13 2 1 2 3 0。1843 0。1891 0。1732 0。1892

14 2 2 3 1 0。1971 0。2116 0。1875 0。2252

15 2 3 1 2 0。1906 0。2037 0。1835 0。2154

16 3 1 3 2 0。1824 0。1909 0。1712 0。1974

17 3 2 1 3 0。1758 0。1876 0。1645 0。1804

18 3 3 2 1 0。1878 0。2019 0。1778 0。2134

C。-P。    Chen    et    al。  /    Expert    Systems  with    Applications    36    (2013)      10752–10759 10755

0。1 lm resolution is utilized。 Fig。 1 shows the dimensions of a spec- imen and the middle locations of the edge of both the x-direction and the y-direction specified that have been selected to measure the amounts of warpage。 The warpage distortion measurement  of d at the x-direction (i。e。, dxexp) and the y-direction (i。e。, dyexp) are given in Table 3。

5。 Simulation  and  experimental  results discussion

The simulation results of warpage distortions of the x-direction (i。e。, dxsim) and the y-direction (i。e。, dysim) are listed in Table 3。 Simultaneously, Table 3 also shows the experimental results。 The objective of this study is to identify an optimal setting that gives a minimized warpage distortion at the x-direction and the y-direc- tion。 The found optimal solution would have to strike the balance between these three-targeted outputs。 Hence, Eq。 (4) shall be se-

Table 4a

ANOVA results of  dxsim。

Source Sum  of squares DOF Mean square F value P value

Model 0。0014 5 0。0003 3246。14