Vol. 2.0650 1.9610 2.0680 2.8260  3.3670

where Ykm is the value  of  the  mth  output  generated by the kth DMU, Xkn is the value of the  nth  input  con- sumed by the kth DMU, Vn and Um are Xkn’s and Ykm’s weights, respectively, whose values are determined by solving the model, Hk is the relative efficiency of the kth DMU, and ε is a small  positive  number.  After solving the CCR DEA model, a DMU is on the efficient frontier

  if its relative efficiency, Hk, is equal to    1.

Three  quality  indices,  warpage,  shrinkage,  and  volu-

produces M outputs. Then, the DEA CCR model can be

metric shrinkage at ejection, are considered in  this paper. Among these three indices, warpage is treated as the output, while shrinkage and volumetric shrinkage at ejection are two inputs in the DEA model. Because the

output in DEA model needs to be maximized and warp- age is apparently the minimized quality index, the trans- formation, 1-warpage, is adopted.

Table 8 Relatively efficient DMUs

DMU Score

44 100

45 100

840 100

871 100

1,151 100

54 97.82

52 97.80

53 97.13

43 96.88

560 94.19

DMUs in italics  represent  the efficient  ones suggested in this  study.

The DEA software, Banxia Frontier Analyst 3, is used to find the efficient frontier of process parameters. The dataset used is the dataset of 1,225 data points created in the previous subsection. Each data point is treated as a DMU. After running Banxia Frontier Analyst 3, data points on the efficient frontier are found in Table 5. There are nine DMUs on the efficient frontier, among which five DMUs have at least one reference count as shown  in Table 6. Therefore, these five DMUs with positive refer- ence counts are treated as the efficient frontier of process parameters in this paper. The levels of each process par- ameter for these five DMUs are shown in Table 7, where the forecasting value of a quality index is its value derived from the corresponding regression equations and the real value of a quality index means its value by re-running Moldflow on this combination of process parameters. The plot of DEA results is shown in Figure 8.

To verify the efficiency of five DMUs found in this paper, we re-run Moldflow on each DMU and then the results are compared with those of 34 = 81 data points which are utilized to set up the regression equations in

‘Setting up the regression response model to create the complete dataset’ subsection. The comparison is accom- plished by executing DEA on 5 efficient DMUs found in this paper and 81 data points. The results are shown in Tables 8 and 9. From Table  9, it can be observed that

Table 9 Efficient DMUs with positive counts

among five efficient DMUs found in this paper, three DMUs are still on the efficient frontier and one DMU is relatively highly efficient with 94.18% DEA score. Only DMU 1,186 is not quite efficient with 71.28%  DEA score, and this may be due to the error of the regression equation at this DMU. It is fair to suggest that the error induced by the regression equation at most of the points is fairly small. Therefore, the efficient frontier of process parameters found by this paper with only 108 (=27 + 81) repeats of experiments can really provide good combina- tions of process parameters for decision   making.