Ergonomic Workstation Setup

Summary

This experiment investigates ergonomic workstation setup. Central composite design to minimize discomfort and maximize productivity by tuning desk height, monitor distance, chair angle, and break frequency.

The design varies 4 factors: desk height cm (cm), ranging from 65 to 80, monitor dist cm (cm), ranging from 50 to 80, chair recline deg (deg), ranging from 90 to 115, and break freq min (min), ranging from 25 to 90. The goal is to optimize 2 responses: comfort score (pts) (maximize) and productivity pct (%) (maximize). Fixed conditions held constant across all runs include monitor size = 27in, chair type = ergonomic.

A Central Composite Design (CCD) was selected to fit a full quadratic response surface model, including curvature and interaction effects. With 4 factors this produces 32 runs including center points and axial (star) points that extend beyond the factorial range.

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 comfort score, the most influential factors were break freq min (34.2%), chair recline deg (25.3%), desk height cm (20.9%). The best observed value was 7.4 (at desk height cm = 72.5, monitor dist cm = 32.1366, chair recline deg = 102.5).

For productivity pct, the most influential factors were chair recline deg (28.9%), monitor dist cm (26.8%), break freq min (26.8%). The best observed value was 100.0 (at desk height cm = 72.5, monitor dist cm = 32.1366, chair recline deg = 102.5).

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
`desk_height_cm`	65	80	cm
`monitor_dist_cm`	50	80	cm
`chair_recline_deg`	90	115	deg
`break_freq_min`	25	90	min

Fixed: monitor_size = 27in, chair_type = ergonomic

Responses

Response	Direction	Unit
`comfort_score`	↑ maximize	pts
`productivity_pct`	↑ maximize	%

Configuration

use_cases/111_ergonomic_workstation/config.json

{
  "metadata": {
    "name": "Ergonomic Workstation Setup",
    "description": "Central composite design to minimize discomfort and maximize productivity by tuning desk height, monitor distance, chair angle, and break frequency"
  },
  "factors": [
    {
      "name": "desk_height_cm",
      "levels": [
        "65",
        "80"
      ],
      "type": "continuous",
      "unit": "cm"
    },
    {
      "name": "monitor_dist_cm",
      "levels": [
        "50",
        "80"
      ],
      "type": "continuous",
      "unit": "cm"
    },
    {
      "name": "chair_recline_deg",
      "levels": [
        "90",
        "115"
      ],
      "type": "continuous",
      "unit": "deg"
    },
    {
      "name": "break_freq_min",
      "levels": [
        "25",
        "90"
      ],
      "type": "continuous",
      "unit": "min"
    }
  ],
  "fixed_factors": {
    "monitor_size": "27in",
    "chair_type": "ergonomic"
  },
  "responses": [
    {
      "name": "comfort_score",
      "optimize": "maximize",
      "unit": "pts"
    },
    {
      "name": "productivity_pct",
      "optimize": "maximize",
      "unit": "%"
    }
  ],
  "settings": {
    "operation": "central_composite",
    "test_script": "use_cases/111_ergonomic_workstation/sim.sh"
  }
}

Experimental Matrix

The Central Composite Design produces 32 runs. Each row is one experiment with specific factor settings.

Run	`desk_height_cm`	`monitor_dist_cm`	`chair_recline_deg`	`break_freq_min`
1	72.5	65	102.5	-13.7039
2	65	80	90	90
3	80	50	115	25
4	80	80	115	90
5	72.5	65	129.886	57.5
6	80	50	115	90
7	72.5	32.1366	102.5	57.5
8	65	80	115	25
9	72.5	65	102.5	57.5
10	80	80	90	25
11	72.5	65	102.5	57.5
12	80	50	90	90
13	72.5	65	102.5	57.5
14	80	80	115	25
15	72.5	65	75.1139	57.5
16	56.0683	65	102.5	57.5
17	72.5	65	102.5	57.5
18	65	50	90	90
19	80	80	90	90
20	72.5	65	102.5	57.5
21	65	50	115	25
22	72.5	65	102.5	57.5
23	88.9317	65	102.5	57.5
24	65	50	115	90
25	72.5	65	102.5	57.5
26	65	80	90	25
27	72.5	65	102.5	128.704
28	72.5	65	102.5	57.5
29	80	50	90	25
30	72.5	97.8634	102.5	57.5
31	65	50	90	25
32	65	80	115	90

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/111_ergonomic_workstation/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/111_ergonomic_workstation/config.json \
    --output use_cases/111_ergonomic_workstation/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/111_ergonomic_workstation/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/111_ergonomic_workstation/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/111_ergonomic_workstation/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/111_ergonomic_workstation/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/111_ergonomic_workstation/config.json \
    --output use_cases/111_ergonomic_workstation/results/report.html

Features Exercised

Feature	Value
Design type	`central_composite`
Factor types	`continuous` (all 4)
Arg style	`double-dash`
Responses	2 (comfort_score ↑, productivity_pct ↑)
Total runs	32

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: comfort_score

Top factors: break_freq_min (34.2%), chair_recline_deg (25.3%), desk_height_cm (20.9%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
desk_height_cm	4	5.4325	1.3581	0.926	0.4749
monitor_dist_cm	4	4.2336	1.0584	0.721	0.5906
chair_recline_deg	4	5.5225	1.3806	0.941	0.4671
break_freq_min	4	27.7736	6.9434	4.733	0.0114
Lack	of	Fit	8	13.7011	1.7126
Pure	Error	7	10.2688
Error	15	23.9699	1.4670
Total	31	66.9322	2.1591

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for comfort_score

Half-Normal Plot of Effects

Model Diagnostics

Response: productivity_pct

Top factors: chair_recline_deg (28.9%), monitor_dist_cm (26.8%), break_freq_min (26.8%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
desk_height_cm	4	57.9464	14.4866	2.543	0.0830
monitor_dist_cm	4	70.5179	17.6295	3.095	0.0481
chair_recline_deg	4	92.7679	23.1920	4.071	0.0198
break_freq_min	4	147.9464	36.9866	6.493	0.0031
Lack	of	Fit	8	9.8214	1.2277
Pure	Error	7	39.8750
Error	15	49.6964	5.6964
Total	31	418.8750	13.5121

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for productivity_pct

Half-Normal Plot of Effects

Model Diagnostics

Response Surface Plots

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

comfort score chair recline deg vs break freq min

comfort score desk height cm vs break freq min

comfort score desk height cm vs chair recline deg

comfort score desk height cm vs monitor dist cm

comfort score monitor dist cm vs break freq min

comfort score monitor dist cm vs chair recline deg

productivity pct chair recline deg vs break freq min

productivity pct desk height cm vs break freq min

productivity pct desk height cm vs chair recline deg

productivity pct desk height cm vs monitor dist cm

productivity pct monitor dist cm vs break freq min

productivity pct monitor dist cm vs chair recline 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 = 0.9545

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`comfort_score`	1.5	0.9545	7.40 0.9545 7.40 pts	↑
`productivity_pct`	1.5	0.9545	100.00 0.9545 100.00 %	↑

Recommended Settings

Factor	Value
`desk_height_cm`	88.9317 cm
`monitor_dist_cm`	65 cm
`chair_recline_deg`	102.5 deg
`break_freq_min`	57.5 min

Source: from observed run #1

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`productivity_pct`	100.00	100.00	+0.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#14	0.7946	desk_height_cm=72.5, monitor_dist_cm=65, chair_recline_deg=75.1139, break_freq_min=57.5
#5	0.7466	desk_height_cm=65, monitor_dist_cm=50, chair_recline_deg=115, break_freq_min=25

Model Quality

Response	R²	Type
`productivity_pct`	0.0843	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
---------------------------------------------------------------------
comfort_score                1.5       0.9545        7.40 pts   ↑
productivity_pct             1.5       0.9545      100.00 %   ↑

Recommended settings:
  desk_height_cm = 88.9317 cm
  monitor_dist_cm = 65 cm
  chair_recline_deg = 102.5 deg
  break_freq_min = 57.5 min
  (from observed run #1)

Trade-off summary:
  comfort_score: 7.40 (best observed: 7.40, sacrifice: +0.00)
  productivity_pct: 100.00 (best observed: 100.00, sacrifice: +0.00)

Model quality:
  comfort_score: R² = 0.0225 (linear)
  productivity_pct: R² = 0.0843 (linear)

Top 3 observed runs by overall desirability:
  1. Run #1 (D=0.9545): desk_height_cm=88.9317, monitor_dist_cm=65, chair_recline_deg=102.5, break_freq_min=57.5
  2. Run #14 (D=0.7946): desk_height_cm=72.5, monitor_dist_cm=65, chair_recline_deg=75.1139, break_freq_min=57.5
  3. Run #5 (D=0.7466): desk_height_cm=65, monitor_dist_cm=50, chair_recline_deg=115, break_freq_min=25

Full Analysis Output

doe analyze
=== Main Effects: comfort_score ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
break_freq_min           2.9750       0.2598            34.2%
chair_recline_deg        2.2000       0.2598            25.3%
desk_height_cm           1.8125       0.2598            20.9%
monitor_dist_cm          1.7000       0.2598            19.6%

=== ANOVA Table: comfort_score ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
desk_height_cm               4       5.4325       1.3581      0.926     0.4749
monitor_dist_cm              4       4.2336       1.0584      0.721     0.5906
chair_recline_deg            4       5.5225       1.3806      0.941     0.4671
break_freq_min               4      27.7736       6.9434      4.733     0.0114
Lack of Fit                  8      13.7011       1.7126      1.167     0.4256
Pure Error                   7      10.2688       1.4670
Error                       15      23.9699       1.4670
Total                       31      66.9322       2.1591

=== Summary Statistics: comfort_score ===

desk_height_cm:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  56.0683             1     6.1000     0.0000     6.1000     6.1000
  65                  8     4.6375     1.9257     1.6000     7.4000
  72.5               14     4.9357     1.2744     2.5000     6.2000
  80                  8     4.2875     1.4357     2.7000     6.2000
  88.9317             1     5.9000     0.0000     5.9000     5.9000

monitor_dist_cm:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  32.1366             1     5.3000     0.0000     5.3000     5.3000
  50                  8     4.5250     1.3014     2.8000     6.2000
  65                 14     4.9786     1.2974     2.5000     6.2000
  80                  8     4.4000     2.0340     1.6000     7.4000
  97.8634             1     6.1000     0.0000     6.1000     6.1000

chair_recline_deg:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  102.5              14     5.0643     1.2616     2.5000     6.1000
  115                 8     4.3625     1.9690     1.6000     7.4000
  129.886             1     6.2000     0.0000     6.2000     6.2000
  75.1139             1     4.0000     0.0000     4.0000     4.0000
  90                  8     4.5625     1.3928     2.2000     6.2000

break_freq_min:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -13.7039            1     2.5000     0.0000     2.5000     2.5000
  128.704             1     4.1000     0.0000     4.1000     4.1000
  25                  8     3.4500     1.4619     1.6000     5.7000
  57.5               14     5.3214     1.0628     2.9000     6.2000
  90                  8     5.4750     1.1659     3.7000     7.4000

=== Main Effects: productivity_pct ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
chair_recline_deg        7.0000       0.6498            28.9%
monitor_dist_cm          6.5000       0.6498            26.8%
break_freq_min           6.5000       0.6498            26.8%
desk_height_cm           4.2500       0.6498            17.5%

=== ANOVA Table: productivity_pct ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
desk_height_cm               4      57.9464      14.4866      2.543     0.0830
monitor_dist_cm              4      70.5179      17.6295      3.095     0.0481
chair_recline_deg            4      92.7679      23.1920      4.071     0.0198
break_freq_min               4     147.9464      36.9866      6.493     0.0031
Lack of Fit                  8       9.8214       1.2277      0.216     0.9767
Pure Error                   7      39.8750       5.6964
Error                       15      49.6964       5.6964
Total                       31     418.8750      13.5121

=== Summary Statistics: productivity_pct ===

desk_height_cm:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  56.0683             1    96.0000     0.0000    96.0000    96.0000
  65                  8    91.7500     5.0920    84.0000   100.0000
  72.5               14    94.4286     2.5933    89.0000    98.0000
  80                  8    92.0000     3.6253    87.0000    97.0000
  88.9317             1    94.0000     0.0000    94.0000    94.0000

monitor_dist_cm:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  32.1366             1    94.0000     0.0000    94.0000    94.0000
  50                  8    92.2500     3.0119    87.0000    96.0000
  65                 14    94.2857     2.4315    89.0000    97.0000
  80                  8    91.5000     5.4511    84.0000   100.0000
  97.8634             1    98.0000     0.0000    98.0000    98.0000

chair_recline_deg:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  102.5              14    94.7857     2.0821    89.0000    98.0000
  115                 8    92.3750     5.2898    84.0000   100.0000
  129.886             1    96.0000     0.0000    96.0000    96.0000
  75.1139             1    89.0000     0.0000    89.0000    89.0000
  90                  8    91.3750     3.2486    86.0000    96.0000

break_freq_min:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -13.7039            1    96.0000     0.0000    96.0000    96.0000
  128.704             1    94.0000     0.0000    94.0000    94.0000
  25                  8    89.5000     3.5051    84.0000    94.0000
  57.5               14    94.4286     2.5933    89.0000    98.0000
  90                  8    94.2500     3.7321    88.0000   100.0000

Optimization Recommendations

doe optimize
=== Optimization: comfort_score ===
Direction: maximize

Best observed run: #1
  desk_height_cm = 72.5
  monitor_dist_cm = 32.1366
  chair_recline_deg = 102.5
  break_freq_min = 57.5
  Value: 7.4

RSM Model (linear, R² = 0.0803, Adj R² = -0.0559):
  Coefficients:
    intercept                      +4.7656
    desk_height_cm                 +0.1682
    monitor_dist_cm                -0.2326
    chair_recline_deg              -0.0800
    break_freq_min                 -0.3483

RSM Model (quadratic, R² = 0.3420, Adj R² = -0.1999):
  Coefficients:
    intercept                      +4.9793
    desk_height_cm                 +0.1682
    monitor_dist_cm                -0.2326
    chair_recline_deg              -0.0800
    break_freq_min                 -0.3483
    desk_height_cm*monitor_dist_cm -0.1375
    desk_height_cm*chair_recline_deg +0.1000
    desk_height_cm*break_freq_min  -0.1000
    monitor_dist_cm*chair_recline_deg +0.5625
    monitor_dist_cm*break_freq_min +0.6125
    chair_recline_deg*break_freq_min -0.2000
    desk_height_cm^2               -0.1892
    monitor_dist_cm^2              +0.2067
    chair_recline_deg^2            -0.1579
    break_freq_min^2               -0.1267

  Curvature analysis:
    monitor_dist_cm                coef=+0.2067  convex (has a minimum)
    desk_height_cm                 coef=-0.1892  concave (has a maximum)
    chair_recline_deg              coef=-0.1579  concave (has a maximum)
    break_freq_min                 coef=-0.1267  concave (has a maximum)

  Notable interactions:
    monitor_dist_cm*break_freq_min coef=+0.6125  (synergistic)
    monitor_dist_cm*chair_recline_deg coef=+0.5625  (synergistic)

  Predicted optimum (from linear model, at observed points):
    desk_height_cm = 80
    monitor_dist_cm = 50
    chair_recline_deg = 90
    break_freq_min = 25
    Predicted value: 5.5946

  Surface optimum (via L-BFGS-B, linear model):
    desk_height_cm = 80
    monitor_dist_cm = 50
    chair_recline_deg = 90
    break_freq_min = 25
    Predicted value: 5.5946

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

Factor importance:
  1. desk_height_cm  (effect: 3.7, contribution: 35.4%)
  2. monitor_dist_cm  (effect: 2.9, contribution: 27.7%)
  3. break_freq_min  (effect: 2.7, contribution: 25.8%)
  4. chair_recline_deg  (effect: 1.2, contribution: 11.1%)

=== Optimization: productivity_pct ===
Direction: maximize

Best observed run: #1
  desk_height_cm = 72.5
  monitor_dist_cm = 32.1366
  chair_recline_deg = 102.5
  break_freq_min = 57.5
  Value: 100.0

RSM Model (linear, R² = 0.1402, Adj R² = 0.0129):
  Coefficients:
    intercept                      +93.1875
    desk_height_cm                 +0.7386
    monitor_dist_cm                -0.5192
    chair_recline_deg              -0.4521
    break_freq_min                 -1.1293

RSM Model (quadratic, R² = 0.4573, Adj R² = 0.0103):
  Coefficients:
    intercept                      +93.6193
    desk_height_cm                 +0.7386
    monitor_dist_cm                -0.5192
    chair_recline_deg              -0.4521
    break_freq_min                 -1.1293
    desk_height_cm*monitor_dist_cm +0.1875
    desk_height_cm*chair_recline_deg +1.0625
    desk_height_cm*break_freq_min  -0.5625
    monitor_dist_cm*chair_recline_deg +1.8125
    monitor_dist_cm*break_freq_min +1.1875
    chair_recline_deg*break_freq_min -1.1875
    desk_height_cm^2               -0.4214
    monitor_dist_cm^2              +0.2036
    chair_recline_deg^2            -0.1089
    break_freq_min^2               -0.2131

  Curvature analysis:
    desk_height_cm                 coef=-0.4214  concave (has a maximum)
    break_freq_min                 coef=-0.2131  concave (has a maximum)
    monitor_dist_cm                coef=+0.2036  convex (has a minimum)
    chair_recline_deg              coef=-0.1089  concave (has a maximum)

  Notable interactions:
    monitor_dist_cm*chair_recline_deg coef=+1.8125  (synergistic)
    monitor_dist_cm*break_freq_min coef=+1.1875  (synergistic)
    chair_recline_deg*break_freq_min coef=-1.1875  (antagonistic)
    desk_height_cm*chair_recline_deg coef=+1.0625  (synergistic)
    desk_height_cm*break_freq_min  coef=-0.5625  (antagonistic)

  Predicted optimum (from linear model, at observed points):
    desk_height_cm = 80
    monitor_dist_cm = 50
    chair_recline_deg = 90
    break_freq_min = 25
    Predicted value: 96.0266

  Surface optimum (via L-BFGS-B, linear model):
    desk_height_cm = 80
    monitor_dist_cm = 50
    chair_recline_deg = 90
    break_freq_min = 25
    Predicted value: 96.0266

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

Factor importance:
  1. monitor_dist_cm  (effect: 12.0, contribution: 34.3%)
  2. desk_height_cm  (effect: 10.0, contribution: 28.6%)
  3. break_freq_min  (effect: 10.0, contribution: 28.6%)
  4. chair_recline_deg  (effect: 3.0, contribution: 8.6%)