number of experiments,
Decide together which effects to distinguish.

This tool DOE run table generator for numeric factorsIt is. Once the purpose and factor range are determined, the number of experiments for multiple designs is compared, and actual conditions, coding values, and random execution order are generated. Statistically indistinguishable effects are indicated by overlap and model rank. The created table is a plan before measuring response values, and is not the result of determining significance or optimal conditions.

If it's your first time: Paper Helicopter Practice

From the example list Practice · Paper helicopterPlease select . The plan is to measure flight time by changing three conditions: wing length, wing width, and body length. Create a total of 11 combinations of 8 lower and upper limit combinations of each condition and 3 intermediate conditions. Drop them from the same height and method, and record the time in Y for each row. The scope is for practice purposes only and can be changed to an actual production size.

factoris the condition to change, levelis the value to put in that condition, Response value Yare the results measured after the experiment. Center pointsis an experiment where all conditions were set to the midpoint, random orderis to mix up the execution order so that changes over time are not limited to specific conditions. After creating a plan, actual experimentation and analysis of results are required.

Recommended Order of Action

1. Select Purpose: Choose between finding influential factors, determining the effect of combining two conditions, or experimenting to find a good one.
2. Enter factor name, unit, lower limit, upper limit: Set a scope that is actually feasible. This version supports 2 to 12 numeric factors. The midpoint is the arithmetic mean of the two limits.
3. Compare budget and design: Click on Recommend to apply it. A recommendation is a proposal that compares the purpose and number of supported designs. It is not a ranking that guarantees power or global optimality. Don't throw away design rows to fit your budget. To choose a different design Choose a designExpand .
4. Center point/repeat/block settings: The default additional center points are 3 per iteration. A full design iteration is an independent experiment in which all factor points, axis points, and center points are performed anew.
5. Create a matrix: Check effect overlap, model rank, and actual execution range, and perform them in Run order. The Run ID identifies both the standard sequence and the repetition.
6. Record and export results: Enter the response value Y and a note in the run table. CSV stores the current notation among actual/coded values. JSON stores plans, sequences, records, and overall overlapping diagnosis, and HTML plans store settings, graphs, and execution tables.

Supported designs

Resolution and effect overlap

• III: Main effects may overlap with 2 factor interactions.
• IV: Main effects and 2 factor interactions are distinct, but 2 factor interactions can overlap.
• V and above: All main effects and 2 factor interactions can be distinguished from each other. Higher order interactions are not automatically separated.

The alias table calculates centered correlations between main-effect columns and two-factor product columns in the generated design. Pairs with |r|≈1 are shown as fully aliased; 0.05<|r|<1 indicates partial correlation. This is not a hypothesis test. Pairwise correlations may miss linear dependencies involving several columns, so the full model rank is calculated separately.

Center point·Repeat·Foldover·Block

Additional center pointis the number per replicate. If the base design already contains center points, as in a three-level full factorial, the displayed total may be higher. Adding center points to a two-level design helps detect overall curvature, but cannot estimate each factor's quadratic term separately.

Invert all Foldoveradds runs with every factor sign reversed for fractional factorial and PB designs. This separates main effects from two-factor interactions. If the reversed design duplicates the original, generation is blocked because it adds no new information. This version does not manage sequential experiment history or foldovers that reverse only selected columns.

Complete block per iterationensures that each iteration has the same overall design, randomizing only within blocks. Displays the model rank and residual degrees of freedom, including block terms. The pure error degree of freedom is Same conditions within the same blockSince it is calculated in repetitions, if the repetitions are divided into blocks, the differences between blocks are not counted as pure errors. Avoid blocking by cutting the design an arbitrary number of times.

Meaning of model diagnosis

The diagnostics distinguish a linear model, a linear model with individual squared terms (additive), a linear model with all two-factor interactions, and a full quadratic model. These are polynomial models for numeric factors; they are not the complete set of categorical interaction contrasts for a three-level factor. Column rank is checked with twice-reorthogonalized Gram–Schmidt. Residual degrees of freedom equal the number of runs minus the rank. Replication only at the center does not establish model adequacy across the entire design region.

“Separable” means the coefficients of the specified model can be identified. Adequate power, high prediction accuracy, small measurement error, independence and a stable process must be checked separately. Once responses are recorded, the “Result analysis” below runs the regression, effect tests and optimum search with the same model terms.

How the result analysis is calculated

The recorded Y responses are fitted by polynomial regression on coded values (−1, 0, +1; CCD axial points at ±α). Columns are built in the order intercept, main effects, 2-factor interactions and square terms, plus block indicator columns if blocking by replicate was used. The least-squares estimates are computed with Householder QR; columns that are fully aliased with other terms in this design are excluded from estimation and this is reported.

Model selection (automatic): Starting from the largest model that can be separately estimated from the recorded data (quadratic → interactions → main effects), the term with the largest p-value at significance level α is removed one at a time. If a higher-order term (interaction or square term) remains, the main effects it contains are kept (hierarchy principle). In a nearly saturated design with 2 or fewer residual degrees of freedom, Lenth’s pseudo standard error is used instead of p-values (PSE = 1.5 × trimmed median, ME = t_{0.975, m/3} × PSE) to screen effects, and the reduced model is then refitted. If you choose the model yourself, it is fitted as is, with no terms removed.

Effects and tests: The effect of a two-level term is twice its coefficient (the change for low→high). For each term, t = coefficient/standard error, and the p-value comes from the t distribution with the residual degrees of freedom. The sum of squares for each term in the ANOVA table is the partial sum of squares (t² × MSE), which equals the sequential sum of squares in an orthogonal design. If the same settings are replicated within the same block, pure error and lack of fit are separated and an F test is performed. If a two-level design has center points, curvature is tested from the difference between the mean of the factorial points and the mean of the center points.

Goodness of fit: R², adjusted R² and predicted R² (PRESS-based, computed from the leverages h_ii) are shown. If adjusted R² and predicted R² differ by more than 0.2, possible overfitting is flagged. The residual plots (vs. fitted values, normal probability, run order) are for visually checking the equal-variance, normality and independence assumptions.

Recommended settings: Within the coded range that was tested, a grid search followed by a coordinate-shrinking search finds the point where predicted Y is highest, lowest or closest to the target value. Factors not in the final model are marked “No effect” and set to their mid-value. For a quadratic model, the stationary point (where the slope is 0) and the signs of the eigenvalues of the Hessian matrix distinguish maximum, minimum and saddle point. The prediction interval is a confidence interval for the mean response, computed as t × √(MSE × xᵀ(XᵀX)⁻¹x). If the recommended setting lies on the boundary of the range, better settings may exist outside it, so further experiments are advised.

Limitations: Only one response (Y) is analyzed; multiple-response optimization, transformations (log, Box–Cox), categorical factors, split-plot structures and covariates are not supported. Missing runs break orthogonality, so effects become partially confounded, and power is low when the number of recorded runs is close to the number of terms. All predictions are model estimates, so verify them with confirmation runs at the recommended settings.

Scope of support and record keeping

The current range is 2 to 12 numeric factors, 2,048 total, 0 to 20 additional center point iterations, and 1 to 10 total iterations. Categorical·Mixinglevel·Prohibited combination·Mixture·Split·DSD·D-optimal user design is not yet available. Deleting certain rows or rounding factors after creation may change the original orthogonality, resolution, and rank.

Your work is automatically saved to your browser's local storage. It is stored separately from general statistical analysis data and is not transmitted to the server. Changing the settings shows the previous execution table separately and locks the export. You can revert plans and records from before creating a new plan with “Restore Previous Plan,” but this restoration history will disappear when you refresh. If you plan to keep it, save it as JSON. The same run sequence is reproduced with the same settings and seeds. The values ​​shown in CSV retain their original numeric precision when exported.

Verification criteria and reference materials

• NIST — Fractional factorial design and generative formula list
• NIST — design resolution and overlap
• NIST — Plackett–Burman table
• NIST — axial distance from CCD
• NIST — Box–Behnken design
• NIST — Role of the center point

Numerical verification includes reference generation equation, column balance/orthogonality, level combination frequency of two columns, resolution/Foldover overlap, 2 order model rank, random order reproducibility, and pure error degree of freedom for each block. It does not imply endorsement by a commercial program.

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