Summary
This experiment investigates salad dressing emulsion stability. Plackett-Burman screening of oil ratio, vinegar acidity, mustard, egg yolk, blending speed, and temperature for emulsion stability and taste.
The design varies 6 factors: oil ratio (%), ranging from 50 to 80, vinegar acidity (%), ranging from 4 to 7, mustard g (g), ranging from 2 to 15, egg yolk count (count), ranging from 0 to 3, blend speed (rpm), ranging from 5000 to 20000, and mix temp (C), ranging from 5 to 25. The goal is to optimize 2 responses: stability hrs (hrs) (maximize) and taste score (pts) (maximize). Fixed conditions held constant across all runs include total volume ml = 500, salt g = 3.
A Plackett-Burman screening design was used to efficiently test 6 factors in only 8 runs. This design assumes interactions are negligible and focuses on identifying the most influential main effects.
Key Findings
For stability hrs, the most influential factors were oil ratio (38.0%), blend speed (36.7%), mix temp (15.3%). The best observed value was 97.0 (at oil ratio = 50, vinegar acidity = 7, mustard g = 2).
For taste score, the most influential factors were mustard g (29.6%), egg yolk count (28.4%), blend speed (22.2%). The best observed value was 8.2 (at oil ratio = 50, vinegar acidity = 7, mustard g = 2).
Recommended Next Steps
- Follow up with a response surface design (CCD or Box-Behnken) on the top 3–4 factors to model curvature and find the true optimum.
- Consider whether any fixed factors should be varied in a future study.
- The screening results can guide factor reduction — drop factors contributing less than 5% and re-run with a smaller, more focused design.
Experimental Setup
Factors
| Factor | Low | High | Unit |
|---|---|---|---|
oil_ratio | 50 | 80 | % |
vinegar_acidity | 4 | 7 | % |
mustard_g | 2 | 15 | g |
egg_yolk_count | 0 | 3 | count |
blend_speed | 5000 | 20000 | rpm |
mix_temp | 5 | 25 | C |
Fixed: total_volume_ml = 500, salt_g = 3
Responses
| Response | Direction | Unit |
|---|---|---|
stability_hrs | ↑ maximize | hrs |
taste_score | ↑ maximize | pts |
Configuration
use_cases/93_salad_dressing_emulsion/config.json
{
"metadata": {
"name": "Salad Dressing Emulsion Stability",
"description": "Plackett-Burman screening of oil ratio, vinegar acidity, mustard, egg yolk, blending speed, and temperature for emulsion stability and taste"
},
"factors": [
{
"name": "oil_ratio",
"levels": [
"50",
"80"
],
"type": "continuous",
"unit": "%"
},
{
"name": "vinegar_acidity",
"levels": [
"4",
"7"
],
"type": "continuous",
"unit": "%"
},
{
"name": "mustard_g",
"levels": [
"2",
"15"
],
"type": "continuous",
"unit": "g"
},
{
"name": "egg_yolk_count",
"levels": [
"0",
"3"
],
"type": "continuous",
"unit": "count"
},
{
"name": "blend_speed",
"levels": [
"5000",
"20000"
],
"type": "continuous",
"unit": "rpm"
},
{
"name": "mix_temp",
"levels": [
"5",
"25"
],
"type": "continuous",
"unit": "C"
}
],
"fixed_factors": {
"total_volume_ml": "500",
"salt_g": "3"
},
"responses": [
{
"name": "stability_hrs",
"optimize": "maximize",
"unit": "hrs"
},
{
"name": "taste_score",
"optimize": "maximize",
"unit": "pts"
}
],
"settings": {
"operation": "plackett_burman",
"test_script": "use_cases/93_salad_dressing_emulsion/sim.sh"
}
}
Experimental Matrix
The Plackett-Burman Design produces 8 runs. Each row is one experiment with specific factor settings.
| Run | oil_ratio | vinegar_acidity | mustard_g | egg_yolk_count | blend_speed | mix_temp |
|---|---|---|---|---|---|---|
| 1 | 80 | 7 | 15 | 0 | 5000 | 5 |
| 2 | 50 | 4 | 15 | 3 | 5000 | 5 |
| 3 | 50 | 7 | 2 | 3 | 5000 | 25 |
| 4 | 80 | 7 | 15 | 3 | 20000 | 25 |
| 5 | 50 | 7 | 2 | 0 | 20000 | 5 |
| 6 | 80 | 4 | 2 | 3 | 20000 | 5 |
| 7 | 50 | 4 | 15 | 0 | 20000 | 25 |
| 8 | 80 | 4 | 2 | 0 | 5000 | 25 |
Step-by-Step Workflow
1
Preview the design
Terminal
$ doe info --config use_cases/93_salad_dressing_emulsion/config.json
2
Generate the runner script
Terminal
$ doe generate --config use_cases/93_salad_dressing_emulsion/config.json \
--output use_cases/93_salad_dressing_emulsion/results/run.sh --seed 42
3
Execute the experiments
Terminal
$ bash use_cases/93_salad_dressing_emulsion/results/run.sh
4
Analyze results
Terminal
$ doe analyze --config use_cases/93_salad_dressing_emulsion/config.json
5
Get optimization recommendations
Terminal
$ doe optimize --config use_cases/93_salad_dressing_emulsion/config.json
6
Multi-objective optimization
With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.
Terminal
$ doe optimize --config use_cases/93_salad_dressing_emulsion/config.json --multi
7
Generate the HTML report
Terminal
$ doe report --config use_cases/93_salad_dressing_emulsion/config.json \
--output use_cases/93_salad_dressing_emulsion/results/report.html
Features Exercised
| Feature | Value |
|---|---|
| Design type | plackett_burman |
| Factor types | continuous (all 6) |
| Arg style | double-dash |
| Responses | 2 (stability_hrs ↑, taste_score ↑) |
| Total runs | 8 |
Analysis Results
Generated from actual experiment runs using the DOE Helper Tool.
Response: stability_hrs
Top factors: oil_ratio (38.0%), blend_speed (36.7%), mix_temp (15.3%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|
| Source | DF | SS | MS | F | p-value |
| oil_ratio | 1 | 1624.5000 | 1624.5000 | 38.336 | 0.0004 |
| vinegar_acidity | 1 | 24.5000 | 24.5000 | 0.578 | 0.4719 |
| mustard_g | 1 | 32.0000 | 32.0000 | 0.755 | 0.4136 |
| egg_yolk_count | 1 | 0.0000 | 0.0000 | 0.000 | 1.0000 |
| blend_speed | 1 | 1512.5000 | 1512.5000 | 35.693 | 0.0006 |
| mix_temp | 1 | 264.5000 | 264.5000 | 6.242 | 0.0411 |
| oil_ratio*vinegar_acidity | 1 | 32.0000 | 32.0000 | 0.755 | 0.4136 |
| oil_ratio*mustard_g | 1 | 24.5000 | 24.5000 | 0.578 | 0.4719 |
| oil_ratio*egg_yolk_count | 1 | 1512.5000 | 1512.5000 | 35.693 | 0.0006 |
| oil_ratio*blend_speed | 1 | 0.0000 | 0.0000 | 0.000 | 1.0000 |
| oil_ratio*mix_temp | 1 | 2312.0000 | 2312.0000 | 54.560 | 0.0002 |
| vinegar_acidity*mustard_g | 1 | 1624.5000 | 1624.5000 | 38.336 | 0.0004 |
| vinegar_acidity*egg_yolk_count | 1 | 264.5000 | 264.5000 | 6.242 | 0.0411 |
| vinegar_acidity*blend_speed | 1 | 2312.0000 | 2312.0000 | 54.560 | 0.0002 |
| vinegar_acidity*mix_temp | 1 | 0.0000 | 0.0000 | 0.000 | 1.0000 |
| mustard_g*egg_yolk_count | 1 | 2312.0000 | 2312.0000 | 54.560 | 0.0002 |
| mustard_g*blend_speed | 1 | 264.5000 | 264.5000 | 6.242 | 0.0411 |
| mustard_g*mix_temp | 1 | 1512.5000 | 1512.5000 | 35.693 | 0.0006 |
| egg_yolk_count*blend_speed | 1 | 1624.5000 | 1624.5000 | 38.336 | 0.0004 |
| egg_yolk_count*mix_temp | 1 | 24.5000 | 24.5000 | 0.578 | 0.4719 |
| blend_speed*mix_temp | 1 | 32.0000 | 32.0000 | 0.755 | 0.4136 |
| Error | (Lenth | PSE) | 7 | 296.6250 | 42.3750 |
| Total | 7 | 5770.0000 | 824.2857 |
Pareto Chart
Main Effects Plot
Normal Probability Plot of Effects
Half-Normal Plot of Effects
Model Diagnostics
Response: taste_score
Top factors: mustard_g (29.6%), egg_yolk_count (28.4%), blend_speed (22.2%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|
| Source | DF | SS | MS | F | p-value |
| oil_ratio | 1 | 0.0050 | 0.0050 | 0.003 | 0.9581 |
| vinegar_acidity | 1 | 0.0050 | 0.0050 | 0.003 | 0.9581 |
| mustard_g | 1 | 2.8800 | 2.8800 | 1.707 | 0.2327 |
| egg_yolk_count | 1 | 2.6450 | 2.6450 | 1.567 | 0.2508 |
| blend_speed | 1 | 1.6200 | 1.6200 | 0.960 | 0.3598 |
| mix_temp | 1 | 0.9800 | 0.9800 | 0.581 | 0.4709 |
| oil_ratio*vinegar_acidity | 1 | 2.8800 | 2.8800 | 1.707 | 0.2327 |
| oil_ratio*mustard_g | 1 | 0.0050 | 0.0050 | 0.003 | 0.9581 |
| oil_ratio*egg_yolk_count | 1 | 1.6200 | 1.6200 | 0.960 | 0.3598 |
| oil_ratio*blend_speed | 1 | 2.6450 | 2.6450 | 1.567 | 0.2508 |
| oil_ratio*mix_temp | 1 | 1.1250 | 1.1250 | 0.667 | 0.4411 |
| vinegar_acidity*mustard_g | 1 | 0.0050 | 0.0050 | 0.003 | 0.9581 |
| vinegar_acidity*egg_yolk_count | 1 | 0.9800 | 0.9800 | 0.581 | 0.4709 |
| vinegar_acidity*blend_speed | 1 | 1.1250 | 1.1250 | 0.667 | 0.4411 |
| vinegar_acidity*mix_temp | 1 | 2.6450 | 2.6450 | 1.567 | 0.2508 |
| mustard_g*egg_yolk_count | 1 | 1.1250 | 1.1250 | 0.667 | 0.4411 |
| mustard_g*blend_speed | 1 | 0.9800 | 0.9800 | 0.581 | 0.4709 |
| mustard_g*mix_temp | 1 | 1.6200 | 1.6200 | 0.960 | 0.3598 |
| egg_yolk_count*blend_speed | 1 | 0.0050 | 0.0050 | 0.003 | 0.9581 |
| egg_yolk_count*mix_temp | 1 | 0.0050 | 0.0050 | 0.003 | 0.9581 |
| blend_speed*mix_temp | 1 | 2.8800 | 2.8800 | 1.707 | 0.2327 |
| Error | (Lenth | PSE) | 7 | 11.8125 | 1.6875 |
| Total | 7 | 9.2600 | 1.3229 |
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.
stability hrs blend speed vs mix temp
stability hrs egg yolk count vs blend speed
stability hrs egg yolk count vs mix temp
stability hrs mustard g vs blend speed
stability hrs mustard g vs egg yolk count
stability hrs mustard g vs mix temp
stability hrs oil ratio vs blend speed
stability hrs oil ratio vs egg yolk count
stability hrs oil ratio vs mix temp
stability hrs oil ratio vs mustard g
stability hrs oil ratio vs vinegar acidity
stability hrs vinegar acidity vs blend speed
stability hrs vinegar acidity vs egg yolk count
stability hrs vinegar acidity vs mix temp
stability hrs vinegar acidity vs mustard g
taste score blend speed vs mix temp
taste score egg yolk count vs blend speed
taste score egg yolk count vs mix temp
taste score mustard g vs blend speed
taste score mustard g vs egg yolk count
taste score mustard g vs mix temp
taste score oil ratio vs blend speed
taste score oil ratio vs egg yolk count
taste score oil ratio vs mix temp
taste score oil ratio vs mustard g
taste score oil ratio vs vinegar acidity
taste score vinegar acidity vs blend speed
taste score vinegar acidity vs egg yolk count
taste score vinegar acidity vs mix temp
taste score vinegar acidity vs mustard g
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 = 0.9545
Per-Response Desirability
| Response | Weight | Desirability | Predicted | Dir |
|---|---|---|---|---|
stability_hrs |
1.5 |
0.9545
|
97.00 0.9545 97.00 hrs | ↑ |
taste_score |
1.5 |
0.9545
|
8.20 0.9545 8.20 pts | ↑ |
Recommended Settings
| Factor | Value |
|---|---|
oil_ratio | 80 % |
vinegar_acidity | 7 % |
mustard_g | 15 g |
egg_yolk_count | 0 count |
blend_speed | 5000 rpm |
mix_temp | 5 C |
Source: from observed run #4
Trade-off Summary
Sacrifice = how much worse than single-objective best.
| Response | Predicted | Best Observed | Sacrifice |
|---|---|---|---|
taste_score | 8.20 | 8.20 | +0.00 |
Top 3 Runs by Desirability
| Run | D | Factor Settings |
|---|---|---|
| #1 | 0.5421 | oil_ratio=50, vinegar_acidity=4, mustard_g=15, egg_yolk_count=0, blend_speed=20000, mix_temp=25 |
| #2 | 0.5203 | oil_ratio=50, vinegar_acidity=4, mustard_g=15, egg_yolk_count=3, blend_speed=5000, mix_temp=5 |
Model Quality
| Response | R² | Type |
|---|---|---|
taste_score | 0.7144 | linear |
Full Multi-Objective Output
doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================
Overall desirability: D = 0.9545
Response Weight Desirability Predicted Direction
---------------------------------------------------------------------
stability_hrs 1.5 0.9545 97.00 hrs ↑
taste_score 1.5 0.9545 8.20 pts ↑
Recommended settings:
oil_ratio = 80 %
vinegar_acidity = 7 %
mustard_g = 15 g
egg_yolk_count = 0 count
blend_speed = 5000 rpm
mix_temp = 5 C
(from observed run #4)
Trade-off summary:
stability_hrs: 97.00 (best observed: 97.00, sacrifice: +0.00)
taste_score: 8.20 (best observed: 8.20, sacrifice: +0.00)
Model quality:
stability_hrs: R² = 1.0000 (linear)
taste_score: R² = 0.7144 (linear)
Top 3 observed runs by overall desirability:
1. Run #4 (D=0.9545): oil_ratio=80, vinegar_acidity=7, mustard_g=15, egg_yolk_count=0, blend_speed=5000, mix_temp=5
2. Run #1 (D=0.5421): oil_ratio=50, vinegar_acidity=4, mustard_g=15, egg_yolk_count=0, blend_speed=20000, mix_temp=25
3. Run #2 (D=0.5203): oil_ratio=50, vinegar_acidity=4, mustard_g=15, egg_yolk_count=3, blend_speed=5000, mix_temp=5
Full Analysis Output
doe analyze
=== Main Effects: stability_hrs ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
oil_ratio 28.5000 10.1507 38.0%
blend_speed -27.5000 10.1507 36.7%
mix_temp -11.5000 10.1507 15.3%
mustard_g 4.0000 10.1507 5.3%
vinegar_acidity 3.5000 10.1507 4.7%
egg_yolk_count 0.0000 10.1507 0.0%
=== ANOVA Table: stability_hrs ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
oil_ratio 1 1624.5000 1624.5000 38.336 0.0004
vinegar_acidity 1 24.5000 24.5000 0.578 0.4719
mustard_g 1 32.0000 32.0000 0.755 0.4136
egg_yolk_count 1 0.0000 0.0000 0.000 1.0000
blend_speed 1 1512.5000 1512.5000 35.693 0.0006
mix_temp 1 264.5000 264.5000 6.242 0.0411
oil_ratio*vinegar_acidity 1 32.0000 32.0000 0.755 0.4136
oil_ratio*mustard_g 1 24.5000 24.5000 0.578 0.4719
oil_ratio*egg_yolk_count 1 1512.5000 1512.5000 35.693 0.0006
oil_ratio*blend_speed 1 0.0000 0.0000 0.000 1.0000
oil_ratio*mix_temp 1 2312.0000 2312.0000 54.560 0.0002
vinegar_acidity*mustard_g 1 1624.5000 1624.5000 38.336 0.0004
vinegar_acidity*egg_yolk_count 1 264.5000 264.5000 6.242 0.0411
vinegar_acidity*blend_speed 1 2312.0000 2312.0000 54.560 0.0002
vinegar_acidity*mix_temp 1 0.0000 0.0000 0.000 1.0000
mustard_g*egg_yolk_count 1 2312.0000 2312.0000 54.560 0.0002
mustard_g*blend_speed 1 264.5000 264.5000 6.242 0.0411
mustard_g*mix_temp 1 1512.5000 1512.5000 35.693 0.0006
egg_yolk_count*blend_speed 1 1624.5000 1624.5000 38.336 0.0004
egg_yolk_count*mix_temp 1 24.5000 24.5000 0.578 0.4719
blend_speed*mix_temp 1 32.0000 32.0000 0.755 0.4136
Error (Lenth PSE) 7 296.6250 42.3750
Total 7 5770.0000 824.2857
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Interaction Effects: stability_hrs ===
Factor A Factor B Interaction % Contribution
------------------------------------------------------------------------
oil_ratio mix_temp -34.0000 13.5%
vinegar_acidity blend_speed -34.0000 13.5%
mustard_g egg_yolk_count -34.0000 13.5%
vinegar_acidity mustard_g -28.5000 11.3%
egg_yolk_count blend_speed -28.5000 11.3%
oil_ratio egg_yolk_count 27.5000 10.9%
mustard_g mix_temp 27.5000 10.9%
vinegar_acidity egg_yolk_count 11.5000 4.6%
mustard_g blend_speed 11.5000 4.6%
oil_ratio vinegar_acidity -4.0000 1.6%
blend_speed mix_temp -4.0000 1.6%
oil_ratio mustard_g -3.5000 1.4%
egg_yolk_count mix_temp -3.5000 1.4%
oil_ratio blend_speed 0.0000 0.0%
vinegar_acidity mix_temp 0.0000 0.0%
=== Summary Statistics: stability_hrs ===
oil_ratio:
Level N Mean Std Min Max
------------------------------------------------------------
50 4 32.2500 20.9662 11.0000 61.0000
80 4 60.7500 30.6961 24.0000 97.0000
vinegar_acidity:
Level N Mean Std Min Max
------------------------------------------------------------
4 4 44.7500 20.2546 26.0000 70.0000
7 4 48.2500 38.7933 11.0000 97.0000
mustard_g:
Level N Mean Std Min Max
------------------------------------------------------------
15 4 44.5000 35.1236 24.0000 97.0000
2 4 48.5000 26.0576 11.0000 70.0000
egg_yolk_count:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 46.5000 22.4277 24.0000 70.0000
3 4 46.5000 37.6873 11.0000 97.0000
blend_speed:
Level N Mean Std Min Max
------------------------------------------------------------
20000 4 60.2500 27.5363 31.0000 97.0000
5000 4 32.7500 25.7083 11.0000 70.0000
mix_temp:
Level N Mean Std Min Max
------------------------------------------------------------
25 4 52.2500 38.6038 11.0000 97.0000
5 4 40.7500 18.5719 24.0000 61.0000
=== Main Effects: taste_score ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
mustard_g -1.2000 0.4066 29.6%
egg_yolk_count 1.1500 0.4066 28.4%
blend_speed -0.9000 0.4066 22.2%
mix_temp 0.7000 0.4066 17.3%
vinegar_acidity -0.0500 0.4066 1.2%
oil_ratio 0.0500 0.4066 1.2%
=== ANOVA Table: taste_score ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
oil_ratio 1 0.0050 0.0050 0.003 0.9581
vinegar_acidity 1 0.0050 0.0050 0.003 0.9581
mustard_g 1 2.8800 2.8800 1.707 0.2327
egg_yolk_count 1 2.6450 2.6450 1.567 0.2508
blend_speed 1 1.6200 1.6200 0.960 0.3598
mix_temp 1 0.9800 0.9800 0.581 0.4709
oil_ratio*vinegar_acidity 1 2.8800 2.8800 1.707 0.2327
oil_ratio*mustard_g 1 0.0050 0.0050 0.003 0.9581
oil_ratio*egg_yolk_count 1 1.6200 1.6200 0.960 0.3598
oil_ratio*blend_speed 1 2.6450 2.6450 1.567 0.2508
oil_ratio*mix_temp 1 1.1250 1.1250 0.667 0.4411
vinegar_acidity*mustard_g 1 0.0050 0.0050 0.003 0.9581
vinegar_acidity*egg_yolk_count 1 0.9800 0.9800 0.581 0.4709
vinegar_acidity*blend_speed 1 1.1250 1.1250 0.667 0.4411
vinegar_acidity*mix_temp 1 2.6450 2.6450 1.567 0.2508
mustard_g*egg_yolk_count 1 1.1250 1.1250 0.667 0.4411
mustard_g*blend_speed 1 0.9800 0.9800 0.581 0.4709
mustard_g*mix_temp 1 1.6200 1.6200 0.960 0.3598
egg_yolk_count*blend_speed 1 0.0050 0.0050 0.003 0.9581
egg_yolk_count*mix_temp 1 0.0050 0.0050 0.003 0.9581
blend_speed*mix_temp 1 2.8800 2.8800 1.707 0.2327
Error (Lenth PSE) 7 11.8125 1.6875
Total 7 9.2600 1.3229
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Interaction Effects: taste_score ===
Factor A Factor B Interaction % Contribution
------------------------------------------------------------------------
oil_ratio vinegar_acidity 1.2000 11.6%
blend_speed mix_temp 1.2000 11.6%
oil_ratio blend_speed -1.1500 11.1%
vinegar_acidity mix_temp -1.1500 11.1%
oil_ratio egg_yolk_count 0.9000 8.7%
mustard_g mix_temp 0.9000 8.7%
oil_ratio mix_temp -0.7500 7.2%
vinegar_acidity blend_speed -0.7500 7.2%
mustard_g egg_yolk_count -0.7500 7.2%
vinegar_acidity egg_yolk_count -0.7000 6.8%
mustard_g blend_speed -0.7000 6.8%
oil_ratio mustard_g 0.0500 0.5%
egg_yolk_count mix_temp 0.0500 0.5%
vinegar_acidity mustard_g -0.0500 0.5%
egg_yolk_count blend_speed -0.0500 0.5%
=== Summary Statistics: taste_score ===
oil_ratio:
Level N Mean Std Min Max
------------------------------------------------------------
50 4 6.5250 1.1147 5.3000 8.0000
80 4 6.5750 1.3574 5.0000 8.2000
vinegar_acidity:
Level N Mean Std Min Max
------------------------------------------------------------
4 4 6.5750 1.2606 5.0000 8.0000
7 4 6.5250 1.2230 5.3000 8.2000
mustard_g:
Level N Mean Std Min Max
------------------------------------------------------------
15 4 7.1500 1.1030 6.1000 8.2000
2 4 5.9500 0.9539 5.0000 7.0000
egg_yolk_count:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 5.9750 0.6702 5.0000 6.5000
3 4 7.1250 1.3251 5.3000 8.2000
blend_speed:
Level N Mean Std Min Max
------------------------------------------------------------
20000 4 7.0000 0.8524 6.3000 8.2000
5000 4 6.1000 1.3491 5.0000 8.0000
mix_temp:
Level N Mean Std Min Max
------------------------------------------------------------
25 4 6.2000 1.4445 5.0000 8.2000
5 4 6.9000 0.8206 6.1000 8.0000
Optimization Recommendations
doe optimize
=== Optimization: stability_hrs ===
Direction: maximize
Best observed run: #4
oil_ratio = 50
vinegar_acidity = 7
mustard_g = 2
egg_yolk_count = 0
blend_speed = 20000
mix_temp = 5
Value: 97.0
RSM Model (linear, R² = 0.8938, Adj R² = 0.2569):
Coefficients:
intercept +46.5000
oil_ratio -4.0000
vinegar_acidity +4.5000
mustard_g -5.5000
egg_yolk_count -18.2500
blend_speed +14.7500
mix_temp +5.2500
Predicted optimum (from linear model, at observed points):
oil_ratio = 50
vinegar_acidity = 7
mustard_g = 2
egg_yolk_count = 0
blend_speed = 20000
mix_temp = 5
Predicted value: 88.2500
Surface optimum (via L-BFGS-B, linear model):
oil_ratio = 50
vinegar_acidity = 7
mustard_g = 2
egg_yolk_count = 0
blend_speed = 20000
mix_temp = 25
Predicted value: 98.7500
Model quality: Good fit — general trends are captured, some noise remains.
Factor importance:
1. egg_yolk_count (effect: -36.5, contribution: 34.9%)
2. blend_speed (effect: -29.5, contribution: 28.2%)
3. mustard_g (effect: 11.0, contribution: 10.5%)
4. mix_temp (effect: -10.5, contribution: 10.0%)
5. vinegar_acidity (effect: 9.0, contribution: 8.6%)
6. oil_ratio (effect: -8.0, contribution: 7.7%)
=== Optimization: taste_score ===
Direction: maximize
Best observed run: #4
oil_ratio = 50
vinegar_acidity = 7
mustard_g = 2
egg_yolk_count = 0
blend_speed = 20000
mix_temp = 5
Value: 8.2
RSM Model (linear, R² = 0.9654, Adj R² = 0.7581):
Coefficients:
intercept +6.5500
oil_ratio +0.4000
vinegar_acidity +0.3500
mustard_g -0.6500
egg_yolk_count +0.0500
blend_speed +0.5000
mix_temp -0.4000
Predicted optimum (from linear model, at observed points):
oil_ratio = 80
vinegar_acidity = 4
mustard_g = 2
egg_yolk_count = 3
blend_speed = 20000
mix_temp = 5
Predicted value: 8.2000
Surface optimum (via L-BFGS-B, linear model):
oil_ratio = 80
vinegar_acidity = 7
mustard_g = 2
egg_yolk_count = 3
blend_speed = 20000
mix_temp = 5
Predicted value: 8.9000
Model quality: Excellent fit — surface predictions are reliable.
Factor importance:
1. mustard_g (effect: 1.3, contribution: 27.7%)
2. blend_speed (effect: -1.0, contribution: 21.3%)
3. oil_ratio (effect: 0.8, contribution: 17.0%)
4. mix_temp (effect: 0.8, contribution: 17.0%)
5. vinegar_acidity (effect: 0.7, contribution: 14.9%)
6. egg_yolk_count (effect: 0.1, contribution: 2.1%)