Summary
This experiment investigates acrylic pour technique. Box-Behnken design to maximize cell formation and color separation by tuning silicone amount, paint consistency, and tilt angle.
The design varies 3 factors: silicone drops (drops), ranging from 1 to 8, consistency (level), ranging from 1 to 5, and tilt deg (deg), ranging from 5 to 30. The goal is to optimize 2 responses: cell count (per_100cm2) (maximize) and color separation (pts) (maximize). Fixed conditions held constant across all runs include medium = floetrol, base = titanium_white.
A Box-Behnken design was chosen because it efficiently fits quadratic models with 3 continuous factors while avoiding extreme corner combinations — requiring only 15 runs instead of the 8 needed for a full factorial at two levels.
Quadratic response surface models were fitted to capture potential curvature and factor interactions. The RSM contour plots below visualize how pairs of factors jointly affect each response.
Key Findings
For cell count, the most influential factors were silicone drops (53.4%), consistency (24.0%), tilt deg (22.7%). The best observed value was 25.0 (at silicone drops = 1, consistency = 5, tilt deg = 17.5).
For color separation, the most influential factors were silicone drops (52.6%), consistency (35.2%), tilt deg (12.3%). The best observed value was 7.0 (at silicone drops = 4.5, consistency = 3, tilt deg = 17.5).
Recommended Next Steps
- Run confirmation experiments at the predicted optimal settings to validate the model.
- Consider whether any fixed factors should be varied in a future study.
Experimental Setup
Factors
| Factor | Low | High | Unit |
|---|
silicone_drops | 1 | 8 | drops |
consistency | 1 | 5 | level |
tilt_deg | 5 | 30 | deg |
Fixed: medium = floetrol, base = titanium_white
Responses
| Response | Direction | Unit |
|---|
cell_count | ↑ maximize | per_100cm2 |
color_separation | ↑ maximize | pts |
Configuration
{
"metadata": {
"name": "Acrylic Pour Technique",
"description": "Box-Behnken design to maximize cell formation and color separation by tuning silicone amount, paint consistency, and tilt angle"
},
"factors": [
{
"name": "silicone_drops",
"levels": [
"1",
"8"
],
"type": "continuous",
"unit": "drops"
},
{
"name": "consistency",
"levels": [
"1",
"5"
],
"type": "continuous",
"unit": "level"
},
{
"name": "tilt_deg",
"levels": [
"5",
"30"
],
"type": "continuous",
"unit": "deg"
}
],
"fixed_factors": {
"medium": "floetrol",
"base": "titanium_white"
},
"responses": [
{
"name": "cell_count",
"optimize": "maximize",
"unit": "per_100cm2"
},
{
"name": "color_separation",
"optimize": "maximize",
"unit": "pts"
}
],
"settings": {
"operation": "box_behnken",
"test_script": "use_cases/283_acrylic_pour/sim.sh"
}
}
Experimental Matrix
The Box-Behnken Design produces 15 runs. Each row is one experiment with specific factor settings.
| Run | silicone_drops | consistency | tilt_deg |
|---|
| 1 | 4.5 | 1 | 5 |
| 2 | 4.5 | 3 | 17.5 |
| 3 | 8 | 3 | 30 |
| 4 | 8 | 3 | 5 |
| 5 | 4.5 | 3 | 17.5 |
| 6 | 4.5 | 3 | 17.5 |
| 7 | 1 | 3 | 30 |
| 8 | 8 | 1 | 17.5 |
| 9 | 4.5 | 1 | 30 |
| 10 | 8 | 5 | 17.5 |
| 11 | 1 | 3 | 5 |
| 12 | 4.5 | 5 | 30 |
| 13 | 1 | 1 | 17.5 |
| 14 | 1 | 5 | 17.5 |
| 15 | 4.5 | 5 | 5 |
Step-by-Step Workflow
1
Preview the design
$ doe info --config use_cases/283_acrylic_pour/config.json
2
Generate the runner script
$ doe generate --config use_cases/283_acrylic_pour/config.json \
--output use_cases/283_acrylic_pour/results/run.sh --seed 42
3
Execute the experiments
$ bash use_cases/283_acrylic_pour/results/run.sh
4
Analyze results
$ doe analyze --config use_cases/283_acrylic_pour/config.json
5
Get optimization recommendations
$ doe optimize --config use_cases/283_acrylic_pour/config.json
6
Multi-objective optimization
With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.
$ doe optimize --config use_cases/283_acrylic_pour/config.json --multi
7
Generate the HTML report
$ doe report --config use_cases/283_acrylic_pour/config.json \
--output use_cases/283_acrylic_pour/results/report.html
Features Exercised
| Feature | Value |
|---|
| Design type | box_behnken |
| Factor types | continuous (all 3) |
| Arg style | double-dash |
| Responses | 2 (cell_count ↑, color_separation ↑) |
| Total runs | 15 |
Analysis Results
Generated from actual experiment runs using the DOE Helper Tool.
Response: cell_count
Top factors: silicone_drops (53.4%), consistency (24.0%), tilt_deg (22.7%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|
| Source | DF | SS | MS | F | p-value |
| silicone_drops | 2 | 263.4762 | 131.7381 | 4.343 | 0.0528 |
| consistency | 2 | 61.1548 | 30.5774 | 1.008 | 0.4070 |
| tilt_deg | 2 | 58.1548 | 29.0774 | 0.959 | 0.4235 |
| Lack | of | Fit | 6 | 239.8810 | 39.9802 |
| Pure | Error | 2 | 60.6667 | | |
| Error | 8 | 300.5476 | 30.3333 | | |
| Total | 14 | 683.3333 | 48.8095 | | |
Pareto Chart
Main Effects Plot
Normal Probability Plot of Effects
Half-Normal Plot of Effects
Model Diagnostics
Response: color_separation
Top factors: silicone_drops (52.6%), consistency (35.2%), tilt_deg (12.3%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|
| Source | DF | SS | MS | F | p-value |
| silicone_drops | 2 | 2.2533 | 1.1266 | 3.380 | 0.0863 |
| consistency | 2 | 1.3308 | 0.6654 | 1.996 | 0.1980 |
| tilt_deg | 2 | 0.1933 | 0.0966 | 0.290 | 0.7559 |
| Lack | of | Fit | 6 | 5.4654 | 0.9109 |
| Pure | Error | 2 | 0.6667 | | |
| Error | 8 | 6.1320 | 0.3333 | | |
| Total | 14 | 9.9093 | 0.7078 | | |
Pareto Chart
Main Effects Plot
Normal Probability Plot of Effects
Half-Normal Plot of Effects
Model Diagnostics
Response Surface Plots
3D surfaces fitted with quadratic RSM. Red dots are observed data points.
cell count consistency vs tilt deg
cell count silicone drops vs consistency
cell count silicone drops vs tilt deg
color separation consistency vs tilt deg
color separation silicone drops vs consistency
color separation silicone drops vs tilt deg
Multi-Objective Optimization
When responses compete, Derringer–Suich desirability finds the best compromise.
Each response is scaled to a 0–1 desirability, then combined via a weighted geometric mean.
Overall Desirability
D = 0.8949
Per-Response Desirability
| Response | Weight | Desirability | Predicted | Dir |
|---|
cell_count |
1.0 |
|
25.00 0.9545 25.00 per_100cm2 |
↑ |
color_separation |
1.5 |
|
6.70 0.8571 6.70 pts |
↑ |
Recommended Settings
| Factor | Value |
|---|
silicone_drops | 8 drops |
consistency | 3 level |
tilt_deg | 30 deg |
Source: from observed run #3
Trade-off Summary
Sacrifice = how much worse than single-objective best.
| Response | Predicted | Best Observed | Sacrifice |
|---|
color_separation | 6.70 | 7.00 | +0.30 |
Top 3 Runs by Desirability
| Run | D | Factor Settings |
|---|
| #12 | 0.8515 | silicone_drops=1, consistency=1, tilt_deg=17.5 |
| #8 | 0.7331 | silicone_drops=1, consistency=3, tilt_deg=30 |
Model Quality
| Response | R² | Type |
|---|
color_separation | 0.7086 | quadratic |
Full Multi-Objective Output
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================
Overall desirability: D = 0.8949
Response Weight Desirability Predicted Direction
---------------------------------------------------------------------
cell_count 1.0 0.9545 25.00 per_100cm2 ↑
color_separation 1.5 0.8571 6.70 pts ↑
Recommended settings:
silicone_drops = 8 drops
consistency = 3 level
tilt_deg = 30 deg
(from observed run #3)
Trade-off summary:
cell_count: 25.00 (best observed: 25.00, sacrifice: +0.00)
color_separation: 6.70 (best observed: 7.00, sacrifice: +0.30)
Model quality:
cell_count: R² = 0.1687 (linear)
color_separation: R² = 0.7086 (quadratic)
Top 3 observed runs by overall desirability:
1. Run #3 (D=0.8949): silicone_drops=8, consistency=3, tilt_deg=30
2. Run #12 (D=0.8515): silicone_drops=1, consistency=1, tilt_deg=17.5
3. Run #8 (D=0.7331): silicone_drops=1, consistency=3, tilt_deg=30
Full Analysis Output
=== Main Effects: cell_count ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
silicone_drops 10.5000 1.8039 53.4%
consistency 4.7143 1.8039 24.0%
tilt_deg 4.4643 1.8039 22.7%
=== ANOVA Table: cell_count ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
silicone_drops 2 263.4762 131.7381 4.343 0.0528
consistency 2 61.1548 30.5774 1.008 0.4070
tilt_deg 2 58.1548 29.0774 0.959 0.4235
Lack of Fit 6 239.8810 39.9802 1.318 0.4916
Pure Error 2 60.6667 30.3333
Error 8 300.5476 30.3333
Total 14 683.3333 48.8095
=== Summary Statistics: cell_count ===
silicone_drops:
Level N Mean Std Min Max
------------------------------------------------------------
1 4 6.5000 6.6081 2.0000 16.0000
4.5 7 15.1429 5.7570 7.0000 23.0000
8 4 17.0000 5.4772 13.0000 25.0000
consistency:
Level N Mean Std Min Max
------------------------------------------------------------
1 4 14.2500 8.8081 2.0000 23.0000
3 7 11.2857 7.8680 2.0000 25.0000
5 4 16.0000 2.4495 13.0000 19.0000
tilt_deg:
Level N Mean Std Min Max
------------------------------------------------------------
17.5 7 11.2857 5.7071 2.0000 17.0000
30 4 14.5000 9.1104 2.0000 23.0000
5 4 15.7500 7.7621 6.0000 25.0000
=== Main Effects: color_separation ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
silicone_drops 1.0250 0.2172 52.6%
consistency 0.6857 0.2172 35.2%
tilt_deg 0.2393 0.2172 12.3%
=== ANOVA Table: color_separation ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
silicone_drops 2 2.2533 1.1266 3.380 0.0863
consistency 2 1.3308 0.6654 1.996 0.1980
tilt_deg 2 0.1933 0.0966 0.290 0.7559
Lack of Fit 6 5.4654 0.9109 2.733 0.2920
Pure Error 2 0.6667 0.3333
Error 8 6.1320 0.3333
Total 14 9.9093 0.7078
=== Summary Statistics: color_separation ===
silicone_drops:
Level N Mean Std Min Max
------------------------------------------------------------
1 4 5.3000 0.8083 4.2000 6.0000
4.5 7 6.0143 0.5956 5.0000 7.0000
8 4 6.3250 1.0905 4.7000 7.0000
consistency:
Level N Mean Std Min Max
------------------------------------------------------------
1 4 5.7500 0.7141 4.7000 6.3000
3 7 5.7143 0.9668 4.2000 6.9000
5 4 6.4000 0.6928 5.8000 7.0000
tilt_deg:
Level N Mean Std Min Max
------------------------------------------------------------
17.5 7 5.7857 0.7537 4.7000 7.0000
30 4 6.0250 1.2971 4.2000 7.0000
5 4 6.0000 0.6481 5.2000 6.7000
Optimization Recommendations
=== Optimization: cell_count ===
Direction: maximize
Best observed run: #3
silicone_drops = 1
consistency = 5
tilt_deg = 17.5
Value: 25.0
RSM Model (linear, R² = 0.0091, Adj R² = -0.2611):
Coefficients:
intercept +13.3333
silicone_drops +0.6250
consistency -0.6250
tilt_deg -0.0000
RSM Model (quadratic, R² = 0.8867, Adj R² = 0.6828):
Coefficients:
intercept +15.3333
silicone_drops +0.6250
consistency -0.6250
tilt_deg +0.0000
silicone_drops*consistency -9.5000
silicone_drops*tilt_deg -3.7500
consistency*tilt_deg -1.2500
silicone_drops^2 -4.6667
consistency^2 +3.8333
tilt_deg^2 -2.9167
Curvature analysis:
silicone_drops coef=-4.6667 concave (has a maximum)
consistency coef=+3.8333 convex (has a minimum)
tilt_deg coef=-2.9167 concave (has a maximum)
Notable interactions:
silicone_drops*consistency coef=-9.5000 (antagonistic)
silicone_drops*tilt_deg coef=-3.7500 (antagonistic)
consistency*tilt_deg coef=-1.2500 (antagonistic)
Predicted optimum (from quadratic model, at observed points):
silicone_drops = 8
consistency = 1
tilt_deg = 17.5
Predicted value: 25.2500
Surface optimum (via L-BFGS-B, quadratic model):
silicone_drops = 8
consistency = 1
tilt_deg = 12.1429
Predicted value: 25.7857
Model quality: Good fit — general trends are captured, some noise remains.
Factor importance:
1. silicone_drops (effect: 5.4, contribution: 40.5%)
2. consistency (effect: 5.0, contribution: 37.8%)
3. tilt_deg (effect: 2.9, contribution: 21.6%)
=== Optimization: color_separation ===
Direction: maximize
Best observed run: #9
silicone_drops = 4.5
consistency = 3
tilt_deg = 17.5
Value: 7.0
RSM Model (linear, R² = 0.4173, Adj R² = 0.2584):
Coefficients:
intercept +5.9067
silicone_drops -0.5750
consistency -0.4250
tilt_deg +0.0750
RSM Model (quadratic, R² = 0.7699, Adj R² = 0.3558):
Coefficients:
intercept +6.1000
silicone_drops -0.5750
consistency -0.4250
tilt_deg +0.0750
silicone_drops*consistency -0.6250
silicone_drops*tilt_deg +0.1250
consistency*tilt_deg -0.0250
silicone_drops^2 -0.6375
consistency^2 +0.2625
tilt_deg^2 +0.0125
Curvature analysis:
silicone_drops coef=-0.6375 concave (has a maximum)
consistency coef=+0.2625 convex (has a minimum)
tilt_deg coef=+0.0125 negligible curvature
Notable interactions:
silicone_drops*consistency coef=-0.6250 (antagonistic)
Predicted optimum (from quadratic model, at observed points):
silicone_drops = 4.5
consistency = 1
tilt_deg = 30
Predicted value: 6.9000
Surface optimum (via L-BFGS-B, quadratic model):
silicone_drops = 4.98039
consistency = 1
tilt_deg = 30
Predicted value: 6.9120
Model quality: Good fit — general trends are captured, some noise remains.
Factor importance:
1. silicone_drops (effect: 1.2, contribution: 55.2%)
2. consistency (effect: 0.8, contribution: 38.1%)
3. tilt_deg (effect: 0.2, contribution: 6.7%)