This guide walks you through creating Box-Behnken designs using Python’s pyDOE3 package. I won’t dive deep into the theory—if you need background on response surface methodology or why Box-Behnken designs are useful, check out Central Composite Design vs. Box-Behnken Design first.

Installation and Setup

First, install the required packages. If you’ve already followed the full factorial or fractional factorial tutorials, you can skip this step:

pip install pyDOE3

Next, import the packages:

from pyDOE3 import bbdesign
import pandas as pd
import numpy as np

The bbdesign() function in pyDOE3 makes creating Box-Behnken designs straightforward. You just need to specify the number of factors and optionally the number of center points.

Understanding the Basic Syntax

Box-Behnken designs require at least 3 factors. The basic syntax is:

bbdesign(n, center)

Where:

• n: Number of factors (minimum 3)
• center: Number of center points. If you leave it out, pyDOE3 will add a reasonable number of center points automatically (for 3 factors, that default is 3).

The design returns coded values (-1, 0, +1) where -1 is the low level, +1 is the high level, and 0 is the center point.

Create a Basic 3-Factor Box-Behnken Design

Let’s start simple with a 3-factor design:

# Create a default 3-factor Box-Behnken design
design = bbdesign(3)
print(design)

Output:

[[-1. -1.  0.]
 [ 1. -1.  0.]
 [-1.  1.  0.]
 [ 1.  1.  0.]
 [-1.  0. -1.]
 [ 1.  0. -1.]
 [-1.  0.  1.]
 [ 1.  0.  1.]
 [ 0. -1. -1.]
 [ 0.  1. -1.]
 [ 0. -1.  1.]
 [ 0.  1.  1.]
 [ 0.  0.  0.]
 [ 0.  0.  0.]
 [ 0.  0.  0.]]

This creates 15 runs: 12 factorial points plus 3 center points. Notice how Box-Behnken designs work—they explore the edges of your experimental space (where two factors are at their extremes and one is at the center) but never test all factors at their extremes simultaneously. That’s the key advantage: no corner points.

Let’s make this more practical by converting to a DataFrame with meaningful names:

# Convert to DataFrame with meaningful names
factors = ['Temperature', 'Pressure', 'Catalyst']
df = pd.DataFrame(design, columns=factors)
print(df)

Output:

	Temperature	Pressure	Catalyst
0	-1.0	-1.0	0.0
1	1.0	-1.0	0.0
2	-1.0	1.0	0.0
3	1.0	1.0	0.0
4	-1.0	0.0	-1.0
5	1.0	0.0	-1.0
6	-1.0	0.0	1.0
7	1.0	0.0	1.0
8	0.0	-1.0	-1.0
9	0.0	1.0	-1.0
10	0.0	-1.0	1.0
11	0.0	1.0	1.0
12	0.0	0.0	0.0
13	0.0	0.0	0.0
14	0.0	0.0	0.0

Complete Workflow: Chemical Reactor Example

Let’s work through a realistic scenario from start to finish. You’re optimizing a chemical reactor and need to understand how temperature, pressure, and catalyst concentration affect yield. Running experiments at extreme combinations (very high temperature AND very high pressure AND maximum catalyst) could damage your equipment or create safety hazards. Box-Behnken is perfect for this situation.

Here’s a complete workflow that takes you from factor definition to a ready-to-use experimental plan:

from pyDOE3 import bbdesign
import pandas as pd
import numpy as np

# 1. DEFINE YOUR EXPERIMENT
factor_levels = {
    "Temperature": (150, 200),    # °C
    "Pressure": (2, 6),           # bar  
    "Catalyst": (0.5, 2.0)        # %
}

# 2. CREATE THE DESIGN
num_factors = len(factor_levels)
design = bbdesign(num_factors, center=3)

# 3. CONVERT TO DATAFRAME
factors = list(factor_levels.keys())
df = pd.DataFrame(design, columns=factors)

# 4. MAP TO REAL VALUES
for factor, (low, high) in factor_levels.items():
    center = (low + high) / 2
    df[factor] = df[factor].map({-1: low, 0: center, 1: high})

# 5. RANDOMIZE RUN ORDER
df = df.sample(frac=1, random_state=42).reset_index(drop=True)

# 6. ADD RUN NUMBERS AND RESPONSE COLUMN
df.index += 1
df.index.name = 'Run'
df['Yield'] = ''  # Empty column for recording results

# 7. EXPORT TO EXCEL
df.to_excel('box_behnken_experiment.xlsx')
print(f"Design created: {len(df)} runs")
print(df.head(10))

Example output (first 10 runs after randomization):

Run	Temperature	Pressure	Catalyst	Yield
1	175.0	2.0	2.00
2	175.0	6.0	2.00
3	150.0	2.0	1.25
4	175.0	4.0	1.25
5	150.0	4.0	2.00
6	175.0	2.0	0.50
7	200.0	2.0	1.25
8	150.0	6.0	1.25
9	175.0	4.0	1.25
10	150.0	4.0	0.50

Notice again that you never test all three factors at their maximum simultaneously (200°C, 6 bar, 2.0% catalyst). This gives you a complete, randomized experimental plan ready for the lab while keeping you within safe operating conditions.

Up Next:

<< How to Create a Central Composite Design in Python >>

<< Central Composite Design vs. Box-Behnken Design >>