 2^4 of Example 6.2 with five centre runs (Problem 6.33)Montgomery (2013) · 4 factors, 21 runs
- The filtration 2^4 of Example 6.2 with four runs at the centre: a test for pure quadratic curvatureMontgomery (2013) · 4 factors, 20 runs
- The yield of a chemical process against reaction time and temperature: a 2^2 with five centre runs, a first-order model and its path of steepest ascentMontgomery (2013) · 2 factors, 9 runs
- Yield in a process development study: time, concentration, pressure and temperature, a single replicate of a 2^4 (Table P6.7) (Problem 6.28)Montgomery (2013) · 4 factors, 16 runs
- Yield in four cycles of an EVOP in concentration and temperature (Problem 11.21)Montgomery (2013) · 1 factor, 20 runs
- Yield of a chemical process at three temperatures and three pressures, a 3^2 run twice (Problem 9.6)Montgomery (2013) · 2 factors, 18 runs
- Yield of a chemical process at three temperatures and three pressures, one replicate on each of two days (Problem 5.21)Montgomery (2013) · 2 factors, 18 runs
- Yield of a chemical process at three temperatures and three pressures, run twice (Problem 5.3)Montgomery (2013) · 2 factors, 18 runs
- Yield of a chemical process at two concentrations of the reactant and two temperatures, twice each (Problem 10.9)Montgomery (2013) · 2 factors, 8 runs
- Yield of a chemical process from a 2^3 with four centre runs whose factor levels were not held where the design set them, fitted by regressionMontgomery (2013) · 3 factors, 12 runs
- Yield of a chemical process: a 2^3 factorial in temperature, pressure and catalyst concentration with four centre runs, fitted by regressionMontgomery (2013) · 3 factors, 12 runs
- Yield of a chemical process: four factors in a 2^4 run twice (Problem 6.7)Montgomery (2013) · 4 factors, 16 runs
- Yield of a chemical process: reactant concentration by amount of catalyst, a 2^2 factorial run three timesMontgomery (2013) · 4 factors, 4 runs
- Yield of isatin: acid strength, reaction time, amount of acid and temperature, a single replicate of a 2^4 (Table P6.11) (Problem 6.38)Montgomery (2013) · 4 factors, 16 runs
- Yield against catalyst A and temperature B, with a centre runSoravia and Orth (2012) · 2 factors, 5 runs
- Yield against catalyst A, temperature B and agitator type CSoravia and Orth (2012) · 3 factors, 8 runs
- Yield of a reaction A to B to C over a 3 x 3 factorial in time and temperature, with a full quadratic modelGoos and Jones (2011) · 2 factors, 9 runs
- Dyestuff manufacture: strength, hue and brightness against six process variables, a 2^6 factorialBox and Draper (2007) · 6 factors, 64 runs
- Dyestuff manufacture: the 64 observations grouped in sets of eight by polysulfide index, time and temperatureBox and Draper (2007) · 3 factors, 8 runs
- Filtration rate of a pilot-plant chemical reactor: temperature, pressure, concentration and stir rate in a 2^4 (Problem 3-1)Anderson and Whitcomb (2007) · 4 factors, 16 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
- Impurity at three temperatures, two pressures and two catalysts, a 3 x 2 x 2 factorial read as a cubeBox and Draper (2007) · 3 factors, 12 runs
- Yield of a chemical process against catalyst, NaOH, agitation and temperature, a 2^4 (Exercises 4.10 and 4.13)Box and Draper (2007) · 4 factors, 16 runs
- Rate constant of cellulose hydrolysis against temperature and sulfuric acid, two readings each (Problem 5 of chapter 4)Schmidt and Launsby (2000) · 2 factors, 9 runs
- Yield in a 2^2 factorial with two centre points, centred on the best run along the path of steepest ascentSchmidt and Launsby (2000) · 2 factors, 6 runs
- Yield in a 2^2 factorial with two centre points: a first-order model and its path of steepest ascentSchmidt and Launsby (2000) · 2 factors, 6 runs
- Yield in a 3^2 factorial over a region that does not hold the optimumSchmidt and Launsby (2000) · 2 factors, 9 runs
- Yield of isatin in an unreplicated 2^4, Davies's data less 6: Lenth's PSE, ME and SMELenth (1989) · 4 factors, 16 runs
- Concentration of product F at five times in a 2^4, with the rate constants fitted run by run (Problem 37 of Part IV)Box, Hunter and Hunter (1978) · 4 factors, 16 runs
- Drying rate against temperature, feed rate and humidity (Problem 9 of Part IV)Box, Hunter and Hunter (1978) · 3 factors, 8 runs
- Drying rate: Problem 9 with the eighth run moved to the centre (Problem 10 of Part IV)Box, Hunter and Hunter (1978) · 3 factors, 8 runs
- Evolutionary operation on a petrochemical plant, phase I: reflux ratio and recycle/purge ratio against cost per tonBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a petrochemical plant, phase IIBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a petrochemical plant, phase IIIBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase I: addition time and stirring rate against optical densityBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase IIBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase IIIBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase IVBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Evolutionary operation on a polymer latex unit, phase VBox, Hunter and Hunter (1978) · 2 factors, 5 runs
- Exercise 15.4: the first-order design with two yields changedBox, Hunter and Hunter (1978) · 2 factors, 7 runs
- Impurity against catalyst, NaOH, agitation and temperature, a randomized 2^4 (Problem 21 of Part III)Box, Hunter and Hunter (1978) · 4 factors, 16 runs
- Pilot plant: the 2^3 factorial run twice, sixteen runs in random orderBox, Hunter and Hunter (1978) · 3 factors, 16 runs
- Pilot plant: yield at two temperatures, two concentrations and two catalysts, each yield the average of two runsBox, Hunter and Hunter (1978) · 3 factors, 8 runs
- Process development: conversion against catalyst charge, temperature, pressure and concentration, an unreplicated 2^4Box, Hunter and Hunter (1978) · 4 factors, 16 runs
- Reactor: percent reacted against feed rate, catalyst, agitation, temperature and concentration, a 2^5 factorial and its two half fractionsBox, Hunter and Hunter (1978) · 5 factors, 32 runs
- Yield against temperature and pH, a duplicated 2^2 (Problem 15 of Part IV)Box, Hunter and Hunter (1978) · 2 factors, 8 runs
- Yield against temperature, catalyst and pH, run in each of two weeks (Problem 8 of Part III)Box, Hunter and Hunter (1978) · 3 factors, 16 runs
- Yield against temperature, concentration and catalyst (Problem 2 of Part III)Box, Hunter and Hunter (1978) · 3 factors, 8 runs
- Yield against temperature, concentration and pH, a 2^3 run unevenly (Problem 23 of Part IV)Box, Hunter and Hunter (1978) · 3 factors, 16 runs
- Yield against temperature, concentration and stirring rate (Problem 10 of Part III)Box, Hunter and Hunter (1978) · 3 factors, 8 runs
- Yield against temperature, pH and agitation rate (Problem 7 of Part III)Box, Hunter and Hunter (1978) · 3 factors, 8 runs
- Yield against temperature, pH and catalyst concentration (Problem 31 of Part IV)Box, Hunter and Hunter (1978) · 3 factors, 8 runs
- Yield against time and temperature: a 2^2 factorial with three centre points, then three runs along the path of steepest ascentBox, Hunter and Hunter (1978) · 2 factors, 10 runs
- Yield and filtration time against condensation temperature and amount of B, a 3^2 (Problem 34 of Part IV)Box, Hunter and Hunter (1978) · 2 factors, 9 runs
- A 2 x 3 x 4 factorial in duplicate: two methods, three temperatures and four batches of raw materialDavies (1956) · 3 factors, 48 runs
- A hypothetical 2^2: the yield of a reaction, to define main effects and interactionDavies (1956) · 2 factors, 4 runs
- Yield in a near-stationary region: a 3^2 factorial, a second-degree fit and its canonical analysisDavies (1956) · 2 factors, 9 runs
- Yield of a direct cotton dyestuff: concentration, volume of free water and amount of a second reactant, a 3^3 factorial in duplicateDavies (1956) · 4 factors, 54 runs
- Yield of a nitration process: time of addition of nitric acid, time of stirring and heel, a 2^3 factorialDavies (1956) · 3 factors, 8 runs
- Yield of an isatin derivative: acid strength, reaction time, amount of acid and temperature, a 2^4 factorialDavies (1956) · 4 factors, 16 runs
- Yield of an organic chemical: quality and amount of ammonium chloride and two units, a 2^3 in duplicate with ABC confounded with four lots of base materialDavies (1956) · 3 factors, 16 runs
- The filtration 2^4 of Example 6.2 without pressure: two replicates of a 2^3, temperature (A) a noise variable (Problem 12.9)Montgomery (2013) · 2 factors, 4 runs
- A 2^2 factorial in temperature and concentration, in original and coded units: coding, orthogonality, information function and scaleless DBox and Draper (2007) · 2 factors, 4 runs
- Activity of a chemical mixture in three active ingredients and a diluent: the path of steepest ascent from a 2^3 factorial, turned along the constraint A + B + C ≤ 100Box and Draper (2007) · 3 factors, 8 runs
Fractional factorial or screening
A planned part of the combinations, to find the factors that matter.
- Colour of a chemical product: solvent/reactant, catalyst/reactant, temperature, reactant purity and reactant pH in a 2^(5-1) (Problem 8.9)Montgomery (2013) · 5 factors, 16 runs
- Filtration rate: the one-half fraction I = ABCD of the pilot plant's 2^4, its runs taken from the full factorialMontgomery (2013) · 4 factors, 8 runs
- Filtration rate: the principal fraction of Example 8.1 and its alternate fraction I = −ABCD, together the full 2^4Montgomery (2013) · 4 factors, 16 runs
- 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
- Yield: condensation temperature, amount of material 1, solvent volume, condensation time and amount of material 2 in a 2^(5-2) (Problem 8.11)Montgomery (2013) · 5 factors, 8 runs
Show the rest
- Half fraction of the agitator experiment: catalyst A, temperature B, agitator type CSoravia and Orth (2012) · 3 factors, 4 runs
- Percentage yield of a reaction in drug manufacture: five factors in a 2^(5-1) resolution V fraction, the path of steepest ascent and its confidence coneBox and Draper (2007) · 5 factors, 20 runs
- Filtration time at a new plant: seven suspected causes in a 2^(7-4) fraction, then its fold-overBox, Hunter and Hunter (1978) · 7 factors, 16 runs
- Filtration in the preparation of a dyestuff: four factors in eight runs, a 2^(4-1) with D = ABCDavies (1956) · 4 factors, 8 runs
- Quality of a basic dyestuff: five factors over three stages in sixteen runs, a 2^(5-1) with E = -ABCDDavies (1956) · 5 factors, 16 runs
- Yield of a laboratory reaction, first stage of steepest ascent: five factors in eight runs, a 2^(5-2) with x4 = x1x2x3 and x5 = -x2x3Davies (1956) · 5 factors, 8 runs
- Yield of a laboratory reaction, second stage of steepest ascent: a 2^(5-2) with x4 = x1x2x3 and x5 = x1x2, around trial (10)Davies (1956) · 5 factors, 8 runs
- Reactor screen: a 17-run definitive screening design in six factors, yield and impurityDunn (2026) · 6 factors, 17 runs
Central composite or Box-Behnken
Extra runs that fit curvature, to find an optimum.
- Chemical process yield: the second 2^2 with centre runs augmented with four axial runs to a rotatable CCDNIST/SEMATECH e-Handbook of Statistical Methods (2020) · 2 factors, 13 runs
- Conversion and activity of a chemical process against time, temperature and catalyst in a central composite design (Problem 11.12)Montgomery (2013) · 3 factors, 20 runs
- Crystal growth against three variables in a central composite design (Problem 11.8)Montgomery (2013) · 3 factors, 20 runs
- Filtration time against temperature and pressure in a central composite design (Problem 11.9)Montgomery (2013) · 2 factors, 13 runs
- The yield, viscosity and molecular weight of Example 11.1's process in a central composite design about 85 minutes and 175°FMontgomery (2013) · 4 factors, 13 runs
Show the rest
- Viscosity of a polymer in a Box-Behnken design in temperature, agitation rate and pressure (Problem 11.11)Montgomery (2013) · 3 factors, 15 runs
- A response of starch vinylation against five coded variables: a half fraction 2^(5-1) with ten axial and six centre runs (Exercise 11.19)Box and Draper (2007) · 5 factors, 32 runs
- Catalytic isomerization of n-pentane: a central composite design with four centre runs, and six further runs to check predictions (Exercise 11.6)Box and Draper (2007) · 3 factors, 24 runs
- Chemical process improvement: a composite design in three factors with unequal axial distances and four centre runs, two responses (Exercise 7.25)Box and Draper (2007) · 3 factors, 18 runs
- Concentration of product in a small continuous reactor: a composite design in four blocks, whose fitted surface is a rising ridge (Example 11.4)Box and Draper (2007) · 3 factors, 24 runs
- DMP from sugar: eight axial trials that complete a central composite design begun in Exercise 4.16 (Exercise 11.16)Box and Draper (2007) · 4 factors, 8 runs
- Exercise 9.1: yield of an ester analogue of jojoba oil against temperature, catalyst and pressure, a central composite design in two blocksBox and Draper (2007) · 3 factors, 19 runs
- Extraction of silica from quartz: quartz size, time, temperature and sodium hydroxide concentration in a central composite design, its axial runs a second block (Exercise 7.26)Box and Draper (2007) · 4 factors, 28 runs
- Percentage yield of a consecutive chemical system against temperature, catalyst concentration and time: a composite design whose fitted surface is a near-stationary planar ridge (Example 11.3)Box and Draper (2007) · 3 factors, 19 runs
- Twenty-five hypothetical observations of MBT production on a 5 x 5 grid, nine of them a composite design: second-order fits to all and to the nine (Exercise 7.13)Box and Draper (2007) · 2 factors, 25 runs
- Yield of mercaptobenzothiazole: reaction time and temperature, twelve runs then five confirmatory runs, second-order fits (Exercise 7.16)Box and Draper (2007) · 2 factors, 17 runs
- Yield in a rotatable central composite design: the second-order model, its stationary point and canonical analysisSchmidt and Launsby (2000) · 2 factors, 10 runs
- Yield against temperature and concentration, a composite design with run order (Problem 36 of Part IV)Box, Hunter and Hunter (1978) · 2 factors, 11 runs
- Yield against time and temperature near the maximum: a 2^2 with centre points, completed by a star to a composite design in two orthogonal blocksBox, Hunter and Hunter (1978) · 2 factors, 12 runs
- Yield of C in a reaction A + B -> C + D: a 2^3 factorial completed to a composite design (alpha = 2), with canonical analysisDavies (1956) · 3 factors, 15 runs
- Face-centred central composite design in T, t and C, 17 runs, against the heat limitDunn (2026) · 3 factors, 17 runs
Other designs
Optimal, blocked, split-plot and other designs made for the problem.
- Reaction time of five ingredients in a 5 x 5 Latin square of batches and days (Problem 4.22)Montgomery (2013) · 2 factors, 25 runs
- Reaction time with four catalysts in a balanced incomplete block design on four batches of raw material, three catalysts in eachMontgomery (2013) · 1 factor, 12 runs
- Yield in a 5 x 5 Graeco-Latin square: batches, acid concentrations, standing times and catalyst concentrations (Problem 4.35)Montgomery (2013) · 4 factors, 25 runs
- Yield of a reaction over a hexagonal region of time and temperature: a 15-run D-optimal design for a cubic modelGoos and Jones (2011) · 2 factors, 15 runs
- Percentage yield of a two-stage chemical process against two temperatures, two reaction times and a concentration: a stationary ridge in five variables (Example 11.5)Box and Draper (2007) · 5 factors, 32 runs
Show the rest
- Loss of product in the mother liquor: five blends of acetanilide in three randomised blocksDavies (1956) · 1 factor, 15 runs
- D-optimal 16-run design for the quadratic model in T, t and C inside the heat limitDunn (2026) · 3 factors, 16 runs
- G-optimal 16-run design for the quadratic model in T, t and C inside the heat limitDunn (2026) · 3 factors, 16 runs
- Reactor optimisation: a 16-run I-optimal design in T, t and C inside a heat limit, with confirmation runsDunn (2026) · 3 factors, 16 runs
- JMP's 20-run D-optimal design in two factors, X3 and X4, choosing twenty of forty raw material samples by their viscosity and molecular weightMontgomery (2013) · 4 factors, 20 runs
- Viscosity and molecular weight of forty raw material samples available for a twenty-run experiment, the twenty chosen starredMontgomery (2013) · 2 factors, 40 runs
- Fedorov's D/G-optimal second-order measure design on the square, set in temperature and timeBox and Draper (2007) · 2 factors, 9 runs