## 1 Introduction  
In recent decades, robust design (RD) has been considered essential for improvement of product quality, as the primary purpose of RD is to seek a set of parameters that make a product insensitive to various sources of noise factors. In other words, RD attempts to minimize the variability of quality characteristics while ensuring that the process mean meets the target value. To solve the RD problem, [PERSON] [1] considered both the process mean and variance as a single performance measure and defined a number of signal-to-noise ratios to obtain the optimal factor settings. Unfortunately, the orthogonal arrays (OAs), statistical analysis, and signal-to-noise ratios associated with this technique were criticized by [PERSON] et al. [2], [PERSON] et al. [3], [PERSON] [4], and [PERSON] [5]. Therefore, [PERSON] and [PERSON] [6] proposed the dual response (DR) approach based on response surface methodology (RSM), in which the process mean and variance are estimated separately as functions of control factors. The result is an RD optimization model in which the process mean is prioritized by setting it as a constraint and the process variability is set as an objective function. From this starting point, the three sequential steps of the RD procedure were generated: design of experiment (DoE), estimation, and optimization. The DoE step exploits information about the relationship between the input and output variables. In the second step, the functional form of this relationship is defined by estimating the model parameters. Ultimately, the optimal settings for the input factors are identified in the third step. As several RD optimization models have been proposed and modified according to various criteria, the optimization step is relatively well developed. The priority criterion was used in the DR models proposed by [PERSON] and [PERSON] [6], [PERSON] and [PERSON] [7], and [PERSON] and [PERSON] [8], whereas the process mean and variance were considered simultaneously in the mean squares error (MSE) model developed by [PERSON] and [PERSON] [9]. The weight criterion was used to consider the trade-off between the mean and variance in the weighted sum models reported by [PERSON] et al. [10], [PERSON] et al. [11], and [PERSON] [12], whereas [PERSON] et al. [13] used the weight criterion in a quality loss function model. [PERSON] and [PERSON] [14; 15] extended the DR model by integrating the customized maximum value on the process bias and variance. Based on the MSE concept, [PERSON] et al. [16] and [PERSON] and [PERSON] [17] proposed generalized linear mixed models and inverse problem models. Using the goal programming approach, [PERSON] and [PERSON] [18] and [PERSON] and [PERSON] [19] introduced prioritized models, whereas [PERSON] [20] and [PERSON] [21] both considered the output responses on the same scale as the desirability functions. In an attempt to identify the Pareto efficient solutions, [PERSON] and [PERSON] [22] and [PERSON] and [PERSON] [23] developed a fuzzy model and a lexicographical weighted Tchebycheff model for the RD multiple-objective optimization problem, respectively. Furthermore, [PERSON] and [PERSON] [24] integrated the economic factor in the economic time-oriented model to handle time-oriented dynamic characteristics, while [PERSON] et al. [25] introduced the lexicographical dynamic goal programming model. The DoE is a systematic method that aims to identify the effects of controllable factors on the quality characteristics of interest. DOE has been developed since the 1920s. [PERSON] [26] reviewed the history of DoE in the published literature. Several DoE techniques were developed and intensively researched as a means of conducting experiments in industrial applications; these include full factorial designs, fractional factorial designs (screening designs), mixture designs, Box-Benken designs, central composite designs (CCD), Taguchi array designs, Latin square designs and other non-conventional methods (D-optimal designs).