Welcome to DOEPY

Design of Experiments Generator in Python (pip install doepy)

<p align="center"> <img width="500" height="250" src="https://raw.githubusercontent.com/tirthajyoti/doepy/master/images/doe_1.PNG"> </p>

Authored and maintained by Dr. Tirthajyoti Sarkar, Fremont, California.

Check my website for details about my other projects and data science/ML articles.

Introduction

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Design of Experiments (DOE) is an important activity for any scientist, engineer, or statistician planning to conduct experimental analysis. This exercise has become critical in this age of rapidly expanding field of data science and associated statistical modeling and machine learning. A well-planned DOE can give a researcher a meaningful data set to act upon with the optimal number of experiments, thus preserving critical resources.

After all, the aim of Data Science is essentially to conduct the highest quality scientific investigation and modeling with real world data. And to do good science with data, one needs to collect it through carefully thought-out experiments to cover all corner cases and reduce any possible bias.

How to use it?

What supporting packages are required?

First make sure you have all the necessary packages installed. You can simply run the .bash (Unix/Linux) and .bat (Windows) files provided in the repo, to install those packages from your command line interface. They contain the following commands,

pip install numpy
pip install pandas
pip install pydoe
pip install diversipy

How to install the package?

(On Linux and Windows) You can use pip to install doepy::

pip install doepy

(On Mac OS), first install pip,

curl https://bootstrap.pypa.io/get-pip.py -o get-pip.py
python get-pip.py

Then proceed as above.

Github

The package is hosted at this Github repo.

Quick start

Let's say you have a design problem with the following table for the parameters range. Imagine this as a generic example of a chemical process in a manufacturing plant. You have 3 levels of Pressure, 3 levels of Temperature, 2 levels of FlowRate, and 2 levels of Time.

Pressure | Temperature | FlowRate | Time ------------ | ------------- | -------------|----------------- 40 | 290 | 0.2 | 5 50 | 320 | 0.3 | 8 70 | 350 | - | -

First, import build module from the package,

from doepy import build

Then, try a simple example by building a full factorial design. We will use build.full_fact() function for this. You have to pass a dictionary object to the function which encodes your experimental data.

build.full_fact(
{'Pressure':[40,55,70],
'Temperature':[290, 320, 350],
'Flow rate':[0.2,0.4], 
'Time':[5,8]}
)

If you build a full-factorial DOE out of this, you should get a table with 3x3x2x2 = 36 entries.

Pressure | Temperature | FlowRate | Time ------------ | ------------- | -------------|----------------- 40 | 290 | 0.2 | 5 50 | 290 | 0.2 | 5 70 | 290 | 0.2 | 5 40 | 320 | 0.2 | 5 ... | ... | ... | ... ...| ... | ... | ... 40 | 290 | 0.3 | 8 50 | 290 | 0.3 | 8 70 | 290 | 0.3 | 8 40 | 320 | 0.3 | 8 ... | ... | ... | ... ...| ... | ... | ...

There are, of course, half-factorial designs to try!

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Latin Hypercube design

Sometimes, a set of randomized design points within a given range could be attractive for the experimenter to asses the impact of the process variables on the output. Monte Carlo simulations are a close example of this approach.

However, a Latin Hypercube design is a better choice for experimental design rather than building a complete random matrix, as it tries to subdivide the sample space in smaller cells and choose only one element out of each subcell. This way, a more uniform spreading of the random sample points can be obtained.

User can choose the density of sample points. For example, if we choose to generate a Latin Hypercube of 12 experiments from the same input files, that could look like,

build.space_filling_lhs(
{'Pressure':[40,55,70],
'Temperature':[290, 320, 350],
'Flow rate':[0.2,0.4], 
'Time':[5,11]},
num_samples = 12
)

Pressure | Temperature | FlowRate | Time ------------ | ------------- | -------------|----------------- 63.16 | 313.32 | 0.37 | 10.52 61.16 | 343.88 | 0.23 | 5.04 57.83 | 327.46 | 0.35 | 9.47 68.61 | 309.81 | 0.35 | 8.39 66.01 | 301.29 | 0.22 | 6.34 45.76 | 347.97 | 0.27 | 6.94 40.48 | 320.72 | 0.29 | 9.68 51.46 | 293.35 | 0.20 | 7.11 43.63 | 334.92 | 0.30 | 7.66 47.87 | 339.68 | 0.26 | 8.59 55.28 | 317.68 | 0.39 | 5.61 53.99 | 297.07 | 0.32 | 10.43

Of course, there is no guarantee that you will get the same matrix if you run this function because this are randomly sampled, but you get the idea!

<p align="center"><img width="400" height="350" src="http://sumo.intec.ugent.be/sites/sumo/files//sed_3d.png"></p>

Other functions to try

Try any one of the following designs,

• Full factorial: build.full_fact()
• 2-level fractional factorial: build.frac_fact_res()
• Plackett-Burman: build.plackett_burman()
• Sukharev grid: build.sukharev()
• Box-Behnken: build.box_behnken()
• Box-Wilson (Central-composite) with center-faced option: build.central_composite() with face='ccf' option
• Box-Wilson (Central-composite) with center-inscribed option: build.central_composite() with face='cci' option
• Box-Wilson (Central-composite) with center-circumscribed option: build.central_composite() with face='ccc' option
• Latin hypercube (simple): build.lhs()
• Latin hypercube (space-filling): build.space_filling_lhs()
• Random k-means cluster: build.random_k_means()
• Maximin reconstruction: build.maximin()
• Halton sequence based: build.halton()
• Uniform random matrix: build.uniform_random()

Read from and write to CSV files

Internally, you pass on a dictionary object and get back a Pandas DataFrame. But, for reading from and writing to CSV files, you have to use the read_write module of the package.

from doepy import read_write
data_in=read_write.read_variables_csv('../Data/params.csv')

Then you can use this data_in object in the DOE generating functions.

For writing back to a CSV,

df_lhs=build.space_filling_lhs(data_in,num_samples=100)
filename = 'lhs'
read_write.write_csv(df_lhs,filename=filename)

You should see a lhs.csv file in your directory.

A simple pipeline for building a DOE table

Combining the build functions and the read_write module, one can devise a simple pipeline to build a DOE from a CSV file input.

Suppose you have a file in your directory called ranges.csv that contains min/max values of an arbitrary number of parameters. Just two lines of code will generate a space-filling Latin hypercube design, based on this file, with 100 randomized samples spanning over the min/max ranges and save it to a file called DOE_table.csv.

from doepy import build, read_write

read_write.write_csv(
build.space_filling_lhs(read_write.read_variables_csv('ranges.csv'),
num_samples=100),
filename='DOE_table.csv'
)

Features

At its heart, doepy is just a collection of functions, which wrap around the core packages (mentioned below) and generate design-of-experiment (DOE) matrices for a statistician or engineer from an arbitrary range of input variables.

Limitation of the foundation packages used

Both the core packages, which act as foundations to this repo, are not complete in the sense that they do not cover all the necessary functions to generate a DOE table that a design engineer may need while planning an experiment. Also, they offer only low-level APIs in the sense that the standard output from them are normalized numpy arrays. It was felt that users, who may not be comfortable in dealing with Python objects directly, should be able to take advantage of their functionalities through a simplified user interface.

Simplified user interface

There are other DOE generators out there, but they generate n-dimensional arrays. doepy is built on the simple theme of being intuitive and easy to work with - for researchers, engineers, and social scientists of all background - not just the ones who can code.

User just needs to provide a simple CSV file with a single table of variables and their ranges (2-level i.e. min/max or 3-level).

Some of the functions work with 2-level min/max range while some others need 3-level ranges from the user (low-mid-high). Intelligence is built into the code to handle the case if the range input is not appropriate and to generate levels by simple linear interpolation from the given input.

The code will generate the DOE as per user's choice and write the matrix in a CSV file on to the disk.

In this way, the only API user needs to be exposed to, are input and output CSV files. These files then can be used in any engineering simulator, software, process-control module, or fed into process equipments.

Pandas DataFrame support

Under the hood, doepy generates Numpy arrays and convert them to Pandas DataFrame. Therefore, programmatically, it is simple to get those Numpy arrays or DataFrames to do more, if the user wishes so.

Coming in a future release - support for more types of files

Support for more input/output types will come in future releases - MS Excel, JSON, etc.

Designs available

• Full factorial,
• 2-level fractional factorial,
• Plackett-Burman,
• Sukharev grid,
• Box-Behnken,
• Box-Wilson (Central-composite) with center-faced option,
• Box-Wilson (Central-comp