Design of Experiment
Step 1: Design variables and performance variables
Since the magnetic connection might not be stable, it is necessary to test how strong these magnetic tapes are attracted.
There are two possible design variables:
1. Number of magnetic tapes on the single plastic box (x1);
2. Area of one magnetic tape (x2).
The only performance variable in this case is the minimum tensile force (y) that pulls two boxes apart.
Step 2: Target and boundaries
For variable x1, it has two levels: 2 (low, denoted as -1) and 3 (high, denoted as 1)
For variable x2, it also has two levels: 19 cm^2 (low, denoted as -1) and 37.5 cm^2 (high, denoted as 1)
For the minimum tensile force, its target value shouldn’t be too high because users might struggle to open this box; and it also shouldn’t be too low because in that case the box can be easily broken into two parts. Ideally, the target value is 8kN, which is identical to the force applied to hold a 0.8kg object.
Step 3: Experiment plan and matrix
The experiment is set up as follows:
There are 4 trials in total. Each variable has two levels as explained above. Each trail consists of a different combination of x1 and x2. For each test, response is tested twice, i.e., the number of replicates is 2. To measure each response, a force gauge is utilized which can directly display the amount of force in kN it has sensed.
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The table below shows the experiment matrix that reveals the experiment setup.
Step 4: Hypothetical data
The following table contains the hypothetical data which are estimated by reasonable assumptions. The average value of y, standard deviation, and variance in each trial are all calculated.
Step 5: Analysis
The average of the variances of the replicates is 2.03.
For main effect, M1, M2, M12 are calculated and ranked from highest to lowest.
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If using 2-sigma method, we noticed that M1 and M2 are larger than 2-sigma, which means the significant effects are x1 and x2.
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Therefore, the predicted main equation becomes:
However, if using graphical method, the plot is shown below:
It means that the significant main effect is only x1.
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The corresponding predicted main equation becomes:
For noise effect, E1, E2, E12 are calculated and ranked by similar method. If using graphical method, the plot we get is:
It means that the significant noise effect is E1.
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The corresponding predicted noise equation becomes:
Based on the experiment result, the combination of x1=1 and x2=-1 can give the response that is close to the target value. In other word, the design parameters will have the following changes: the number of magnetic tapes on the single box will be 3, and the area of one magnetic tape will be 19 cm^2.