Documentation / Studies / Design of experiments

I — The bench

An experiment is designed before it is run

A design is decided while there is still nothing to analyze. The DOE bench holds that gap the same way the gage bench does: it takes the factors and their real settings, generates the design, issues a randomized run sheet in the operator’s own units, and fits the effects when the numbers come back from the line.

Ref: Montgomery, Design and Analysis of Experiments, 8th Ed.
AvailabilityIn the running product
AccountPro tier and above
DesignsSeven families
Ceiling4,096 runs
declare factors in real units
  → generate a design (coded matrix + decoded settings)
  → carry the randomized run sheet to the line
  → record responses by standard order
  → fit the effects through the engine

II — The declaration

FieldBehavior
factorsEach carries a name, its units, and its low and high setting — the values as they exist on the machine rather than coded levels.
responseWhat is measured, and in what units. A design is agnostic to the response; a study is not.
objectiveWhat the experiment is meant to settle, in words. It travels with the study rather than living in someone’s notebook.
designOne of the seven families below. An unrecognised name is refused and listed back, never quietly resolved to something adjacent.
optionsResolution, center points, levels and whether the run order is randomized — passed to the generator only when supplied.

III — The seven designs

DesignReached for when
Full factorialFew factors, and every interaction matters. Refused past 12 factors, which is 4,096 runs, with a pointer at screening instead.
Fractional factorialMore factors than the available run budget; resolution decides which effects alias onto which.
Plackett–BurmanMany factors, main effects only, the smallest screening run count.
Definitive screeningScreening that does not confound main effects with two-factor interactions, and can detect curvature.
Central compositeResponse surface work: quadratic terms and an optimum rather than a ranking.
Box–BehnkenResponse surface without the axial points, when the corners of the region are not runnable.
TaguchiOrthogonal arrays in the robust-design tradition.
Mixture and split-plot designs are not generated. Split-plot analysis is available, in two forms, and is described in section VI, but the bench does not lay out mixture or split-plot experiments. The list above is a whitelist rather than a catalog, deliberately: the engine knows more design theory than this bench exposes, and exposing it is a decision rather than an oversight.

IV — The run sheet

A generated design comes back twice over: the coded matrix that the statistics are done in, and the decoded settings in the units the operator will dial in. Fractional designs also return their defining relation and alias structure, so what is confounded with what is readable before the experiment is run rather than discovered afterwards.

The generated design is stored rather than regenerated. That is the whole reason the study keeps state: a randomized order recomputed between printing the sheet and reading the results back would silently misalign every measurement with the run it belongs to. Re-generating over a study that already has responses recorded against it is refused for the same reason.

V — Recording results

Responses are keyed by standard order. Standard order is the design’s own identity for a row; run position is only where that row landed on this particular sheet. Filing by standard order is what lets a randomization be re-read, or a sheet be reprinted, without the measurements moving under it, and it is what the fit pairs against.

VI — The fit

Recorded results are fitted through the same engine door as every other analysis in SVEND, returning the effects with the design that produced them rather than as a bare regression on a table of numbers.

Split-plot experiments are fitted by two separate laws, kept deliberately apart. The balanced form reads each stratum’s error from the symmetry of the design itself. The REML form estimates the variance components instead, which is what a real plant needs when the whole plots are unequal or runs were lost, the ordinary condition rather than the exceptional one.

VII — Boundaries

  1. 4,096 runs is the ceiling. A physical experiment does not exceed it, and a request for one must not occupy a worker building it.
  2. Constrained and irregular design regions are not supported. Factor ranges are independent low/high settings; a region containing an unrunnable corner is not expressible.
  3. Optimal designs are not generated here. D-, I- and A-optimal construction is engine territory the bench does not expose.
  4. The bench designs and fits; it does not select. Choosing a design against a budget and a set of assumptions remains the experimenter’s judgment.