Design Of Experiment

To practice Design of Experiments I will be documenting my process of solving a case study on popcorn (Case 1)

Context

Data

Process for Full Factorial

First things first, we shall transfer the data to an excel sheet

In order to analyse the data and determine the effect of each factor and the ranking of each factor from most affecting to the least we first have to find out what the average of each factor when it is negative(-)/low point and when it is positive(+)/high point. For example for A, the runs 1,4,5 and 6 are all when A is high so taking the average of that (3.5+1.2+0.7+0.3)/4 =1.425 and we can do the same for when A is low so take the results of run 2,3,7,8 and finding the average (1.6+0.7+0.5+3.1)/4 = 1.475. This should be done for B and C as well and the results are shown below.

Using this results, we can plot a graph to get our rankings.

The way to interpret the graph is that the higher the gradient, the more it affects the results. Thus from the graph, we can say that C has the biggest effect on the results followed by B and lastly the one with the lowest gradient is A so it has the lowest effect in the results.

Now we can determine the interaction effects.

For this we have compare A x B, A x C and B x C.

Using A x B as an example, to compare them we have see the average of low B at low and high A and the same with high B, the average of high B at low and High A. For the first scenario we have to find runs with low B and low A which is 3 and 8 and the second scenario, low B and high A, runs 1 and 5 will be chosen.

Using the average of the 2 scenarios and finding the difference gives us the effect of B on A.

This technique should be repeated for the other 5 scenarios.

Using these values, a graph can be made and the effect can also be determined. The closer the lines are to parallel, the less effect they have on each other. For the graph above, the difference in gradient is relatively high and lines are far from parallel thus A affects B quite a bit.

For the A x C graph, the lines are very close to parallel thus they do not affect each other that much.

For the B x C graph, the lines are far from parallel and the gradient difference is high thus they affect each other a lot as well.

From this datas we can conclude the order of the most affecting factor to the least and also that A does not really affect the C factor, A affects B by quite a bit and A affects C by a lot.

Fractional factorial analysis

For this we have to pick out a wide range of data that has at leas 2 points in each negative and positve for each factor. For this runs 4,5,7,8 are sufficient.

Similarly to the first technique we will be finding the average of each factor at high and low.

The results of calculations can be seen below.

Now once again we can graph the numbers to get 3 lines with different gradients.

To intepret this graph, the largest gradient is the most affecting factor so is C, B and A in decreasing order.

From this data we can conclude the most affecting factors in order.

In conclusion I think I have learnt a good skill in designing experiments and this really helps with important infomation that we might need to find for our FYP.

Thats all for this blog. Hope to do more next time!

Excel sheet: https://1drv.ms/x/s!Am_IQa84carUhSlJSNFioel0vHHg?e=CuJLzs