Design of Experiments (DOE)

Highly specialised requests are first checked for feasibility from this information. Please do not send confidential data through the public form; describe it first and agree secure transfer afterwards.

1. 01Enquiry and requirement assessment
2. 02Technical scoping and proposal
3. 03Execution
4. 04Quality review and delivery, with an agreed round of revisions

Read the full project workflow.

In depth: how the work is done

1. Defining factors, levels and responses

   The first step is to list the factors that might influence the outcome, their feasible ranges and the responses to be measured. Factors may be continuous, such as temperature or speed, or categorical, such as material supplier. We discuss which factors are controllable, which are noise and which constraints make some combinations infeasible. Responses are defined with measurement methods and expected variability, since the design must be sensitive enough to detect effects that matter.

2. Selecting a design: factorial, fractional and screening

   Full factorial designs test every combination of levels and estimate all interactions, but run counts grow quickly. Fractional factorials use a carefully chosen subset, accepting that some effects are confounded with others, and are appropriate when higher-order interactions are expected to be small. Screening designs identify the few important factors among many. When regions of interest are irregular or constraints are tight, optimal designs generated by algorithms can be used.

3. Randomisation, blocking and replication

   Randomising run order protects against drifts and hidden variables. Blocking groups runs that share a nuisance factor, such as a day or batch, so that its effect does not contaminate the factor effects. Replication provides an estimate of pure error and increases the power to detect effects. Centre points allow a check for curvature. We balance these needs against the practical limits of material and time.

4. Analysis and sequential experimentation

   Data are analysed by fitting models for the responses, examining which effects are significant, checking residuals and assessing whether the model adequately represents the system. The result is not just a list of significant factors but a predictive relationship and a plan for the next stage, which may include a response-surface design near the optimum or confirmation runs to test predictions. Sequential experimentation is often more efficient than one large design.

5. Practical execution of the plan

   A good design can be spoiled in execution. We provide the run sheet in randomised order, recommend recording of nuisance conditions such as ambient temperature, operator and material lot, and suggest how to handle failed or missing runs without breaking the design's structure. Before the full programme begins, a small pilot may be recommended to check that responses can be measured with adequate precision. These practical steps help ensure that the data collected can actually be analysed as designed.

Common pitfalls this service helps avoid

• One-factor-at-a-time testing. This approach misses interactions and uses runs inefficiently.
• Ignoring run order. Running all low levels first and high levels later confounds factor effects with time-related drift.
• Choosing ranges too narrow. If factor ranges are tiny, effects may be buried in noise and the study uninformative.
• Skipping confirmation. Predictions from a fitted model should be tested with new runs before being relied on.

What good reporting looks like

Reporting a designed experiment includes the objective, factors and levels with justification, the design type and its confounding structure, randomisation and blocking, the data, the fitted model with diagnostics and the conclusions with uncertainty. The design matrix and run order are provided so the experiments can be carried out, and the analysis is documented for inclusion in a thesis or paper. Recommendations for follow-up experiments identify where further runs would most reduce uncertainty.

An illustrative scenario

Hypothetical example written for explanation. It is not a client case, a result or a testimonial.

Consider a manufacturing study of four process parameters, each at two levels. A full factorial would need sixteen runs, and the team can afford eight. A half-fraction design is chosen with the confounding pattern documented, and run order is randomised across two shifts using blocking. Analysis shows that two factors and one interaction dominate the response. Confirmation runs at the predicted best setting are then carried out to test the model before the setting is adopted.

Questions to settle before you begin

• Which factors do I think matter, and over what ranges?
• How many runs can I afford, including replicates?
• Which nuisance variables should I block?
• Which factor combinations are infeasible?
• How will I confirm the model's predictions?

Key terms

Factorial design

An experiment that varies several factors together across all or selected combinations.

Interaction

A situation where the effect of one factor depends on the level of another.

Blocking

Grouping runs to remove the effect of a nuisance variable.

Randomisation

Assigning run order or treatments by chance to avoid bias.

Confounding (aliasing)

Inability to distinguish two effects because the design varies them together.

Working together on Engineering Data Analysis & Statistics projects

Data analysis engagements start with a data description before any modelling: what was measured, how, under what conditions, with which instruments and with what known problems. Sharing a small sample or a data dictionary first is usually enough to scope the work. Analyses are documented step by step so that every figure and table can be reproduced from the supplied data, and code or workflow files can be provided on request. Please avoid sending confidential or personal data through the public form; secure transfer can be arranged after scoping. Conclusions are phrased with the uncertainty the data justify, not stronger.

Few projects need a single service in isolation. These are the services most often combined with this one.

• Engineering Statistical Analysis

  Statistical analysis of experimental, simulation and field data, with method selection justified by the data and the research question, and results reported with effect sizes and uncertainty rather than p-values alone.

• Response Surface Methodology (RSM)

  Sequential experimentation and modelling to relate responses to several factors and locate favourable operating conditions, using central composite or Box-Behnken style designs and fitted quadratic surfaces.

• Regression & Predictive Modelling

  Development of regression and predictive models for engineering responses, from interpretable linear models to more flexible approaches, with validation designed to detect overfitting and extrapolation risk.

• Multi-Objective Optimisation

  Optimisation with conflicting objectives, such as cost, weight and performance, producing Pareto-optimal trade-off sets rather than a single answer.