Product Development Engineers Ltd

Our first tool release – Mixtures DoE tool!

Design of Experiments infographic explaining DoE tools, factor effects, process optimisation and common experiment types.

Today, we are excited to announce the release of our first subscriber tool, enabling you to carry out Mixtures DoE-type work at a tiny fraction of the cost of more established tools. We shall follow this up with a whole suite of DoE-type analysis tools over the coming weeks and months. You can get access to the tool here:-

Mixture experiments infographic explaining mixture design, Scheffé models, simplex plots, contour maps and formulation optimisation.
Mixture experiments help engineers and formulation specialists understand how component proportions affect performance, cost and the optimum blend.

What it is

A browser-based statistical experiment design tool for mixture experiments — situations where you are varying the proportions of ingredients in a formulation and want to understand how those proportions drive one or more measured outcomes. It takes you from a blank project through to a fitted model, visualisation, and optimised formulation, entirely within a guided wizard interface.

Who should use it

Anyone who needs to optimise a recipe, formulation, or blend and wants a statistically rigorous approach rather than trial and error. No statistical software or specialist knowledge is required beyond an understanding of what you are making and what you want to measure. Typical users:

  • Formulation chemists designing paints, adhesives, cosmetics, pharmaceuticals, or food products
  • Food scientists and chefs balancing ingredient proportions for flavour, texture, or shelf life
  • Materials scientists developing alloys, composites, concrete mixes, or polymer blends
  • Agricultural researchers optimising fertiliser or pesticide mixtures
  • Flavour and fragrance houses blending base notes
  • Bioprocessing teams optimising nutrient media compositions

The tool is appropriate for anyone from a practising engineer with no statistics background to an experienced DoE practitioner.

Application examples

  • Sunscreen formulation: Three UV-filter actives at varying proportions; responses are SPF, skin feel score, and stability index
  • Concrete mix design: Cement, fly ash, and slag; response is compressive strength at 28 days
  • Blended whisky: Five malt whiskies at varying proportions; responses are flavour panel scores for smokiness, sweetness, and finish
  • Polymer coating: Resin, hardener, and diluent; responses are viscosity, adhesion, and gloss
  • Fertiliser blend: Nitrogen, phosphorus, and potassium sources; response is crop yield
  • Animal feed: Three protein sources; responses are growth rate and feed conversion ratio

How it works — step by step

Step 1 — Project setup

You name your project and optionally add free-text notes covering objectives, background, constraints, or client details. This acts as the project record that appears in your exported report.

Mixture DoE software setup screen for a silicon etch rate experiment with project name and notes fields.
Define the mixture experiment at project level before specifying design type, components, responses, model terms and analysis settings.

Once you have one or more projects available, each is stored and viewable from a home page, along with its current status. We recommend that you create HTML reports for offline copies of your work (see later).

Mixture Design Tool dashboard showing saved mixture DoE projects, status labels, update dates and project actions.
Manage mixture DoE projects from a single dashboard, with clear project status, update tracking and quick access to existing analyses.

Step 2 — Design type

You select from six mixture design types using a simple card-button selector:

DesignWhen to use
Simplex-Lattice (SLD)Standard choice; systematic coverage of the simplex at evenly spaced proportions
Augmented SLDSLD plus the overall centroid; better for detecting curvature; the recommended default
Simplex-Centroid (SCD)All pure components, all equal binary blends, all equal tertiary blends, and the centroid
Augmented SCDSCD plus interior check blends; highest resolution for detecting non-linear effects
Extreme Vertices (EV)Constrained mixtures where components have lower and upper limits; covers the corners of the feasible region
D-optimalWhen you want to specify an exact number of runs and let the algorithm choose the most informative ones

For SLD and ASLD, you also select the lattice degree (1–4), which controls how many intermediate points are generated.

Mixture design selection screen showing Simplex-Lattice, Augmented SLD, Simplex-Centroid, Extreme Vertices and D-optimal design options.
Select the appropriate mixture design method for unconstrained or constrained formulation experiments, including SLD, simplex-centroid and D-optimal designs.

Step 3 — Components

You define between 2 and 8 components, giving each a name and optionally setting lower and upper bound percentages. The tool validates in real time that your bounds form a feasible mixture (sum of lower bounds ≤ 100 ≤ sum of upper bounds). EV and D-optimal designs use these bounds directly; the other designs apply a pseudo-component transformation internally so the analysis is carried out correctly in the constrained space.

Mixture DoE component setup screen showing three mixture components with optional lower and upper bounds.
Define mixture components and optional formulation bounds so the software can generate the correct feasible design space.

Step 4 — Responses

You name one or more response variables (e.g. Viscosity, Yield, Flavour Score) and give each a unit. These become the columns you will fill in with measured data later. Multiple responses are fully supported throughout all subsequent steps. In the graphic below, you can also see the navigation bar for your project.

Mixture DoE response setup screen showing etch rate entered as the measured experimental response.
Add one or more measured responses before generating the randomised mixture experiment run sheet.

Step 5 — Run sheet

The tool generates your design and presents a table of runs showing each component proportion for each experimental run. The run order is randomised. You can see a breakdown of how many vertices, edge midpoints, face points, centroids, and check blends are in the design, and optionally add replicates per point type. The run sheet is available as a CSV download to take to the lab.

Mixture DoE run sheet showing an Augmented SLD design with vertices, edges, centroid points and replicate settings.
Generate a randomised mixture DoE run sheet with point types, component percentages and configurable replicates.

Step 6 — Data entry

You enter your measured response values directly into a table, one row per run. If you have collected data in a spreadsheet, you can upload a CSV or Excel file and the tool matches rows by run order number. Data is auto-saved continuously so nothing is lost if you close the browser.

Mixture experiment data entry screen showing component settings and etch rate response values for each run.
Enter measured response data directly against each mixture run, preserving the randomised run order and design structure.

Step 7 — Model terms

You select which Scheffé polynomial terms to include in your model:

  • Linear: main-effect blend terms only (β₁x₁ + β₂x₂ + β₃x₃…)
  • Quadratic: adds pairwise interaction terms (βᵢⱼxᵢxⱼ); most common starting model
  • Special cubic: adds three-component product terms (βᵢⱼₖxᵢxⱼxₖ)
  • Full cubic: additionally adds delta terms (βᵢⱼxᵢxⱼ(xᵢ−xⱼ)) for asymmetric binary blending behaviour

Quick-select buttons let you choose a complete model level in one click. A live summary shows your number of runs (n), number of model parameters (p), and error degrees of freedom (n−p), with a warning if error df falls below 3 — the practical minimum for meaningful inference.

Mixture DoE model terms screen showing linear, quadratic and special cubic Scheffé terms selected for analysis.
Select Scheffé polynomial model terms and confirm model degrees of freedom before running mixture DoE analysis.

Step 8 — Analysis

For each response, the tool fits your chosen Scheffé model by ordinary least squares and presents:

  • ANOVA table with sequential sums of squares, F-statistic, and p-value for the model
  • Coefficients table with the estimate and standard error for each term
  • Model equation written out explicitly
  • R² and adjusted R² as overall fit metrics
  • Residual standard deviation (S)

All responses are available as tabs.

Mixture DoE ANOVA table for etch rate showing model, linear, interaction and special cubic terms with F-values and p-values.
Review mixture model ANOVA results to identify statistically significant components and interaction effects.
Scheffé coefficient table showing mixture model coefficients, standard errors, p-values, R-squared and prediction equation.
Inspect Scheffé model coefficients, model fit statistics and the fitted prediction equation for the mixture response.

Step 9 — Plots

Four visualisation types are available per response, selectable as tabs:

  • Ternary plot (3-component experiments only): a filled contour surface plotted on the simplex triangle, showing your predicted response across the whole mixture space
Ternary mixture plot showing fitted etch rate response points across a three-component mixture design space.
Visualise the fitted response across the three-component mixture space using a ternary plot.
  • Trace plot (Cox method): traces the predicted response as each component is increased from its centroid proportion while the others are held in constant ratio — one line per component
Cox trace plot for mixture DoE showing how etch rate changes as each component amount is varied.
Use Cox trace plots to compare the influence of each mixture component on the predicted response.
  • Trace plot (Piepel method): a variant of the trace plot using Piepel’s parameterisation, preferred when the centroid is not a natural reference point
Piepel trace plot for mixture DoE showing response changes from the centroid towards pure component vertices.
Piepel trace plots show how the predicted response changes along directions from the mixture centroid to component vertices.
  • Pareto of effects: a horizontal bar chart of standardised coefficients, useful for identifying which terms drive most of the variation
Pareto chart of standardised effects for mixture DoE terms showing significant component and interaction effects.
Rank mixture model effects by statistical importance using a Pareto chart of standardised effects.
  • Residuals: predicted vs. actual plot and a normal Q-Q plot for checking model assumptions
Mixture DoE residual diagnostics showing normal probability and residuals versus fitted values plots.
Check mixture model assumptions using residual diagnostic plots before relying on prediction and optimisation results.

Step 10 — Optimise

Two sub-modes:

Predict at a setting: You enter a specific formulation (component proportions summing to 100%) and the tool returns the predicted value for every response under the fitted model. Useful for checking a known formula or an intermediate blend before committing to a run.

Mixture DoE prediction screen showing component settings, predicted etch rate, confidence interval and prediction interval.
Predict the response at a specified mixture formulation with confidence and prediction intervals for engineering interpretation.

Response optimiser: You set a goal for each response — maximise, minimise, or hit a target value — along with acceptable bounds. The tool searches 10,000 candidate formulations sampled uniformly across the feasible mixture space and returns the formulation that maximises the overall desirability score (a geometric mean of the individual per-response desirability functions). Your best formulation and its predicted response values are displayed and included in the report.

Mixture DoE response optimiser showing optimal component percentages, predicted etch rate and desirability score.
Optimise mixture component proportions against response goals to identify the best predicted formulation.

Report export

At any point from Step 8 onwards you can export a full HTML report containing your project metadata, component and run tables, ANOVA and coefficient results, model equations, and all plots — ready to share with colleagues or attach to a project record.

Downloaded mixture design analysis report showing design summary, components, responses and run sheet for a silicon etch rate experiment.
Export a complete offline HTML report documenting the mixture design, run sheet, fitted model and analysis results.

Validation

We have carried out a number of manual test cases validations versus well known studies, as well as running a round-trip validation test set on a range of permutations to check internal consistency. We have also carried out many tests with synthetically generated ‘noisy’ data and compared the tools results for these with suitable benchmarking applications. Each page and each report simply carries the following disclaimer:

Disclaimer:
Although care has been taken to ensure that the calculated values are correct, users should verify the output.
Product Development Engineers Ltd and other parties associated with this software and website assume no responsibilities for
errors or misuse of this software, or damage arising from use of this software.

Mixture DoE validation test output showing passed checks for SLD model combinations, ANOVA, R-squared, MSE and standard errors.
Round-trip validation confirms that executable mixture design combinations reproduce expected model statistics and analysis outputs.

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