Design Of Experiment

 What is Design Of Experiments (DOE)?

  • A statistics-based approach to designing experiments.
  • A methodology to obtain knowledge of a complex, multi-variable process with the fewest trials possible.
  • An optimization of the experimental process itself.
  • The backbone of any product design as well as any process/product improvement efforts.


Fundamentals of DOE

  • Response variable (dependent)
  • Factor (independent)
  • Level
  • Treatment


Goal of experimentation

It is to study the effects of factors (independent variable) affecting the results (dependent variable).


Full Factorial

  • Infeasible to run all treatments
  • Time consuming

Highlighted in yellow - low
Non-highlighted - high
A - Concentration of coagulant added
B - Treatment temperature
C - Stirring speed

Determine the effect of single factors 

  1. Calculate the average of all the EIGHT runs.

  2. Plot '-' and '+' for different factors on the same line graph.

  3. Compare the three different lines.
The steepest gradient of the '-' and '+' line of a factor has the most effect. 
The most gentle gradient of the '-' and '+' line of a factor has the least effect. 

Determine the interaction effects

  1. Calculate the average of all the EIGHT runs.

  2. Plot the effect of AxB at '-' and '+'.

  3. Compare the two lines at '-' and '+'.
  4. Repeat for AxC and BxC.
If the '-' and '+' has a big gradient and is not parallel, it said to have interactions between the two factors.
If the '-' and '+' has a margin gradient and is  parallel, it said to have no interactions between the two factors.


Fractional Factorial

  • Represent Full Factorial
Orthogonal to Full Factorial. All factors occur the same number of times.
Highlighted in yellow - low
Non-highlighted - high
A - Concentration of coagulant added
B - Treatment temperature
C - Stirring speed

Determine the effect of single factors

  1. Select the FOUR runs.
  2. Calculate the average of the FOUR runs.

  3. Plot '-' and '+' for different factors on the same line graph.

  4. Compare the three different lines.
The steepest gradient of the '-' and '+' line of a factor has the most effect. 
The most gentle gradient of the '-' and '+' line of a factor has the least effect. 

Determine the interaction effects

  1. Select the FOUR runs.
  2. Plot the effect of AxB at '-' and '+'.

  3. Compare the two lines at '-' and '+'.
  4. Repeat for AxC and BxC.
If the '-' and '+' has a big gradient and is not parallel, it said to have interactions between the two factors.
If the '-' and '+' has a margin gradient and is  parallel, it said to have no interactions between the two factors.

Link to excel file for Design Of Experiment data analysis


Reflection

The method for data analysis is quite tedious as there are many data to look at and might get confused. The data in this assignment is only eight runs. When during the DOE for practical trial, more than 8 runs is needed. This may cause errors during data analysis and needed to be done meticulously. To test for ranking of main effect, fractional factorial is usable to represent full factorial. But unable to have the same conclusion as the interactions between the two factors.