Control Factors Level 1 Level 2 Level 3 Stirring Time (ST) 2 4 6 Cast Temperature (CT) 700 750 800 Percentage Reinforcement (PR) 0 0.75 1.5 produce L9 and L16 orthogonal array for the above data
Question
Control Factors Level 1 Level 2 Level 3 Stirring Time (ST) 2 4 6 Cast Temperature (CT) 700 750 800 Percentage Reinforcement (PR) 0 0.75 1.5 produce L9 and L16 orthogonal array for the above data
Solution
Sure, I can help with that.
The L9 and L16 orthogonal arrays are used in experimental design to determine the effect of multiple variables on an outcome. They are called "orthogonal" because each factor is independent of the others.
The L9 orthogonal array is a 3^3 design, meaning it can accommodate 3 factors at 3 levels each. The L16 orthogonal array is a 4^2 design, meaning it can accommodate 4 factors at 2 levels each.
Given your data, you have 3 factors (Stirring Time, Cast Temperature, Percentage Reinforcement) at 3 levels each. Therefore, you can use an L9 orthogonal array.
Here's how you can set up the L9 orthogonal array:
| Experiment | Stirring Time | Cast Temperature | Percentage Reinforcement |
|---|---|---|---|
| 1 | 2 | 700 | 0 |
| 2 | 2 | 750 | 0.75 |
| 3 | 2 | 800 | 1.5 |
| 4 | 4 | 700 | 0.75 |
| 5 | 4 | 750 | 1.5 |
| 6 | 4 | 800 | 0 |
| 7 | 6 | 700 | 1.5 |
| 8 | 6 | 750 | 0 |
| 9 | 6 | 800 | 0.75 |
However, your data does not fit into an L16 orthogonal array because you have 3 levels for each factor, not 2. The L16 array is used when you have 4 factors at 2 levels each.
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