Consider given Exercise. The design factors are A, B, C, and D, each at three levels. These are assigned to an orthogonal array (inner array) with the factors A, B, C, and D assigned to columns 1, 2, 3, and 4, respectively.
Suppose that, in addition to the three main effects of the noise factors E, F, and G, it is felt that the interaction effects E × F and E × G should be investigated. What type of design would you use for the outer array? Suppose the outer array selected is L8, with the assignments as follows: E to column 1, F to column 2, E × F to column 3, G to column 4, and E × G to column 5. The remaining two columns are assigned to the experimental error.
Table 1 shows the moisture content of the eight replications for each of the nine experiments in the inner array. The coded target value is 20. Show the complete parameter design layout using the Taguchi method. Calculate the mean response and the appropriate signal-to-noise ratios. Plot the average S/N ratios and the average responses and discuss how the design factor levels are to be selected. Use the average response plots to determine the existence of the interaction effects A × E, B × F, E × F, and E × G. What are the optimal settings of the design parameters using Taguchi's parameter design approach?
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Table 1
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Inner-Array Experiment
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Outer-Array Experiment
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1
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2
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3
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4
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5
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6
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7
|
8
|
|
1
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19.3
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20.2
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19.1
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18.4
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21.1
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20.6
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19.5
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18.7
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|
2
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20.6
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18.5
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20.2
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19.4
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20.1
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16.3
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17.2
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19.4
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3
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18.3
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20.7
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19.4
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17.6
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20.4
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17.3
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18.2
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19.2
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4
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20.8
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21.2
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20.2
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19.9
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21.7
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22.2
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20.4
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20.6
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5
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18.7
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19.8
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19.4
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17.2
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18.5
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19.7
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18.8
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18.4
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6
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21.1
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20.2
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22.4
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20.5
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18.7
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21.4
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21.8
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20.6
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7
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17.5
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18.3
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20.0
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18.8
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20.2
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17.7
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17.9
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18.2
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8
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20.4
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21.2
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22.4
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21.9
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21.5
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20.8
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22.5
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21.7
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9
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18.0
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20.2
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17.6
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22.4
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17.2
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21.6
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18.5
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19.2
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Exercise
In a food processing plant, four design parameters, A, B, C, and D, each at three levels, have been identified as having an effect on the moisture content in packaged meat. Three noise factors, E, F, and G, each at two levels, are also to be investigated in the experiment. In the inner array, an L9 orthogonal array is used with the factors A, B, C, and D assigned to columns 1, 2, 3, and 4, respectively. For the outer array, an L4 orthogonal array is used with the noise factors E, F, and G assigned to columns 1, 2, and 3, respectively.
Table 2 shows the moisture content in a coded scale for four replications of each of the nine experiments in the inner array. It is preferable that the moisture content be around a coded value of 20. Show the complete parameter design layout using the Taguchi method. Calculate the mean response and the appropriate signal-to-noise ratio. Plot the average S/N ratios and the average responses and discuss how the design factor levels are to be selected. Use the average response plots to determine the existence of possible interactions B× E and C× F. What are the optimal settings of the design parameters using Taguchi's parameter design approach?
| Table 2 |
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Inner-Array Experiment
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Outer-Array Experiment
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1
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2
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3
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4
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1
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18.5
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21.2
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20.5
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19.3
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2
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16.8
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17.3
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20.9
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18.5
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3
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21.1
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21.8
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20.6
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19.4
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4
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20.2
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17.7
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19.8
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20.8
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5
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16.2
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21.5
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21.2
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21.4
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|
6
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18.3
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18.5
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17.8
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17.2
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|
7
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20.6
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21.4
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16.8
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19.5
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|
8
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17.5
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20.0
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21.0
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20.4
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|
9
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20.4
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18.8
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19.6
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18.3
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