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8 changes: 4 additions & 4 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -117,7 +117,7 @@ After this, a simple menu will be printed on the screen and you will be prompted
At this time, **No**. I plan to work on turning this into a full-fledged Python library which can be installed from PyPi repository by a PIP command. But I cannot promise any timeline for that :-) ***If somebody wants to collaborate and work on an installer, please feel free to do so.***

## Examples <a name="Examples"></a>
Let's say the input file contains the following table for the parameters range. Imagine this as a generic example of a checmical process in a plant.
Let's say the input file contains the following table for the parameters range. Imagine this as a generic example of a chemical process in a plant.

Pressure | Temperature | FlowRate | Time
------------ | ------------- | -------------|-----------------
Expand Down Expand Up @@ -157,7 +157,7 @@ Pressure | Temperature | FlowRate | Time
70 | 350 | 0.4 | 11

### Fractional-factorial design <a name="FracFactorial"></a>
Clearly the full-factorial designs grows quickly! Engineers and scientists therefore often use half-factorial/fractional-factorial designs where they confound one or more factors with other factors and build a reduced DOE. Let's say we decide to build a 2-level fractional factorial of this set of variables with the 4th variables as the confounding factor (i.e. not an independent variable but as a function of other variables). If the functional relationship is "A B C BC" i.e. the 4th parameter vary depending only on 2nd and 3rd parameter, the output table could look like,
Clearly, the full-factorial designs grows quickly! Engineers and scientists therefore often use half-factorial/fractional-factorial designs where they confound one or more factors with other factors and build a reduced DOE. Let's say we decide to build a 2-level fractional factorial of this set of variables with the 4th variable as the confounding factor (i.e. not an independent variable but as a function of other variables). If the functional relationship is "A B C BC" i.e. the 4th parameter vary depending only on 2nd and 3rd parameter, the output table could look like,

Pressure | Temperature | FlowRate | Time
------------ | ------------- | -------------|-----------------
Expand All @@ -172,12 +172,12 @@ Pressure | Temperature | FlowRate | Time

### Central-composite design <a name="CentralComposite"></a>
<p align="center"><img width="400" height="150" src="http://www.ece.northwestern.edu/local-apps/matlabhelp/toolbox/stats/doe_cc.gif"></p>
A Box-Wilson Central Composite Design, commonly called 'a central composite design,' contains an imbedded factorial or fractional factorial design with center points that is augmented with a group of 'star points' that allow estimation of curvature. One central composite design consists of cube points at the corners of a unit cube that is the product of the intervals [-1,1], star points along the axes at or outside the cube, and center points at the origin. Central composite designs are of three types. Circumscribed (CCC) designs are as described above. Inscribed (CCI) designs are as described above, but scaled so the star points take the values -1 and +1, and the cube points lie in the interior of the cube. Faced (CCF) designs have the star points on the faces of the cube. Faced designs have three levels per factor, in contrast with the other types that have five levels per factor. The following figure shows these three types of designs for three factors. [Read this page] (http://blog.minitab.com/blog/understanding-statistics/getting-started-with-factorial-design-of-experiments-doe) for more information about this kind of design philosophy.
A Box-Wilson Central Composite Design, commonly called 'a central composite design,' contains an embedded factorial or fractional factorial design with center points that is augmented with a group of 'star points' that allow estimation of curvature. One central composite design consists of cube points at the corners of a unit cube that is the product of the intervals [-1,1], star points along the axes at or outside the cube, and center points at the origin. Central composite designs are of three types. Circumscribed (CCC) designs are as described above. Inscribed (CCI) designs are as described above, but scaled so the star points take the values -1 and +1, and the cube points lie in the interior of the cube. Faced (CCF) designs have the star points on the faces of the cube. Faced designs have three levels per factor, in contrast with the other types that have five levels per factor. The following figure shows these three types of designs for three factors. [Read this page] (http://blog.minitab.com/blog/understanding-statistics/getting-started-with-factorial-design-of-experiments-doe) for more information about this kind of design philosophy.

### Latin Hypercube design <a name="LatinHypercube"></a>
<p align="center"><img width="400" height="350" src="http://sumo.intec.ugent.be/sites/sumo/files//sed_3d.png"></p>

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](https://en.wikipedia.org/wiki/Monte_Carlo_method) are close example of this approach. However, a Latin Hypercube design is 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,
Sometimes, a set of ***randomized design points within a given range*** could be attractive for the experimenter to assess the impact of the process variables on the output. [Monte Carlo simulations](https://en.wikipedia.org/wiki/Monte_Carlo_method) are close example of this approach. However, a Latin Hypercube design is better choice for experimental design rather than building a complete random matrix as it tries to subdivide the sample space into 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. Users 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,

Pressure | Temperature | FlowRate | Time
------------ | ------------- | -------------|-----------------
Expand Down