Design of Experiment

 DESIGN OF EXPERIMENTS!!

Case study 2

In this case study, I am the Chief Safety Officer(CSO) therefore I am tasked to operate Design of experiments on case 2. Both full and fractional factorial designs.

We will start with the Full Factorial design:



With the given data, I was able to input it into the DOE template so that it would make things more convenient for me. I input the data into the column R1 since I was given only 1 run.

 

With the template already set and the formulas done for us, the spread sheet will calculate the means for each factor as shown below:


From here we can plot scatter graphs and compare the gradients of all the lines. The line with a steeper gradient tells us that that factor is the most significant out of the 3. This means that that factor will cause a more effective change to the whole experiment.

 


From here we can see that the gradient of the line of  factor C(stirrer speed) is the steepest. Therefore we can conclude that it will provide the most significant change in the experiment.

 We can see that when Factor A(concentration of coagulant added) decreases from 2% to 1%, the mean pollutant discharged decreases from quite significantly from 17.5lb/day to 5 lb/day.

For factor B(treatment temperature), when decreased from 100ºF to 72ºF, the mean pollutant discharged decreases from 12lb/day to 10.5lb/day. Not very significant.

For factor C(stirring speed), when decreased from 400rpm to 200rpm, the mean pollutant discharged increases significantly from 4 lb/day to 18.5lb/day.

Therefore we can rank the factors in order of how significant the effects of the factors are. 1 being the most significant.

1) Stirring speed

2) Concentration of coagulant added

3) Treatment temperature

Next we will be comparing the interactions between each of the factors with each other.

We will start with A and B:

We can then plot a graph to compare which factor is more significant in affecting each other. 

We can see that there is not much of a difference between the value of the gradients of the means of A at different levels of B. However, there is still a change of 1 between the means of A at the levels of B. at high B, there is a slight steepness of -13 as compared to at low B with a steepness of -12. Thus I can say that the interaction between A and B is not significant.

We must repeat this process for A and C, and B and C.

For A and C:



From the graph we can see that the gradients of both lines do not defer as much again. Only by 2. Hence the interactions of these factors are not significant.

 For B and C:


We can see from the graph that the gradients of the means of B at different levels of C is very drastic. Therefore we can say the interactions between B and C are very significant.

In conclusion we can say that Factor C( stirring speed) is the most significant followed by factor A(concentration of coagulant added) and then factor B(treatment temperature). B and C produces the most interaction. There is little interaction between AxC and AxB.

FRACTIONAL FACTORIAL DATA ANALYSIS

Given below are the runs that I have chosen to be used as for my fractional factorial data analysis. Which is to me applicable to the statistical orthogonality.

From here, we can plot a graph to see how the different factors affect the experiments.




 
From this graph we can see that Factor C possesses the steepest gradient of 14. For factors A and B, the gradient of the line is the same. Therefore we can finally deduce the rankings of the factors due to the steepness of the gradients and after the whole DOE test

1) Stirrer speed

2) Concentration of coagulants

3) Treatment temperature

Here are the links to the relevant documents:

Full factorial:

Workings for full factorial:

Fractional factorial:

























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