In This Guide
A proposed central composite plan can introduce factor settings beyond earlier low/high levels. Review the physical axial points before treating a matrix as executable.
The statistical question
A central composite design augments a factorial portion with center and axial, or star, points. Circumscribed, inscribed and face-centered versions place those points differently. In a circumscribed form, axial coordinates can exceed the original coded low/high range. A design chosen for statistical properties must still be mapped to physical settings and checked against the permitted trial region.
An illustrative review example
Suppose fictional factor A uses center 50 units and scale 10 units per coded step. Original coded limits of minus one and plus one map to 40 and 60. A proposed axial distance of 1.5 maps to 35 and 65 units. Those points extend beyond the earlier range. The calculation explains the coordinate map only; it does not authorize those values or recommend an axial distance for a real process.
Prepare the evidence for discussion
Retain the design type, axial distance, physical transformation and authorized limits for every factor. Ask the trial owner whether a different design or scaling is required when a proposed point is infeasible. Include combined-factor restrictions as well as individual bounds. Do not trim inconvenient runs and continue claiming the original design properties without statistical review. Keep the final approved matrix and executed settings linked.
Map star points before approval
This blank worksheet is for your own project. It contains no H M machine trial result.
| Question to resolve | Evidence to retain |
|---|---|
| Design version | Circumscribed, inscribed or face-centered |
| Axial coordinate | Stated distance from center |
| Physical mapping | Center plus coordinate times scale |
| Feasibility | Approved individual and combined bounds |
Customer Questions
Can star points lie outside earlier low/high settings?
They can in a circumscribed design; the specific design type and scaling determine their positions.
Does a statistical design authorize a machine setting?
No. Physical limits and trial authorization must be reviewed separately.
Can infeasible points simply be removed without review?
Changing the matrix can change its estimation and design properties.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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