Sequential design-of-experiments case study in R.
Individual graduate applied-statistics project focused on improving the yield of an instructor-provided chemical-process model.
I designed and analyzed six sequential experiments under a 75-run budget. Each experiment informed the next, moving from broad eight-factor screening to a focused response-surface study and confirmation testing.
Result: improved confirmed mean yield from an approximately 50% baseline to 90.88%.
Identify influential process factors and determine a high-yield operating region while using limited experimental runs efficiently.
The process included eight continuous factors, labeled A through H.
- Initial screening: 16-run Resolution IV fractional-factorial design across eight factors
- Follow-up factorial: 8-run study focused on B, D, and F
- B-level refinement: 4-run comparison to refine factor B
- Regional factorial study: 8-run factorial design plus 4 center-point replicates for B, E, and G
- Response-surface expansion: 6 axial runs completing a face-centered central composite design
- Confirmation: 12 independent runs at the selected operating setting
Total experimental runs used: 58 of 75 available
- Fractional-factorial screening
- Lenth's pseudo standard error for unreplicated designs
- Factorial effect and interaction analysis
- Center-point analysis
- Face-centered central composite design
- Quadratic response-surface modeling
- Stationary-point analysis
- Confirmation runs with confidence and prediction intervals
| Metric | Result |
|---|---|
| Experimental-run budget | 75 runs |
| Experimental runs used | 58 runs |
| Selected confirmation setting | B = 5, E = 7.5, G = 5 |
| Quadratic-model predicted yield | 91.54% |
| Confirmation-run mean yield | 90.88% |
| 95% confidence interval for mean yield | 89.94% to 91.82% |
| 95% prediction interval for one future run | 87.51% to 94.25% |
The quadratic response-surface model identified a promising operating region rather than a clean interior optimum. The stationary point was classified as a saddle point, so the selected setting was validated through independent confirmation runs.
The contour plot shows modeled yield across factors B and E while holding G at 5. The black point marks the selected confirmation setting.
Twelve confirmation runs at the selected setting produced a mean yield of 90.88%.
r/
01_initial_screening.R
02_follow_up_factorial.R
03_b_refinement.R
04_factorial_center_points.R
05_axial_runs.R
06_quadratic_response_surface.R
07_confirmation_runs.R
08_generate_portfolio_outputs.R
outputs/
figures/
confirmation_runs.png
predicted_yield_contours.png
tables/
key_results.csv
run_all.R
Open the project in RStudio and run:
source("run_all.R")
source("r/08_generate_portfolio_outputs.R")All response data are embedded in the scripts, so the analysis can be reproduced without external files.
R, experimental design, factorial analysis, response-surface methodology, regression diagnostics, and data visualization.
Download the complete applied-statistics report (PDF)
This is an educational case study based on an instructor-provided chemical-process model. It is not a real industrial deployment or production recommendation.
Ali Hasanov