Summary
This experiment investigates windshield defog strategy. Fractional factorial of fan speed, temperature setting, AC mode, recirculation, and rear defrost to minimize defog time and energy use.
The design varies 5 factors: fan speed (level), ranging from 1 to 5, temp setting (C), ranging from 18 to 30, ac on (bool), ranging from 0 to 1, recirc (bool), ranging from 0 to 1, and rear defrost (bool), ranging from 0 to 1. The goal is to optimize 2 responses: defog time sec (sec) (minimize) and energy watts (W) (minimize). Fixed conditions held constant across all runs include ambient temp = 2C, humidity = 85pct.
A fractional factorial design reduces the number of runs from 32 to 8 by deliberately confounding higher-order interactions. This is ideal for screening — identifying which of the 5 factors matter most before investing in a full study.
Key Findings
For defog time sec, the most influential factors were rear defrost (53.0%), fan speed (17.2%), temp setting (11.9%). The best observed value was 37.0 (at fan speed = 1, temp setting = 30, ac on = 1).
For energy watts, the most influential factors were rear defrost (38.7%), fan speed (30.9%), ac on (16.8%). The best observed value was 133.0 (at fan speed = 1, temp setting = 30, ac on = 0).
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 |
|---|---|---|---|
fan_speed | 1 | 5 | level |
temp_setting | 18 | 30 | C |
ac_on | 0 | 1 | bool |
recirc | 0 | 1 | bool |
rear_defrost | 0 | 1 | bool |
Fixed: ambient_temp = 2C, humidity = 85pct
Responses
| Response | Direction | Unit |
|---|---|---|
defog_time_sec | ↓ minimize | sec |
energy_watts | ↓ minimize | W |
Configuration
use_cases/126_windshield_defog/config.json
{
"metadata": {
"name": "Windshield Defog Strategy",
"description": "Fractional factorial of fan speed, temperature setting, AC mode, recirculation, and rear defrost to minimize defog time and energy use"
},
"factors": [
{
"name": "fan_speed",
"levels": [
"1",
"5"
],
"type": "continuous",
"unit": "level"
},
{
"name": "temp_setting",
"levels": [
"18",
"30"
],
"type": "continuous",
"unit": "C"
},
{
"name": "ac_on",
"levels": [
"0",
"1"
],
"type": "continuous",
"unit": "bool"
},
{
"name": "recirc",
"levels": [
"0",
"1"
],
"type": "continuous",
"unit": "bool"
},
{
"name": "rear_defrost",
"levels": [
"0",
"1"
],
"type": "continuous",
"unit": "bool"
}
],
"fixed_factors": {
"ambient_temp": "2C",
"humidity": "85pct"
},
"responses": [
{
"name": "defog_time_sec",
"optimize": "minimize",
"unit": "sec"
},
{
"name": "energy_watts",
"optimize": "minimize",
"unit": "W"
}
],
"settings": {
"operation": "fractional_factorial",
"test_script": "use_cases/126_windshield_defog/sim.sh"
}
}
Experimental Matrix
The Fractional Factorial Design produces 8 runs. Each row is one experiment with specific factor settings.
| Run | fan_speed | temp_setting | ac_on | recirc | rear_defrost |
|---|---|---|---|---|---|
| 1 | 1 | 30 | 1 | 0 | 0 |
| 2 | 5 | 18 | 0 | 0 | 0 |
| 3 | 5 | 30 | 0 | 1 | 0 |
| 4 | 5 | 30 | 1 | 1 | 1 |
| 5 | 1 | 30 | 0 | 0 | 1 |
| 6 | 5 | 18 | 1 | 0 | 1 |
| 7 | 1 | 18 | 0 | 1 | 1 |
| 8 | 1 | 18 | 1 | 1 | 0 |
Step-by-Step Workflow
1
Preview the design
Terminal
$ doe info --config use_cases/126_windshield_defog/config.json
2
Generate the runner script
Terminal
$ doe generate --config use_cases/126_windshield_defog/config.json \
--output use_cases/126_windshield_defog/results/run.sh --seed 42
3
Execute the experiments
Terminal
$ bash use_cases/126_windshield_defog/results/run.sh
4
Analyze results
Terminal
$ doe analyze --config use_cases/126_windshield_defog/config.json
5
Get optimization recommendations
Terminal
$ doe optimize --config use_cases/126_windshield_defog/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/126_windshield_defog/config.json --multi
7
Generate the HTML report
Terminal
$ doe report --config use_cases/126_windshield_defog/config.json \
--output use_cases/126_windshield_defog/results/report.html
Features Exercised
| Feature | Value |
|---|---|
| Design type | fractional_factorial |
| Factor types | continuous (all 5) |
| Arg style | double-dash |
| Responses | 2 (defog_time_sec ↓, energy_watts ↓) |
| Total runs | 8 |
Analysis Results
Generated from actual experiment runs using the DOE Helper Tool.
Response: defog_time_sec
Top factors: rear_defrost (53.0%), fan_speed (17.2%), temp_setting (11.9%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|
| Source | DF | SS | MS | F | p-value |
| fan_speed | 1 | 1540.1250 | 1540.1250 | 0.667 | 0.4513 |
| temp_setting | 1 | 741.1250 | 741.1250 | 0.321 | 0.5956 |
| ac_on | 1 | 378.1250 | 378.1250 | 0.164 | 0.7025 |
| recirc | 1 | 465.1250 | 465.1250 | 0.201 | 0.6724 |
| rear_defrost | 1 | 14706.1250 | 14706.1250 | 6.366 | 0.0530 |
| fan_speed*temp_setting | 1 | 465.1250 | 465.1250 | 0.201 | 0.6724 |
| fan_speed*ac_on | 1 | 14706.1250 | 14706.1250 | 6.366 | 0.0530 |
| fan_speed*recirc | 1 | 741.1250 | 741.1250 | 0.321 | 0.5956 |
| fan_speed*rear_defrost | 1 | 378.1250 | 378.1250 | 0.164 | 0.7025 |
| temp_setting*ac_on | 1 | 2775.1250 | 2775.1250 | 1.201 | 0.3230 |
| temp_setting*recirc | 1 | 1540.1250 | 1540.1250 | 0.667 | 0.4513 |
| temp_setting*rear_defrost | 1 | 2556.1250 | 2556.1250 | 1.106 | 0.3410 |
| ac_on*recirc | 1 | 2556.1250 | 2556.1250 | 1.106 | 0.3410 |
| ac_on*rear_defrost | 1 | 1540.1250 | 1540.1250 | 0.667 | 0.4513 |
| recirc*rear_defrost | 1 | 2775.1250 | 2775.1250 | 1.201 | 0.3230 |
| Error | (Lenth | PSE) | 5 | 11550.9375 | 2310.1875 |
| Total | 7 | 23161.8750 | 3308.8393 |
Pareto Chart
Main Effects Plot
Normal Probability Plot of Effects
Half-Normal Plot of Effects
Model Diagnostics
Response: energy_watts
Top factors: rear_defrost (38.7%), fan_speed (30.9%), ac_on (16.8%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|
| Source | DF | SS | MS | F | p-value |
| fan_speed | 1 | 74112.5000 | 74112.5000 | 17.567 | 0.0086 |
| temp_setting | 1 | 6962.0000 | 6962.0000 | 1.650 | 0.2552 |
| ac_on | 1 | 22050.0000 | 22050.0000 | 5.227 | 0.0710 |
| recirc | 1 | 1300.5000 | 1300.5000 | 0.308 | 0.6027 |
| rear_defrost | 1 | 116644.5000 | 116644.5000 | 27.649 | 0.0033 |
| fan_speed*temp_setting | 1 | 1300.5000 | 1300.5000 | 0.308 | 0.6027 |
| fan_speed*ac_on | 1 | 116644.5000 | 116644.5000 | 27.649 | 0.0033 |
| fan_speed*recirc | 1 | 6962.0000 | 6962.0000 | 1.650 | 0.2552 |
| fan_speed*rear_defrost | 1 | 22050.0000 | 22050.0000 | 5.227 | 0.0710 |
| temp_setting*ac_on | 1 | 2.0000 | 2.0000 | 0.000 | 0.9835 |
| temp_setting*recirc | 1 | 74112.5000 | 74112.5000 | 17.567 | 0.0086 |
| temp_setting*rear_defrost | 1 | 2812.5000 | 2812.5000 | 0.667 | 0.4513 |
| ac_on*recirc | 1 | 2812.5000 | 2812.5000 | 0.667 | 0.4513 |
| ac_on*rear_defrost | 1 | 74112.5000 | 74112.5000 | 17.567 | 0.0086 |
| recirc*rear_defrost | 1 | 2.0000 | 2.0000 | 0.000 | 0.9835 |
| Error | (Lenth | PSE) | 5 | 21093.7500 | 4218.7500 |
| Total | 7 | 223884.0000 | 31983.4286 |
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.
defog time sec ac on vs rear defrost
defog time sec ac on vs recirc
defog time sec fan speed vs ac on
defog time sec fan speed vs rear defrost
defog time sec fan speed vs recirc
defog time sec fan speed vs temp setting
defog time sec recirc vs rear defrost
defog time sec temp setting vs ac on
defog time sec temp setting vs rear defrost
defog time sec temp setting vs recirc
energy watts ac on vs rear defrost
energy watts ac on vs recirc
energy watts fan speed vs ac on
energy watts fan speed vs rear defrost
energy watts fan speed vs recirc
energy watts fan speed vs temp setting
energy watts recirc vs rear defrost
energy watts temp setting vs ac on
energy watts temp setting vs rear defrost
energy watts temp setting vs recirc
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 = 0.7405
Per-Response Desirability
| Response | Weight | Desirability | Predicted | Dir |
|---|---|---|---|---|
defog_time_sec |
1.5 |
0.8209
|
62.00 0.8209 62.00 sec | ↓ |
energy_watts |
1.0 |
0.6344
|
308.00 0.6344 308.00 W | ↓ |
Recommended Settings
| Factor | Value |
|---|---|
fan_speed | 1 level |
temp_setting | 30 C |
ac_on | 0 bool |
recirc | 0 bool |
rear_defrost | 1 bool |
Source: from observed run #1
Trade-off Summary
Sacrifice = how much worse than single-objective best.
| Response | Predicted | Best Observed | Sacrifice |
|---|---|---|---|
energy_watts | 308.00 | 133.00 | +175.00 |
Top 3 Runs by Desirability
| Run | D | Factor Settings |
|---|---|---|
| #2 | 0.6114 | fan_speed=1, temp_setting=18, ac_on=1, recirc=1, rear_defrost=0 |
| #6 | 0.5732 | fan_speed=5, temp_setting=18, ac_on=1, recirc=0, rear_defrost=1 |
Model Quality
| Response | R² | Type |
|---|---|---|
energy_watts | 0.7727 | linear |
Full Multi-Objective Output
doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================
Overall desirability: D = 0.7405
Response Weight Desirability Predicted Direction
---------------------------------------------------------------------
defog_time_sec 1.5 0.8209 62.00 sec ↓
energy_watts 1.0 0.6344 308.00 W ↓
Recommended settings:
fan_speed = 1 level
temp_setting = 30 C
ac_on = 0 bool
recirc = 0 bool
rear_defrost = 1 bool
(from observed run #1)
Trade-off summary:
defog_time_sec: 62.00 (best observed: 37.00, sacrifice: +25.00)
energy_watts: 308.00 (best observed: 133.00, sacrifice: +175.00)
Model quality:
defog_time_sec: R² = 0.8763 (linear)
energy_watts: R² = 0.7727 (linear)
Top 3 observed runs by overall desirability:
1. Run #1 (D=0.7405): fan_speed=1, temp_setting=30, ac_on=0, recirc=0, rear_defrost=1
2. Run #2 (D=0.6114): fan_speed=1, temp_setting=18, ac_on=1, recirc=1, rear_defrost=0
3. Run #6 (D=0.5732): fan_speed=5, temp_setting=18, ac_on=1, recirc=0, rear_defrost=1
Full Analysis Output
doe analyze
=== Main Effects: defog_time_sec ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
rear_defrost -85.7500 20.3373 53.0%
fan_speed 27.7500 20.3373 17.2%
temp_setting -19.2500 20.3373 11.9%
recirc 15.2500 20.3373 9.4%
ac_on 13.7500 20.3373 8.5%
=== ANOVA Table: defog_time_sec ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
fan_speed 1 1540.1250 1540.1250 0.667 0.4513
temp_setting 1 741.1250 741.1250 0.321 0.5956
ac_on 1 378.1250 378.1250 0.164 0.7025
recirc 1 465.1250 465.1250 0.201 0.6724
rear_defrost 1 14706.1250 14706.1250 6.366 0.0530
fan_speed*temp_setting 1 465.1250 465.1250 0.201 0.6724
fan_speed*ac_on 1 14706.1250 14706.1250 6.366 0.0530
fan_speed*recirc 1 741.1250 741.1250 0.321 0.5956
fan_speed*rear_defrost 1 378.1250 378.1250 0.164 0.7025
temp_setting*ac_on 1 2775.1250 2775.1250 1.201 0.3230
temp_setting*recirc 1 1540.1250 1540.1250 0.667 0.4513
temp_setting*rear_defrost 1 2556.1250 2556.1250 1.106 0.3410
ac_on*recirc 1 2556.1250 2556.1250 1.106 0.3410
ac_on*rear_defrost 1 1540.1250 1540.1250 0.667 0.4513
recirc*rear_defrost 1 2775.1250 2775.1250 1.201 0.3230
Error (Lenth PSE) 5 11550.9375 2310.1875
Total 7 23161.8750 3308.8393
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Interaction Effects: defog_time_sec ===
Factor A Factor B Interaction % Contribution
------------------------------------------------------------------------
fan_speed ac_on -85.7500 25.6%
temp_setting ac_on 37.2500 11.1%
recirc rear_defrost 37.2500 11.1%
temp_setting rear_defrost 35.7500 10.7%
ac_on recirc 35.7500 10.7%
temp_setting recirc 27.7500 8.3%
ac_on rear_defrost 27.7500 8.3%
fan_speed recirc -19.2500 5.7%
fan_speed temp_setting 15.2500 4.5%
fan_speed rear_defrost 13.7500 4.1%
=== Summary Statistics: defog_time_sec ===
fan_speed:
Level N Mean Std Min Max
------------------------------------------------------------
1 4 104.7500 60.8078 37.0000 171.0000
5 4 132.5000 59.2424 62.0000 207.0000
temp_setting:
Level N Mean Std Min Max
------------------------------------------------------------
18 4 128.2500 71.8117 62.0000 207.0000
30 4 109.0000 48.1318 37.0000 138.0000
ac_on:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 111.7500 74.1502 37.0000 207.0000
1 4 125.5000 45.7857 62.0000 171.0000
recirc:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 111.0000 77.0757 37.0000 207.0000
1 4 126.2500 40.3103 73.0000 171.0000
rear_defrost:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 161.5000 35.1426 130.0000 207.0000
1 4 75.7500 39.7943 37.0000 131.0000
=== Main Effects: energy_watts ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
rear_defrost 241.5000 63.2292 38.7%
fan_speed -192.5000 63.2292 30.9%
ac_on -105.0000 63.2292 16.8%
temp_setting -59.0000 63.2292 9.5%
recirc 25.5000 63.2292 4.1%
=== ANOVA Table: energy_watts ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
fan_speed 1 74112.5000 74112.5000 17.567 0.0086
temp_setting 1 6962.0000 6962.0000 1.650 0.2552
ac_on 1 22050.0000 22050.0000 5.227 0.0710
recirc 1 1300.5000 1300.5000 0.308 0.6027
rear_defrost 1 116644.5000 116644.5000 27.649 0.0033
fan_speed*temp_setting 1 1300.5000 1300.5000 0.308 0.6027
fan_speed*ac_on 1 116644.5000 116644.5000 27.649 0.0033
fan_speed*recirc 1 6962.0000 6962.0000 1.650 0.2552
fan_speed*rear_defrost 1 22050.0000 22050.0000 5.227 0.0710
temp_setting*ac_on 1 2.0000 2.0000 0.000 0.9835
temp_setting*recirc 1 74112.5000 74112.5000 17.567 0.0086
temp_setting*rear_defrost 1 2812.5000 2812.5000 0.667 0.4513
ac_on*recirc 1 2812.5000 2812.5000 0.667 0.4513
ac_on*rear_defrost 1 74112.5000 74112.5000 17.567 0.0086
recirc*rear_defrost 1 2.0000 2.0000 0.000 0.9835
Error (Lenth PSE) 5 21093.7500 4218.7500
Total 7 223884.0000 31983.4286
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Interaction Effects: energy_watts ===
Factor A Factor B Interaction % Contribution
------------------------------------------------------------------------
fan_speed ac_on 241.5000 27.0%
temp_setting recirc -192.5000 21.6%
ac_on rear_defrost -192.5000 21.6%
fan_speed rear_defrost -105.0000 11.8%
fan_speed recirc -59.0000 6.6%
temp_setting rear_defrost -37.5000 4.2%
ac_on recirc -37.5000 4.2%
fan_speed temp_setting 25.5000 2.9%
temp_setting ac_on -1.0000 0.1%
recirc rear_defrost -1.0000 0.1%
=== Summary Statistics: energy_watts ===
fan_speed:
Level N Mean Std Min Max
------------------------------------------------------------
1 4 396.2500 206.9901 199.0000 630.0000
5 4 203.7500 84.1363 133.0000 308.0000
temp_setting:
Level N Mean Std Min Max
------------------------------------------------------------
18 4 329.5000 213.0579 133.0000 630.0000
30 4 270.5000 164.0539 138.0000 509.0000
ac_on:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 352.5000 255.4010 133.0000 630.0000
1 4 247.5000 45.2585 199.0000 308.0000
recirc:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 287.2500 164.5041 133.0000 509.0000
1 4 312.7500 217.1012 138.0000 630.0000
rear_defrost:
Level N Mean Std Min Max
------------------------------------------------------------
0 4 179.2500 54.2241 133.0000 247.0000
1 4 420.7500 181.1250 236.0000 630.0000
Optimization Recommendations
doe optimize
=== Optimization: defog_time_sec ===
Direction: minimize
Best observed run: #6
fan_speed = 1
temp_setting = 30
ac_on = 1
recirc = 0
rear_defrost = 0
Value: 37.0
RSM Model (linear, R² = 0.8514, Adj R² = 0.4798):
Coefficients:
intercept +118.6250
fan_speed +6.6250
temp_setting -9.6250
ac_on -15.8750
recirc -19.6250
rear_defrost +41.1250
Predicted optimum (from linear model, at observed points):
fan_speed = 5
temp_setting = 18
ac_on = 1
recirc = 0
rear_defrost = 1
Predicted value: 179.7500
Surface optimum (via L-BFGS-B, linear model):
fan_speed = 1
temp_setting = 30
ac_on = 1
recirc = 1
rear_defrost = 0
Predicted value: 25.7500
Model quality: Good fit — general trends are captured, some noise remains.
Factor importance:
1. rear_defrost (effect: 82.2, contribution: 44.3%)
2. recirc (effect: -39.2, contribution: 21.1%)
3. ac_on (effect: -31.8, contribution: 17.1%)
4. temp_setting (effect: -19.2, contribution: 10.4%)
5. fan_speed (effect: 13.2, contribution: 7.1%)
=== Optimization: energy_watts ===
Direction: minimize
Best observed run: #7
fan_speed = 1
temp_setting = 30
ac_on = 0
recirc = 0
rear_defrost = 1
Value: 133.0
RSM Model (linear, R² = 0.9466, Adj R² = 0.8130):
Coefficients:
intercept +300.0000
fan_speed -77.0000
temp_setting -28.0000
ac_on +81.0000
recirc +28.0000
rear_defrost -111.5000
Predicted optimum (from linear model, at observed points):
fan_speed = 1
temp_setting = 18
ac_on = 1
recirc = 1
rear_defrost = 0
Predicted value: 625.5000
Surface optimum (via L-BFGS-B, linear model):
fan_speed = 5
temp_setting = 30
ac_on = 0
recirc = 0
rear_defrost = 1
Predicted value: -25.5000
Model quality: Excellent fit — surface predictions are reliable.
Factor importance:
1. rear_defrost (effect: -223.0, contribution: 34.3%)
2. ac_on (effect: 162.0, contribution: 24.9%)
3. fan_speed (effect: -154.0, contribution: 23.7%)
4. temp_setting (effect: -56.0, contribution: 8.6%)
5. recirc (effect: 56.0, contribution: 8.6%)