Dunn · 2026
Process Improvement using Data
- Matches
Factorial gives the book's answers.
Examples
Each example, and how closely Factorial gives its answers.
Elsewhere
- Brittleness index, reactor TK104 against TK107: t-test and least squares give the same intervalExample · section Using linear least squares modelsMatches
- Randomization (permutation) reference distribution: first 8 TK104 and first 9 TK107 brittleness valuesExample · Table of Case A (254 ... 525) and Case B (338 ... 517)Matches
- Conversion against temperature T and substrate S: main effects by handExample · Factor low/high level tableMatches
- Conversion, where temperature and substrate interact: effects by handExample · Runs with coded and actual settings and y [%]Matches
- Pollutant discharged: chemical C, temperature T and stirring speed SExample · Runs with run order, C, T [°F], S [rpm] and y [lb]Matches
- A 2^4 factorial assessed with a Pareto plot, Lenth's method and a half-normal plotExample · Pareto plot of effect magnitudes, with the Lenth ME and SME linesMatches
- A 2^4 factorial, refitted with its significant effects A, B, D and BDExample · section Refitting the model after removing nonsignificant effectsMatches
- A saturated 2^(7-4) resolution III design: seven factors in eight runsExample · Run table of Experiment, A, B, C, D=AB, E=AC, F=BC, G=ABC and yMatches
- Why heredity matters: a 2^2 factorial fitted with the interaction but without its parent main effectsExample · section Three principles behind screening: sparsity, hierarchy, and heredityMatches
- Bioreactor profit: the first 2^2 factorial around the baselineExample · Table (Experiment, T (actual), S (actual), T (coded), S (coded), Profit)Matches
- Bioreactor profit: the second 2^2 factorial, centred on run 6Example · Table (Experiment, T (actual), S (actual), T, S, Profit)Matches
- Bioreactor profit: the second factorial augmented to a rotatable central composite designExample · X matrix and y vector in the math block (rows y_8, y_9, y_10, y_11, y_6, y_13, y_14, y_15, y_16)Matches
- Bioreactor CCD around 343 K, 1.60 g/L: the profit response and its quadratic modelExample · Table (Experiment, x_T, x_S, T (actual), S (actual), Profit [$/day], Purity [%])Matches
- Bioreactor CCD around 343 K, 1.60 g/L: the purity response and its quadratic modelExample · Table (Experiment, x_T, x_S, T (actual), S (actual), Profit [$/day], Purity [%])Matches
- Bioreactor profit and purity optimized together: sweet spot, Derringer-Suich desirability, prediction intervalsExample · Table of the runsMatches
- Worked OMARS study: four factors on a simulated fed-batch bioreactor, 27-run OMARS plus three centre runs in two blocksCase study · Factor rangesMatches
- Reactor screen: a 17-run definitive screening design in six factors, yield and impurityCase study · section Finding the factors that matter, in seventeen runsMatches
- Web sales: free-shipping threshold and a required profile, run on eight TuesdaysExercise · Data table of Date, Free shipping over ..., Profile required before transaction and Total sales madeMatches
- Bioreactor yield: a 2^4 full factorial in feed rate, inoculant size, substrate concentration and DO set-pointExercise · Y vector in standard order, printed inlineMatches
- Bioreactor yield: the 2^(4-1) half fraction with D = ABCExercise · Solution part 4: 8-run half-fraction table of Experiment, Feed rate, Inoculant size, Feed concentration and DO set pointMatches
- Side product formed: temperature and surfactant, 2^2 with two centre points over two daysExercise · Table of Experiment, Run order, Day, A, B and Side product formedMatches
- Conversion of a chemical reaction: temperature, pH and agitation rate in a 2^3 factorialExercise · Table of Experiment, A, B, C and yMatches
- Shrinkage of injection-molded film: seven factors in eight runsExercise · Table of Experiment, A-G and yMatches
- Breaded chicken strips: cooking time, oven rack and preheating in a 2^3 factorialExercise · Table of Experiment, D, R, P and TasteMatches
- Breaded chicken: the 2^(3-1) half fraction with P = DRExercise · section ExercisesMatches
- Microgel-hydrogel composite: sodium fluorescein released, central composite design with axial runs at 1.4Exercise · Table of Experiment, Order, M = microgel weight [%], H = hydrogel weight [%] and yMatches
- Biological drug yield: steepest ascent from a 2^(4-1) fractional factorial modelExercise · section ExercisesMatches
- Coating process: yield and cost models, sweet spot and overall desirabilityExercise · section ExercisesMatches
- Splitting 12 runs between levels A and B: equal variances, equal costsDesign · Table after 'The first call above ... gives:': Runs at A, Runs at B, Variance, EfficiencyMatches
- Splitting 12 runs between levels A and B: level B nine times as variableDesign · Table after 'The second call above ... gives:': Runs at A, Runs at B, Variance, EfficiencyMatches
- Splitting a cost budget of 24 between levels A and B: a run at A costs twice as muchDesign · section How many runs at each level?Matches
- A 2^3 factorial run in two blocks of four (two raw-material batches), blocks confounded with ABCDesign · Sign table: Experiment, A, B, C, AB, AC, BC, ABC (batch), Response yMatches
- A 2^3 factorial with every combination repeatedDesign · section Standard error: from replicate runs or from an external datasetMatches
- A 2^3 factorial with three centre pointsDesign · section Standard error: from replicate runs or from an external datasetMatches
- Cell-culture bioreactor by-product: five two-level factors, why a full 2^5 is too costlyDesign · section Fractional factorial designsMatches
- Half fraction of a 2^3 factorial, generated by C = ABDesign · Table of Experiment, A, B and C = ABMatches
- The complementary half fraction, C = -AB, which completes the 2^3 factorialDesign · Table of Experiment, A, B and C = -ABMatches
- Half fraction of a 2^4 factorial, generated by D = ABCDesign · section Generators and defining relationshipsMatches
- Half fraction of a 2^4 factorial generated by D = AC, a poorer choiceDesign · section Generators and defining relationshipsMatches
- Block defining relations for a 2^k factorial in two blocks (k = 3, 4, 5)Design · Table of k, Design, Block 1 defining relation and Block 2 defining relationMatches
- A 2^3 factorial in four blocks of two: the poor choice D = ABC, E = BCDesign · Table of Lot of material, D and EMatches
- A 2^3 factorial in four blocks of two: the better choice D = AB, E = ACDesign · Table of Lot of material, D and EMatches
- Eight factors in 16 runs: a 2^(8-4) resolution IV design (Example 2)Design · section Highly fractionated designs: beyond half-fractionsMatches
- Five factors in 16 runs: a 2^(5-1) resolution V half fraction, E = ABCDDesign · section Design resolutionMatches
- Trade-off table cell: 7 factors in 16 runs, a 2^(7-3) resolution IV designDesign · Trade off tableMatches
- Fold-over on one factor: re-running the 2^(7-4) saturated design with the sign of C switchedDesign · section Design foldoverMatches
- Full fold-over of the 2^(7-4) saturated design: 16 runs of resolution IVDesign · section Design foldoverMatches
- Projectivity of a 2^(3-1) half fraction: dropping one factor leaves a 2^2 full factorialDesign · Projectivity of a half fraction in 3 factorsMatches
- Projectivity of a 2^(6-2) resolution IV design: an embedded full factorial in any 3 factorsDesign · section ProjectivityMatches
- A six-factor definitive screening design in 13 runsDesign · The run matrix of a six-factor definitive screening design (13 runs), shown in construction orderMatches
- Box-Behnken design in 3 factorsDesign · Run counts for a Box-Behnken designMatches
- Box-Behnken design in 4 factorsDesign · Run counts for a Box-Behnken designMatches
- Box-Behnken design in 5 factorsDesign · Run counts for a Box-Behnken designMatches
- Box-Behnken design in 6 factorsDesign · Run counts for a Box-Behnken designMatches
- Box-Behnken design in 7 factorsDesign · Run counts for a Box-Behnken designMatches
- Central composite design in 3 factors (axial distance and comparison with a Box-Behnken design)Design · Box-Behnken compared with central composite designsMatches
- One factor at three levels {-1, 0, +1} with the quadratic model: the information-matrix worked exampleDesign · section A worked example: the information matrix of a small designMatches
- Four-run D-optimal design for the two-factor interaction model on [-1, +1]^2 (the 2^2 factorial), reached by point-exchange and coordinate-exchangeDesign · The two exchange algorithms on the same four-run problemMatches
- Point-exchange starting design {(-1,-1), (0,1), (1,0), (1,1)} for the two-factor interaction modelDesign · The two exchange algorithms on the same four-run problemMatches
- Point-exchange design after the first swap: {(-1,-1), (-1,1), (1,0), (1,1)}Design · The two exchange algorithms on the same four-run problemMatches
- A four-level categorical factor, one run per level: the determinant under three codingsDesign · section Categorical factors with several levelsMatches
- Base three-run design {-1, 0, +1}: prediction variance, SPV and its row of the four-design tableDesign · Four candidate designs for the single-factor quadratic modelMatches
- Base three-run design with all three runs repeated (six runs)Design · Four candidate designs for the single-factor quadratic modelMatches
- Base three-run design plus two replicate centre points (five runs)Design · Four candidate designs for the single-factor quadratic modelMatches
- Base three-run design plus one point at x = -1 and one at x = +1 (five runs)Design · Four candidate designs for the single-factor quadratic modelMatches
- Nine-run definitive screening design in four factors (the running comparison)Design · Comparing the nine-run DSD with the thirteen-run OMARS designMatches
- Thirteen-run OMARS design in four factors (the running comparison)Design · Comparing the nine-run DSD with the thirteen-run OMARS designMatches
- Full 2^5 factorial plus two centre points, against the 11-term main-effects-and-quadratic modelDesign · Which designs can fit the five-factor main-effects-and-quadratic modelMatches
- Resolution-V 2^(5-1) fractional factorial plus two centre points, against the 11-term modelDesign · Which designs can fit the five-factor main-effects-and-quadratic modelMatches
- Face-centred central composite design in five factors on a resolution-V half-fraction cube (32 runs)Design · Which designs can fit the five-factor main-effects-and-quadratic modelMatches
- Box-Behnken design in five factors (40 design runs plus 6 centre runs)Design · Which designs can fit the five-factor main-effects-and-quadratic modelMatches
- Twenty-five-run OMARS design in five factors (24 design runs folded around one centre run)Design · Which designs can fit the five-factor main-effects-and-quadratic modelMatches
- Thirteen-run definitive screening design in five factorsDesign · Which designs can fit the five-factor main-effects-and-quadratic modelMatches
- The estimability frontier of a foldover with one centre run, for three to seven factorsDesign · The estimability frontier, against the parameter count it has to clearMatches
- Four-factor 19-run OMARS foldover, scored against the full second-order modelDesign · The estimability frontier N = k^2 + k + 1 for a foldover, against the parameter count of the full second-order model and the size of a definitive screening designMatches
- Four-factor 21-run OMARS foldover at the estimability frontierDesign · The estimability frontier N = k^2 + k + 1 for a foldover, against the parameter count of the full second-order model and the size of a definitive screening designMatches
- Four-factor 19-run non-foldover OMARS design that estimates the full second-order modelDesign · section How many runs a second-order model needsMatches
- The OMARS trade-off table: capability class and error df by run count and number of factorsDesign · Text block: output of omars_trade_off_table(anchors=True)Matches
- Six factors in seventeen runs, read from the OMARS trade-off tableDesign · section Three worked examplesMatches
- Five factors at 13, 17 and 31 runs, read from the OMARS trade-off tableDesign · section Three worked examplesMatches
- Four factors in nineteen runs (inside the band) against twenty-one runs (the frontier)Design · section Three worked examplesMatches
- Every regular two-level fraction with eight runs and four factorsDesign · section What a cell in either table reportsMatches
- Every regular two-level fraction with sixteen runs and seven factorsDesign · section What a cell in either table reportsMatches
- Twelve three-factor design points with one centre run (13 runs)Design · Nine candidate measures down the three-factor column of the OMARS trade-off tableMatches
- Box-Behnken design in three factors: the twelve points with three centre runs (15 runs)Design · Nine candidate measures down the three-factor column of the OMARS trade-off tableMatches
- Twelve three-factor design points with five centre runs (17 runs)Design · Nine candidate measures down the three-factor column of the OMARS trade-off tableMatches
- Best attainable measures over every three-factor OMARS design of each sizeDesign · Nine candidate measures down the three-factor column of the OMARS trade-off tableMatches
- Best attainable measures over four-factor OMARS foldovers of each sizeDesign · The nine measures of the three-factor figure, for the four-factor column of the OMARS trade-off tableMatches
- The smallest definitive screening design for six factors (13 runs)Design · section Finding the factors that matter, in seventeen runsMatches
- Face-centred central composite design in T, t and C, 17 runs, against the heat limitDesign · The face-centred CCD (left) and the I-optimal design (right) in the plane of temperature and catalyst loadingMatches
- D-optimal objective for a 2^3 factorial, and after moving runs 2 and 3Design · Table of Experiment, A, B and CMatches
- Soil treatment screening: six factors plus soil heap in nine runsDesign · Solution table of Experiment, A, B, C, D=AB, E=AC, F=BC and G=ABCMatches
- A 2^3 factorial in two blocks of four, blocks confounded with ABCDesign · Solution table of Experiment, A, B, C and ABCMatches
Not yet
Answers the book prints that Factorial cannot compute yet, by what it lacks.
- The library's curvature test needs pure error from two or more centre runs, and this design has one; the book's difference is run 6 less the mean of the four corners, 688 - 670.25 = 17.75, which agrees with 'about $18'
- The number of regular eight-run four-factor fractions, a count from the book's own enumeration of every choice of generators (regular_fractions); no check kind or library function counts designs
- The number of regular sixteen-run seven-factor fractions, a count from the book's own enumeration of every choice of generators (regular_fractions); no check kind or library function counts designs
- The number of sixteen-run seven-factor fractions of resolution IV, a count from the book's own enumeration of every choice of generators (regular_fractions); no check kind or library function counts designs
- The best resolution over every 32-run seven-factor regular fraction, from the book's own enumeration; generate_design makes a seven-factor fraction of 16 runs when resolution IV is asked and of 64 runs when resolution V is asked, never 32, so design_property cannot reach this design without generators the book does not give. The book's CI checks this echoed value
Show the rest
- The number of 32-run seven-factor fractions of resolution IV (the sum 40 + 25 + 30 of the printed counts), a count from the book's own enumeration of every choice of generators (regular_fractions); no check kind or library function counts designs
- A comparison of the fifteen-run Box-Behnken design with the best value over every fifteen-run three-factor OMARS design on the nine measures, from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue
- A comparison of the nine-run DSD with every nine-run three-factor OMARS design on six measures, from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue
- The best max |r| over every seventeen-run three-factor OMARS design, from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue; compare_designs and omars_properties give 0.05556 for one design that attains it, the twelve points with five centre runs (verified)
- The best max |r| over every nineteen-run three-factor OMARS design, from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue; the design attaining it is not printed
- The number of three-factor OMARS designs of 21 runs with one centre run, a count from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue
- A statement that the six measures of the first two rows pick four different 21-run designs, from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue
- The best attainable variance factor of a quadratic over every 19-run three-factor OMARS design with one centre run, from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue; the design attaining it is not printed
- The power at the best attainable quadratic variance factor over every 19-run three-factor OMARS design (non-central F, |beta|/sigma = 1, alpha = 0.05), from the book's figure script, which scores every three-factor OMARS design of each size; no check kind or library function enumerates the OMARS catalogue; the design attaining it is not printed