Table 4 Levels of process parameters Table 5 DMUs on the efficient frontier

hence only these four parameters are considered in the regression analysis in the next  subsection.

Setting up the regression response model to create the complete dataset

To obtain a more complete efficient frontier for the process parameters, more data are required. The regres- sion model, the response surface model, is utilized to create more data. In order to have better forecasting accuracy of the regression model, the complete experi- ment design with four significant process factors is executed again on Moldflow before the regression equa- tions are established. The results are shown in the Appendix B.

The results of the complete experiment design with four significant process factors are then utilized to set up the second-order response surface model by the regression analysis of statistics software, SPSS. Three re- sponse surface equations for three quality indices are found below:

surface equations, Equations 1, 2, 3, are exploited to create more data points. Because DEA software, Banxia Frontier Analyst 3, has the limitation on the maximal number of data points (also called decision making units (DMUs)), the design of data points to be created is explained below. Based on the results of ANOVA, because injection time and packing pressure are more significant than the other two process parameters, there are seven levels selected for these two process parameters and five levels for the other two parameters. Therefore, there are 5 × 7 × 7 × 5 = 1,225 data points to be created by Equations 1, 2, 3. The  levels of each process parameter are listed in Table 4. Note  that in Table 4, all levels of each parameter all fall its range of operation in Table 2.

Warp ¼ 1:45−0:011 INP−0:238 INT−0:00823 PP Determining the efficient frontier of process parameters by DEA

þ0:000046 INP2 þ 0:108 INT2 þ 0:000016 PP2 DEA is a technique to evaluate the relative efficiency    of

−0:00176 INP m INT þ 0:00001 INP m PP many  DMUs by  analyzing  multiple  inputs  and multiple

þ0:00211 INT m PP; outputs  of  each  DMU.  Its  goal  is  to  find  the efficient

ð1Þ DMUs,  also  called  efficient  frontier  in  the  literature of

DEA.  This  research  uses  the  standard  DEA    Charnes,

Shrink ¼ 1:32−0:0145 INP þ 0:35 INT þ 0:000086 INP2

þ0:0603  INT2−0:000013  PP2−0:00593  INP m INT

−0:000026 INP m PP þ 0:00122 INT m PP;

ð2Þ

Cooper, and Rhodes (CCR) (Charnes et al. 1978)  model to find the  efficient  frontier  of  DMUs which  is created in the previous subsection. The mathematical model of DEA CCR is briefly outlined below. Suppose that there are  K  DMUs,  each  of  which  consumes  N  inputs   and

Table 6 The reference counts of the efficient DMUs

Volume ¼ 27:0−0:348 INP þ 0:00165 INP2 þ 2:74 INT2

−0:00035 PP2−0:0751 INP m INT−0:000613 INP m PT

þ0:0369 INT m PP þ 0:0839 INT m PT:

ð3Þ

The normal probability plots are provided in Figures 5, 6, 7 to justify the validity of the regression analysis.

To find a more complete efficient frontier of process parameters, more data are required. Regressed     response