Design-Expert 25 supports planned experiments for learning which factors matter and finding useful operating conditions. Define the decision first, then connect the design, measured responses, fitted models, and confirmation runs.
A useful design expert workflow begins with a question that the available experiment can answer. State whether the next study must screen factors, describe curvature, formulate a blend, or refine an existing region.
Record these decisions before allocating runs:
- Response definitions, measurement units, and acceptance limits.
- Controllable factors and the ranges the process can actually reach.
- Mixture components, if proportions must total a fixed amount.
- Restrictions on run order or combinations of settings.
- Available runs, including replication and confirmation work.
- Model terms needed to support the intended conclusion.
Design-Expert DOE software includes a Design Wizard that guides design choice within the experimental budget. Use the version 25 documentation to distinguish the available study types and evaluation tools.
The accompanying files belong to PyDOE, an independent Python package used here to illustrate DOE methods. The Python examples run externally; embedded Python integration in Stat-Ease documentation is identified as a Stat-Ease 360 feature.
PyDOE separates polynomial model construction in model.py from design generation in optimal.py. Its criterion.py and efficiency.py illustrate how design assessment depends on the model and criterion.
Keep the chosen model and feasible region attached to any efficiency comparison. A favorable design score does not establish the quality of response measurements.
Use factorial screening to investigate several factors together. Before interpreting an effect, establish which other effects may be aliased with it in the selected fraction.
Distinguish the following in the experiment record:
- Standard design order and the actual execution order.
- Intended settings and achieved settings.
- Independent experimental replicates and repeated instrument readings.
- Treatment effects and planned block effects.
For an external illustration, this PyDOE example creates a three-factor two-level matrix and maps it to illustrative physical settings. The columns represent temperature in degrees Celsius, time in minutes, and speed in rpm; substitute justified ranges before using any experimental plan.
import numpy as np
from pydoe import ff2n
coded = ff2n(3)
low, high = np.array([30, 5, 100]), np.array([50, 15, 200])
settings = low + (coded + 1) * (high - low) / 2
print(settings)This matrix has eight treatment combinations. It does not include a randomized execution schedule, blocks, or independent replicates.
PyDOE's factorial.py implements full and fractional factorial construction. plackett_burman.py provides another screening construction, while fold.py illustrates foldover augmentation. Compare blocking separately through blocking.py; selected construction cases appear in test_factorial.py.
In Design-Expert, retain the aliasing information with the interpretation of a screening result. If two explanations remain indistinguishable, use follow-up runs that address that ambiguity.
A response-surface study asks how the response changes across a region. Check the reachability of every proposed point before committing materials or machine time.
Center runs, axial points, and factorial points have different roles in a central composite design. The axial distance determines whether some settings extend beyond the factorial portion.
For an external geometry comparison, PyDOE can generate a face-centered central composite design:
from pydoe import ccdesign
coded_rsm = ccdesign(3, center=(3, 3), face="ccf")
print(coded_rsm.min(axis=0))
print(coded_rsm.max(axis=0))The coordinates are coded levels, not physical temperatures or concentrations. A face-centered choice places axial points on the factor bounds; other central composite choices can produce different ranges. Review the design's statistical properties as well as its physical feasibility.
PyDOE assembles these designs in central_composite.py, with axial geometry in star.py. Repeated centers are constructed in center_design.py. A different response-surface arrangement appears in box_behnken.py, and example composite matrices appear in test_composite.py.
After fitting a suitable Design-Expert model, inspect contour and surface plots within the studied region. When displaying two factors, record the fixed values of the others. A different fixed-factor setting can produce a different slice of the same fitted model.
Avoid presenting extrapolated settings as though they had been covered by the experiment. Record any proposed extension as a separate experimental decision.
Mixture components share a total. Increasing one proportion requires a corresponding change elsewhere, so component proportions cannot all vary independently.
Define the total consistently as fractions, percentages, or another stated basis. Specify individual component bounds and any additional restrictions before choosing blend points.
In the supplied PyDOE references, simplex.py constructs standard simplex designs. extreme_vertices.py addresses component bounds, while axial.py illustrates mixture screening points.
For a basic independent check of a three-component fractional recipe, use Python's standard library:
from math import isclose
blend = {"binder": 0.45, "filler": 0.35, "additive": 0.20}
valid = all(0 <= value <= 1 for value in blend.values())
valid = valid and isclose(sum(blend.values()), 1.0, abs_tol=1e-9)
print("Valid fractional total:", valid)The check covers nonnegative fractions and their total. Apply the actual ingredient bounds and compatibility restrictions separately.
Temperature and mixing time are process variables rather than mixture proportions. PyDOE illustrates crossing those variable types in process.py; construction checks are collected in test_mixture.py.
In Design-Expert, choose the study structure that represents the formulation and process factors together. Keep the component basis visible when interpreting coefficients or comparing recipes.
Analyze each measured response separately in Design-Expert. Choose the model, inspect ANOVA, and review diagnostics before relying on its predictions.
Use the documented analysis sequence to connect the Fit Summary, model selection, diagnostics, and interpretation.
| Evidence | Interpretation to examine |
|---|---|
| Model terms and hierarchy | Whether the chosen terms express a defensible relationship |
| Lack of fit, when estimable | Whether model discrepancy is large relative to the available pure-error estimate |
| Residuals against predicted values | Whether the spread or structure suggests an inadequate model |
| Residuals against execution order | Whether drift or another time-related effect remains |
| Unusual observations | Whether measurement, execution, or genuine process behavior explains them |
Investigate an unusual result against the experiment log before excluding it. Record the reason for any exclusion and retain the original observation.
The supplied build_regression_matrix.py illustrates expansion from factor coordinates into regression terms. That distinction matters: a run table and a fitted model matrix do not contain the same information.
A high fit statistic alone does not establish useful prediction. Keep the diagnostics, experimental coverage, and practical interpretation together when accepting a response model.
Set goals and limits for each response before comparing numerical solutions. Design-Expert's optimization tools search for factor combinations that satisfy the modeled criteria. Graphical optimization can help examine an acceptable region alongside numerical candidates.
Treat desirability as a summary of the goals entered. Changing a response limit or priority changes the optimization question.
For each candidate, retain:
- Actual factor settings or component proportions.
- Predicted responses and applicable interval estimates.
- The goals, limits, and priorities used in optimization.
- Practical restrictions that may favor a nearby operating point.
- The conditions and measurements of independent confirmation runs.
Use the post-analysis tools to connect point prediction with confirmation. Compare new measurements with the appropriate model-based interval and the practical acceptance limits.
If confirmation is unsatisfactory, investigate execution and model adequacy before adopting the candidate. Preserve the design, measured data, analysis choices, and confirmation record so that the next study can build on them.
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