DOE

 HELLO👋 and welcome back to another blog👀. so this week we learnt about design of experiments also known as DOE. To let you understand more in depth I did a documentation of my task which was given. This task was given so that we can understand better on how we can use DOE in the future. so scroll down to understand better👌👇.

DOCUMENTATION

Firstly I converted my given data from the case study into excel. therefore this will make it easier for you as all calculations will be automatically calculated for you.😱

Factor A= diameter, 10 cm and 15 cm

Factor B= microwaving time, 4 minutes and 6 minutes

Factor C= power, 75% and 100%

From the data obtained we can determine the effects on the single factors.

when diameter decreases from 15cm to 10 cm, the amount of bullets decreases from 3.5g to 0.7g.

when microwaving time increases from 4mins to 6mins, the amount of bullets decreases from 3.1g to 1.6g.

when the power setting of microwave increases 75% to 100%, the amount of bullets decreases from 1.2g to 0.3g .

FULL FACTORIAL💫

Since we have obtained all the values needed, we will move on to doing the full factorial. we have all our values ready to be distributed now 😁!!

To find the significance rankings we have to put these values in a graph. you would get something like this. we would be mainly using the gradients to compare.😸

From this graph we have obtained we can define our significance rankings by looking at the gradients. Hence C is the most significant. This is due to the gradient being the steepest. B is less significant than C but more significant than A. This is due to the line of B being less steeper than C but more steeper than A. A is the least significant.  This is due to the line being the least steepest compared to all 3 factors. Therefore C>B>A.

now we will move onto finding out the interactions between different factors.

NOW we will need to calculate the different values. this is what i did😎:

Calculations: 

At LOW B, Average of low A=(3.1+0.7)/2=1.9

At LOW B, Average of high A=(3.5+0.7)/2=2.1

At LOW B, total effect of A=(2.1-1.9)=0.2 (increase) 

At HIGH B, Average of low A=(1.6+0.5)/2=1.05

At HIGH B, Average of high A=(1.2+0.3)/2=0.75

At HIGH B, total effect of A=(0.75-1.05)=-0.3 (decrease)

From this I can observe that both line has different gradients. one has a negative gradient while the other has a positive gradient. hence, even though it is not shown in the graph, both will intersect at one point. therefore there will be an interaction between A and B.

Calculations: 

At LOW C, Average of low A=(3.1+1.6)/2=2.35

At LOW C, Average of high A=(3.5+1.2)/2=2.35

At LOW C, total effect of A=(2.35-2.35)=0 (decrease) 

At HIGH C, Average of low A=(0.7+0.5)/2=0.6

At HIGH C, Average of high A=(0.7+0.3)/2=0.5

At HIGH C, total effect of A=(0.5-0.6)=-0.1 (decrease)

From this I can observe that both line has different gradients. one has a negative gradient while the other has a positive gradient. hence, even though it is not shown in the graph, both will intersect at one point. therefore there will be an interaction between A and C. 

Calculations: 

At LOW C, Average of low B=(3.5+3.1)/2=3.3

At LOW C, Average of high B=(1.6+1.2)/2=1.4

At LOW C, total effect of B=(1.4-3.3)=-1.9 (decrease) 

At HIGH C, Average of low B=(0.7+0.5)/2=0.6

At HIGH C, Average of high B=(0.7+0.3)/2=0.5

At HIGH C, total effect of B=(0.5-0.6)=-0.1 (decrease)

From this I can observe that both line has different negative gradients.  Hence, even though it is not shown in the graph, both will intersect at one point. therefore there will be an interaction between C and B.

CONCLUSION😆: therefore seen from the graphs above B and C has shown bigger interactions as the gradients are both negative and has a larger difference compared to AxB and AxC. nonetheless the points for all interactions will intersect each other to form interactions between each other.

FRACTIONAL FACTORIAL🔆

for fractional factorial, we need to choose 4 runs which has an equal amount of upper and lower limits for each factor. I choose runs 2,3,4 and 5💥.

similarly to full factorial💭💭, from the data obtained we can determine the effects on the single factors.

when diameter increases from 10cm to 15 cm, the amount of bullets increases from 0.7g to 1.2g.

when microwaving time decreases from 6mins to 4mins, the amount of bullets decreases from 1.6g to 0.7g.

when the power setting of microwave increases 75% to 100%, the amount of bullets decreases from 1.2g to 0.7g .

we will be doing the same thing for our fractional to find out the significance as well as rankings. we would be also using gradients to compare😃.

From this graph we have obtained we can define our significance rankings by looking at the gradients. Hence C is the most significant. This is due to the gradient being the steepest. A is less significant than C but more significant than B . This is due to the line of A being less steeper than C but more steeper than B. B is the least significant.  This is due to the line being the least steepest compared to all 3 factors. Therefore C>A>B.

now we will move onto finding out the interactions between different factors.

NOW we will need to calculate the different values. I did the same as what i did for full factorial😎😎:

Calculations: 

At LOW B, the low A=0.7

At LOW B, the high A=0.7

At LOW B, the effect A= 0

At HIGH B, the low A=1.6

At HIGH B, the high A=1.2

At HIGH B, the effect A=1.2-1.6=-0.4

From this graph, there is one line with an equation and another with no gradient. Hence even though it is not shown in the graph line of HIGH B will intersect line of LOW B. Therefore there will be an interaction between of A and B.

Calculations: 

At LOW C, the low A=1.6

At LOW C, the high A=1.2

At LOW C, the effect A= 1.2-1.6=-0.4

At HIGH C, the low A=0.7

At HIGH C, the high A=0.7

At HIGH C, the effect A=0

From this graph, there is one line with an equation and another with no gradient. Hence even though it is not shown in the graph line of LOW C will intersect line of HIGH C. Therefore there will be an interaction between of A and C.

As we are unable to obtain the low value of B for the low factor C😔, we are able to conduct an interaction data analysis between B and C. This is because in the 4 runs selected in my fractional factorial data analysis, there are no high B and C in the runs selected.

CONCLUSION💣💣:

From the graphs above, the trend is quite similar but since there is a difference in the significance ranking, there will be some deviations when prototyping this set-up. this also showed me that the points i chose were not orthogonal as what I assumed at first. due to not obtaining some points for my fractional factorial, all the interactions were not able to be seen. therefore full factorial will be a better way to sort out the data for this data that I have used and obtained.

link to my excel spreadsheet with all my graphs:

https://docs.google.com/spreadsheets/d/17u6jJSlsuc8CBQ8yuLZEb6yw9qyPSDPr/edit?usp=sharing&ouid=103213109638966602220&rtpof=true&sd=true