Design Of Experiments

As an engineering student. It is important that we need have the skills to set up an experiment and collect the results to analyse the different factors. Thus, in this week's lesson, we learned about the design of experiments. It is a methodology to obtain the knowledge of a complex, multivariable process with the fewest trials possible by using the skills call fractional factories design. To enhance what I lesson in the lessons, I will practice the design of the experiment skill by using a case study. 

Case study:

In a wastewater treatment facility, a combination of coagulant chemicals, treatment temperature, and stirring speed were identified as a critical factor to treat the wastewater. the clean water produced is recycled back into the main process and at the same time reduce the amount of the pollutant discharged by the plant.

8 runs were performed and the data are shown below.

The response variable (y) is the amount of pollutant discharge(Ib/day)

A = concentration of coagulant added, 1% and 2% by weight

B = treatment temperature, 72 degrees Fahrenheit  and 100 degrees Fahrenheit

C = Stirring speed, 200 rpm and 400 rpm

Full factorial data analysis

As all 3 factors have 2 individual levels, I can simply represent the higher level using '+' and the lower value using '-'. This will be easier when I apply the graphical method later.

To determine which factor has the most significant effect on the water treatment by using the experimental results obtained above, I need to use excel to help me plot the graph. Firstly, calculate the difference in the amount of pollutant discharge(y) when the factor is at two levels. 

Use the line graph the plot the 3 factors in one graph where the y-axis is the amount of pollutant discharge and the x-axis is the level of the factor.

From the graph when can see that C has the steepest gradient. Thus we can interpret that Factor C which is the stirring speed is the most significant factor in water treatment. When the stirring speed increase from a low level to a high level, the amount of the pollutant water discharge flow rate decrease most significantly. We can also see that B has the least steep gradient. Thus we can interpret that Factor B which is the treatment temperature is the least significant factor in water treatment. The ranking of the factors will be:

1. Stirring speed 
2. The concentration of coagulant added
3. Treatment temperature

The graphical method can be also used to determine the interaction effect which it to see how the effect of one factor on the response variable is different at different levels of the other factor.

The first step I do is to calculate the average values of C at the different levels of A and C.

With the results I obtain, I can plot the graph to analyse the interaction between factors A and C. From the graph, we can see that the gradient of both lines is positive and has different values. This means that at high A, factor C has a greater effect on the water treatment as it shows a steeper gradient on the graph. Therefore that is a significant interaction between A and C.

Perform the same step for factors A and B.

From the graph, we can see that the gradient of both lines is negative and has very small different values. This means that at both low A and high A, factor B has a similar effect on the water treatment as it shows a similar gradient on the graph. Therefore that is a minor interaction between A and B.

Now we plot the factors B and C.

From the graph, we can see that the gradient of both lines is positive and has very small different values. This means that at both low B and high B, factor C has a similar performance on the water treatment as it shows a similar gradient on the graph. Therefore that is a minor interaction between B and C.

In conclusion, after doing the data analysis of the experimental result, we can say that factor C which is the stirring speed is the most effective on the water treatment. However, factor C  has significant interaction with factor A which is the concentration of coagulant added. Factor C perform very differently when the A change.

Factional factorial data analysis

Although full factorial data analysis is a very effective way to study our experimental results. It is tedious to conduct the experiment so many times. Thus we use the factional factorial data analysis to help us achieve the same outcome with lesser time spent.

Before we polt the graph in excel, we need to select the 4 experiment results from the 8 runs. The 4 runs I select are  

• 2
• 3
• 5
• 8

The reason I selected these 4 RUNS is that all factors for both low level and high level occur the same number of times. This is a balanced design for the experiment and it is statistically orthogonal. Then I use excel to calculate the mean result of the 4 runs

 Plot the graph for the 3 factors on excel. 

From the graph when can see that C has the steepest gradient. Thus we can interpret that Factor C which is the stirring speed is the most significant factor in water treatment. When the stirring speed increase from a low level to a high level, the amount of the pollutant water discharge flow rate decrease most significantly. We can also see that both A and B have the same gradient. Thus we can interpret that Factor A and B which is the concentration of coagulant added and treatment temperature have the same effect in water treatment. Thus the ranking of the 3 factors will be：

1. Stirring speed 
2. The concentration of coagulant added / Treatment temperature

This result is slightly different from what I obtain when I use the full factorial data analysis. The highest-ranking factors are still the stirring speed but the concentration of coagulant added and Treatment temperature show the same effect when I analyze the data using fractional factorial. This is because the fractional factorial has lesser data point compared to the full factorial. the accuracy of the conclusion may be affected. but a similar trend is shown when I used factional factorial data analysis. Thus, It is considered when the data point we need to be collected is extremely large.

Hyperlink for full factorial data analysis:

https://docs.google.com/spreadsheets/d/1wghFDixlUp47ubyPW3dUINP05rBrkh3m/edit?usp=sharing&ouid=111612840397745602826&rtpof=true&sd=true

Hyperlink for fractional factorial data analysis:

https://docs.google.com/spreadsheets/d/1vh_JJHFa8u05i5eiYVmgmVQuPV9Decs1/edit?usp=sharing&ouid=111612840397745602826&rtpof=true&sd=true