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methods, and the process of trial and error consumes a significant amount of time and cost. Therefore, both methods cannot meet the requirement of the current market.

Researchers have applied various kinds of methods, e.g., artificial neural network and/or fuzzy logic (Liao et al. 2004a, b; Kurtaran et al. 2005; Ozcelik and Erzurumlu 2006), genetic algorithm (Kurtaran et al. 2005; Ozcelik and Erzurumlu 2006), design of experiments (Huang and Tai, 2001; Liao et al. 2004a, b), and response surface method (Ozcelik and Erzurumlu 2005; Kurtaran and Erzurumlu 2006; Chen et al. 2010) to optimize the initial process parameter setting of plastic injection molding. However, most studies focus on the single optimal com- bination of  process  parameters by different  optimization

techniques. It is well known that when multiple quality characteristics are considered, the trade-off relationships exist among these quality characteristics, and these rela- tionships make the task of finding the optimal combin- ation rather complicated if not impossible. Instead of finding a single optimal combination of process parame- ters, this research seeks the efficient frontier of process pa- rameters by data envelopment analysis (DEA).

The remainder of this paper  is  organized  as follows: the ‘Literature review on the optimization of process parameters for injection molding’ section will review re- lated work in the literature. The properties of the ma- terial and product used in this paper will be addressed in the ‘Materials and product’ section. The ‘Experimental design and methodology’ section will discuss the experi- mental design and the procedure of finding the efficient frontier of process parameters. Finally,  the  summary and concluding remarks are provided in the ‘Summary and  conclusions’ section.

Literature review on the optimization of process parameters for injection molding

The literature of optimization for injection molding is briefly addressed in this section. Kim and Lee (1997) discussed different geometries for plastic parts to im- prove the parts’ warpage by Taguchi’s orthogonal experi- ment design. To avoid producing flaws of silver streaks for automobile plastic bumpers, Taguchi’s optimization method is utilized to decide the optimal values for the process  parameters  by  Chen  et  al.  (1997).  The    same

optimization method was also used by several works (Huang and Tai 2001; Liu and Chen 2002; Liao et al. 2004a, b; Oktem et al. 2007) to find the optimal combi- nations of process parameters for different plastic prod- ucts. In these works, warpages and shrinkages of plastic parts were usually considered as their quality indices. Moldflow, a mold flow analysis software, was used to simulate a real injection machine by Erzurumlu and Ozcelik (2006). Several techniques including the Taguchi’s method, the neural networks, and the genetic algorithm were combined to optimize the process parameters.

The response surface methodology (RSM) is another popular method to optimize the  process  parameters  in the literature. The complete model of RSM was first established by Box and Wilson (1951). To improve two quality indices, within-wafer non-uniformity and the re- moval rate, of the chemical–mechanical planarization process in semiconductor manufacturing, dual RSM was proposed by Fan (2000) to optimize five process parame- ters. In order to avoid the difficulty of minimizing both quality indices, one was treated as the primary response put in the objective function and the other was the sec- ondary response placed in the constraint. Two works developed RSM combined with different optimization techniques (Ozcelik and Erzurumlu 2006; Chiang and Chang 2007). Chen et al. (2010) applied dual RSM to im- prove the quality of plastic injection molding. Warpage is the primary response (and is treated as the objective func- tion), while shrinkage is the secondary response (and is then set as the constraint) in their work.