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Taguchi’s Orthogonal Array Experiment  483


             However, in the compound factor method, there is a partial loss of orthogo-
             nality. The two compound factors are not orthogonal to each other, but each
             of them is orthogonal to other factors in the experiment.

           13.4 Taguchi Experiment Data Analysis

           There are many similarities between the data analysis of the Taguchi
           experiment and “classical” design of experiment.
             In Taguchi experimental data analysis, the following three items are
           very important:

           1. Analysis of variance (ANOVA)
           2. Main-effects chart and interaction chart
           3. Optimization and prediction of expected response


           13.4.1 Analysis of variance
           There is actually no difference between analysis of variance of classical
           DOE and Taguchi DOE. First, we compute the sum of squares (SS), then
           the mean squares (MS), where an MS is computed by dividing the SS by
           the degree of freedom. In Taguchi DOE, the F test is not as important as
           that of classical DOE. Sometimes, the relative importance of each factor
           is computed by its percentage contribution to the total sum of squares.
             For each column of an orthogonal array, assume that there are k
           levels, and for each level t, the total sum of response at tth level is rep-
           resented by T t , the total sum of responses is represented by T, the total
           number of runs is N, and the number of replicates is n; then for each
           column, the sum of squares is

                                      k     k        T 2
                                                2
                              SS           
  T t                      (13.1)
                                    N 
 n  t  1     N 
 n
             Example 13.11 A truck front fender’s injection-molded polyurethane bumpers
             suffer from too much porosity. So a team of engineers conducted a Taguchi
             experiment design project to study the effects of several factors to the porosity:

                     Factors         Low     High
               A  Mold temperature    A 1     A 2
               B Chemical temperature  B 1    B 2
               D  Throughput          D 1     D 2
               E  Index               E 1     E 2
               G  Cure time           G 1     G 2

             Interactions AB and BD are also considered
               The following L 8 orthogonal array is used for each run, and two mea-
             surements of porosity are taken; for porosity values, the smaller, the better:
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