Mead (Honey Wine) Production

Summary

This experiment investigates mead (honey wine) production. Box-Behnken design to maximize honey character and minimize fermentation stalls by tuning honey-to-water ratio, nutrient additions, and pH adjustment.

The design varies 3 factors: honey ratio kg L (kg/L), ranging from 0.3 to 0.5, nutrient g L (g/L), ranging from 0.5 to 3.0, and ph target (pH), ranging from 3.5 to 4.5. The goal is to optimize 2 responses: honey character (pts) (maximize) and completion days (days) (minimize). Fixed conditions held constant across all runs include honey type = wildflower, yeast = d47.

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 honey character, the most influential factors were nutrient g L (38.6%), ph target (32.3%), honey ratio kg L (29.1%). The best observed value was 7.2 (at honey ratio kg L = 0.5, nutrient g L = 1.75, ph target = 4.5).

For completion days, the most influential factors were honey ratio kg L (41.2%), ph target (38.8%), nutrient g L (20.1%). The best observed value was 15.0 (at honey ratio kg L = 0.4, nutrient g L = 3, ph target = 3.5).

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
`honey_ratio_kg_L`	0.3	0.5	kg/L
`nutrient_g_L`	0.5	3.0	g/L
`ph_target`	3.5	4.5	pH

Fixed: honey_type = wildflower, yeast = d47

Responses

Response	Direction	Unit
`honey_character`	↑ maximize	pts
`completion_days`	↓ minimize	days

Configuration

use_cases/241_mead_honey_wine/config.json

{
  "metadata": {
    "name": "Mead (Honey Wine) Production",
    "description": "Box-Behnken design to maximize honey character and minimize fermentation stalls by tuning honey-to-water ratio, nutrient additions, and pH adjustment"
  },
  "factors": [
    {
      "name": "honey_ratio_kg_L",
      "levels": [
        "0.3",
        "0.5"
      ],
      "type": "continuous",
      "unit": "kg/L"
    },
    {
      "name": "nutrient_g_L",
      "levels": [
        "0.5",
        "3.0"
      ],
      "type": "continuous",
      "unit": "g/L"
    },
    {
      "name": "ph_target",
      "levels": [
        "3.5",
        "4.5"
      ],
      "type": "continuous",
      "unit": "pH"
    }
  ],
  "fixed_factors": {
    "honey_type": "wildflower",
    "yeast": "d47"
  },
  "responses": [
    {
      "name": "honey_character",
      "optimize": "maximize",
      "unit": "pts"
    },
    {
      "name": "completion_days",
      "optimize": "minimize",
      "unit": "days"
    }
  ],
  "settings": {
    "operation": "box_behnken",
    "test_script": "use_cases/241_mead_honey_wine/sim.sh"
  }
}

Experimental Matrix

The Box-Behnken Design produces 15 runs. Each row is one experiment with specific factor settings.

Run	`honey_ratio_kg_L`	`nutrient_g_L`	`ph_target`
1	0.4	0.5	3.5
2	0.4	1.75	4
3	0.5	1.75	4.5
4	0.5	1.75	3.5
5	0.4	1.75	4
6	0.4	1.75	4
7	0.3	1.75	4.5
8	0.5	0.5	4
9	0.4	0.5	4.5
10	0.5	3	4
11	0.3	1.75	3.5
12	0.4	3	4.5
13	0.3	0.5	4
14	0.3	3	4
15	0.4	3	3.5

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/241_mead_honey_wine/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/241_mead_honey_wine/config.json \
    --output use_cases/241_mead_honey_wine/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/241_mead_honey_wine/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/241_mead_honey_wine/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/241_mead_honey_wine/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/241_mead_honey_wine/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/241_mead_honey_wine/config.json \
    --output use_cases/241_mead_honey_wine/results/report.html

Features Exercised

Feature	Value
Design type	`box_behnken`
Factor types	`continuous` (all 3)
Arg style	`double-dash`
Responses	2 (honey_character ↑, completion_days ↓)
Total runs	15

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: honey_character

Top factors: nutrient_g_L (38.6%), ph_target (32.3%), honey_ratio_kg_L (29.1%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
honey_ratio_kg_L	2	0.5355	0.2678	0.241	0.7912
nutrient_g_L	2	0.9252	0.4626	0.417	0.6727
ph_target	2	0.6255	0.3128	0.282	0.7616
Lack	of	Fit	6	2.7110	0.4518
Pure	Error	2	2.2200
Error	8	4.9310	1.1100
Total	14	7.0173	0.5012

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for honey_character

Half-Normal Plot of Effects

Model Diagnostics

Response: completion_days

Top factors: honey_ratio_kg_L (41.2%), ph_target (38.8%), nutrient_g_L (20.1%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
honey_ratio_kg_L	2	229.9929	114.9964	0.843	0.4652
nutrient_g_L	2	48.9929	24.4964	0.180	0.8388
ph_target	2	218.3857	109.1929	0.801	0.4819
Lack	of	Fit	6	583.5619	97.2603
Pure	Error	2	272.6667
Error	8	856.2286	136.3333
Total	14	1353.6000	96.6857

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for completion_days

Half-Normal Plot of Effects

Model Diagnostics

Response Surface Plots

3D surfaces fitted with quadratic RSM. Red dots are observed data points.

completion days honey ratio kg L vs nutrient g L

completion days honey ratio kg L vs ph target

completion days nutrient g L vs ph target

honey character honey ratio kg L vs nutrient g L

honey character honey ratio kg L vs ph target

honey character nutrient g L vs ph target

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 = 0.7238

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`honey_character`	1.5	0.6515	6.50 0.6515 6.50 pts	↑
`completion_days`	1.0	0.8476	19.00 0.8476 19.00 days	↓

Recommended Settings

Factor	Value
`honey_ratio_kg_L`	0.4 kg/L
`nutrient_g_L`	1.75 g/L
`ph_target`	4 pH

Source: from observed run #12

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`completion_days`	19.00	15.00	+4.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#6	0.6449	honey_ratio_kg_L=0.3, nutrient_g_L=0.5, ph_target=4
#3	0.6313	honey_ratio_kg_L=0.5, nutrient_g_L=0.5, ph_target=4

Model Quality

Response	R²	Type
`completion_days`	0.2839	linear

Full Multi-Objective Output

doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================

Overall desirability: D = 0.7238

Response                  Weight Desirability    Predicted  Direction
---------------------------------------------------------------------
honey_character              1.5       0.6515        6.50 pts   ↑
completion_days              1.0       0.8476       19.00 days   ↓

Recommended settings:
  honey_ratio_kg_L = 0.4 kg/L
  nutrient_g_L = 1.75 g/L
  ph_target = 4 pH
  (from observed run #12)

Trade-off summary:
  honey_character: 6.50 (best observed: 7.20, sacrifice: +0.70)
  completion_days: 19.00 (best observed: 15.00, sacrifice: +4.00)

Model quality:
  honey_character: R² = 0.7639 (quadratic)
  completion_days: R² = 0.2839 (linear)

Top 3 observed runs by overall desirability:
  1. Run #12 (D=0.7238): honey_ratio_kg_L=0.4, nutrient_g_L=1.75, ph_target=4
  2. Run #6 (D=0.6449): honey_ratio_kg_L=0.3, nutrient_g_L=0.5, ph_target=4
  3. Run #3 (D=0.6313): honey_ratio_kg_L=0.5, nutrient_g_L=0.5, ph_target=4

Full Analysis Output

doe analyze
=== Main Effects: honey_character ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
nutrient_g_L             0.5679       0.1828            38.6%
ph_target                0.4750       0.1828            32.3%
honey_ratio_kg_L         0.4286       0.1828            29.1%

=== ANOVA Table: honey_character ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
honey_ratio_kg_L             2       0.5355       0.2678      0.241     0.7912
nutrient_g_L                 2       0.9252       0.4626      0.417     0.6727
ph_target                    2       0.6255       0.3128      0.282     0.7616
Lack of Fit                  6       2.7110       0.4518      0.407     0.8338
Pure Error                   2       2.2200       1.1100
Error                        8       4.9310       1.1100
Total                       14       7.0173       0.5012

=== Summary Statistics: honey_character ===

honey_ratio_kg_L:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0.3                 4     6.1750     0.7274     5.1000     6.7000
  0.4                 7     6.1714     0.8118     5.1000     7.2000
  0.5                 4     6.6000     0.5598     5.9000     7.1000

nutrient_g_L:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0.5                 4     5.8750     0.9674     5.1000     7.1000
  1.75                7     6.4429     0.6803     5.1000     7.2000
  3                   4     6.4250     0.4113     5.9000     6.9000

ph_target:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  3.5                 4     6.6250     0.3862     6.2000     7.0000
  4                   7     6.1714     0.8577     5.1000     7.2000
  4.5                 4     6.1500     0.7141     5.1000     6.7000

=== Main Effects: completion_days ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
honey_ratio_kg_L         9.7500       2.5388            41.2%
ph_target                9.1786       2.5388            38.8%
nutrient_g_L             4.7500       2.5388            20.1%

=== ANOVA Table: completion_days ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
honey_ratio_kg_L             2     229.9929     114.9964      0.843     0.4652
nutrient_g_L                 2      48.9929      24.4964      0.180     0.8388
ph_target                    2     218.3857     109.1929      0.801     0.4819
Lack of Fit                  6     583.5619      97.2603      0.713     0.6834
Pure Error                   2     272.6667     136.3333
Error                        8     856.2286     136.3333
Total                       14    1353.6000      96.6857

=== Summary Statistics: completion_days ===

honey_ratio_kg_L:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0.3                 4    29.2500    10.4043    19.0000    43.0000
  0.4                 7    30.8571     9.3529    15.0000    44.0000
  0.5                 4    39.0000     9.5568    26.0000    49.0000

nutrient_g_L:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0.5                 4    29.7500     7.6757    24.0000    41.0000
  1.75                7    33.1429    11.3053    15.0000    49.0000
  3                   4    34.5000    10.9697    19.0000    44.0000

ph_target:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  3.5                 4    38.7500     9.1788    28.0000    49.0000
  4                   7    29.5714    10.5334    15.0000    41.0000
  4.5                 4    31.7500     8.5000    26.0000    44.0000

Optimization Recommendations

doe optimize
=== Optimization: honey_character ===
Direction: maximize

Best observed run: #3
  honey_ratio_kg_L = 0.5
  nutrient_g_L = 1.75
  ph_target = 4.5
  Value: 7.2

RSM Model (linear, R² = 0.1970, Adj R² = -0.0220):
  Coefficients:
    intercept                      +6.2867
    honey_ratio_kg_L               +0.0125
    nutrient_g_L                   -0.3875
    ph_target                      +0.1500

RSM Model (quadratic, R² = 0.6277, Adj R² = -0.0424):
  Coefficients:
    intercept                      +6.0000
    honey_ratio_kg_L               +0.0125
    nutrient_g_L                   -0.3875
    ph_target                      +0.1500
    honey_ratio_kg_L*nutrient_g_L  +0.2250
    honey_ratio_kg_L*ph_target     -0.0500
    nutrient_g_L*ph_target         +0.0000
    honey_ratio_kg_L^2             +0.7875
    nutrient_g_L^2                 -0.3125
    ph_target^2                    +0.0625

  Curvature analysis:
    honey_ratio_kg_L               coef=+0.7875  convex (has a minimum)
    nutrient_g_L                   coef=-0.3125  concave (has a maximum)
    ph_target                      coef=+0.0625  negligible curvature

  Predicted optimum (from linear model, at observed points):
    honey_ratio_kg_L = 0.4
    nutrient_g_L = 0.5
    ph_target = 4.5
    Predicted value: 6.8242

  Surface optimum (via L-BFGS-B, linear model):
    honey_ratio_kg_L = 0.5
    nutrient_g_L = 0.5
    ph_target = 4.5
    Predicted value: 6.8367

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. honey_ratio_kg_L  (effect: 0.8, contribution: 43.2%)
  2. nutrient_g_L  (effect: 0.8, contribution: 40.9%)
  3. ph_target  (effect: 0.3, contribution: 15.8%)

=== Optimization: completion_days ===
Direction: minimize

Best observed run: #14
  honey_ratio_kg_L = 0.4
  nutrient_g_L = 3
  ph_target = 3.5
  Value: 15.0

RSM Model (linear, R² = 0.2789, Adj R² = 0.0822):
  Coefficients:
    intercept                      +32.6000
    honey_ratio_kg_L               -3.7500
    nutrient_g_L                   -5.7500
    ph_target                      -0.2500

RSM Model (quadratic, R² = 0.7443, Adj R² = 0.2839):
  Coefficients:
    intercept                      +37.6667
    honey_ratio_kg_L               -3.7500
    nutrient_g_L                   -5.7500
    ph_target                      -0.2500
    honey_ratio_kg_L*nutrient_g_L  -1.0000
    honey_ratio_kg_L*ph_target     +2.5000
    nutrient_g_L*ph_target         +7.0000
    honey_ratio_kg_L^2             +0.6667
    nutrient_g_L^2                 -10.3333
    ph_target^2                    +0.1667

  Curvature analysis:
    nutrient_g_L                   coef=-10.3333  concave (has a maximum)
    honey_ratio_kg_L               coef=+0.6667  convex (has a minimum)
    ph_target                      coef=+0.1667  convex (has a minimum)

  Notable interactions:
    nutrient_g_L*ph_target         coef=+7.0000  (synergistic)
    honey_ratio_kg_L*ph_target     coef=+2.5000  (synergistic)
    honey_ratio_kg_L*nutrient_g_L  coef=-1.0000  (antagonistic)

  Predicted optimum (from quadratic model, at observed points):
    honey_ratio_kg_L = 0.3
    nutrient_g_L = 1.75
    ph_target = 3.5
    Predicted value: 45.0000

  Surface optimum (via L-BFGS-B, quadratic model):
    honey_ratio_kg_L = 0.5
    nutrient_g_L = 3
    ph_target = 3.5
    Predicted value: 8.4167

  Model quality: Good fit — general trends are captured, some noise remains.

Factor importance:
  1. nutrient_g_L  (effect: 16.1, contribution: 65.2%)
  2. honey_ratio_kg_L  (effect: 7.5, contribution: 30.3%)
  3. ph_target  (effect: 1.1, contribution: 4.5%)