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To simultaneously optimize the parameter robust design of dynamic multiple responses is difficult due to product complexity; however, the design is what determines most of the production time, cost, and quality. Although several methods tackling this problem have been published, they have proven unable to effectively resolve the situation if a system has continuous control factors. This work proposes a data mining approach, consisting of four stages based on artificial neural networks (ANN), desirability functions, and a simulated annealing (SA) algorithm to resolve the problems of dynamic parameter design with multiple responses. An ANN is employed to build a system’s response function model. Desirability functions are used to evaluate the performance measures of multiple responses. A SA algorithm is applied to obtain the best factor settings through the response function model. By using the proposed approach, the obtained best factor settings can be any values within their upper and lower bounds so that the system’s multiple responses have the least sensitivity to noise factors along the magnitude of the signal factor. An example from the literature is illustrated to confirm the feasibility and effectiveness of the proposed approach.

The robust design has been successfully applied to a variety of industry problems for upgrading product quality since Taguchi first introduced this method in 1980. The objective of robust design is to reduce response variation in products and processes by selecting the settings of control factors which provide the best performance and the least sensitivity to noise factors. To execute the robust design, Taguchi employs an orthogonal array (OA) to arrange the experiments and uses signal-to-noise ratios (SNRs) to evaluate the response of an experimental run. A two-step optimization procedure is then used to determine the optimal factor combination to simultaneously reduce the response variation and bring the mean close to the target value. The robust design method can be applied to problems of both static and dynamic systems. Static systems are defined as those whose desired output of the system has a fixed target value whereas dynamic systems are those whose target value depends on the input signal set by the system operator (Tsui, 1999). Recent reviews of robust design and its applications can be found in Robinson, Borror, and Myers (2004) and Zang, Friswell, and Mottershead (2005). Although the robust design method has wide applications in practice, it has some limitations (Maghsoodloo, Ozdemir, Jordan, & Huang, 2004). In particular, it can only be used for optimizing single response problems. Several methods have been proposed to resolve multiple response problems (see Derringer and Suich, 1980, Kim and Lin, 2000, Liao, 2005, Liao, 2006, Su and Tong, 1997, Tong and Su, 1997 and Wu and Chyu, 2004); however, these methods cannot treat the problems of dynamic systems. Recently, several researchers have begun to study robust design problems of dynamic multiple responses. A dynamic system with multiple responses can be represented by a P-diagram (Parameter Diagram), such as that shown in Fig. 1. The goal is to determine the best settings for the control factors so that simultaneously the system’s multiple responses have the least sensitivity to noise factors along the magnitude of the signal factor.In recent years, there have been a number of articles published which focus on the method of determining the optimal parameter settings of a dynamic multiple response problem. Tong, Wang, Chen, and Chen (2004) adopted principal component analysis (PCA) and the technique for order preference by similarity to ideal solution (TOPSIS) to derive an overall performance index (OPI) for dynamic multiple responses. Wu and Yeh (2005) presented multiple polynomial regression models to minimize the total quality loss of dynamic multiple response systems. Hsieh, Tong, Chiu, and Yeh (2005) employed regression analysis to screen out the significant factors affecting the variation and sensitivity of a system; then, applied desirability function to optimize the parameter design. Wang and Tong (2005) incorporated the TOPSIS into the grey relation model to determine the optimal parameter settings of a dynamic multiple response problem. Moreover, Chang (2006) proposed an artificial neural network (ANN) approach to optimize a dynamic case containing three responses. The approach employed an ANN to construct the response model of the dynamic responses and applied desirability functions to integrate three types of dynamic responses into a single index. The response model was then used to predict all possible responses by inputting full factor/level combinations and to evaluate their indices. Despite the fact that numerical examples were used to demonstrate the abilities of the above methods, these methods could only obtain the best solution among the specified control factor levels. In other words, they were unable to achieve the real optimal factor combination if the control factors had continuous values. Alternative recent publications have revealed that the data mining approach which integrates ANN and meta-heuristics is a useful method for resolving the problems of continuous control factors (Hou et al., 2006, Hsu et al., 2006, Huang and Hung, 2006 and Su et al., 2005). Su and Chang (2000) showed the functional relationship between responses and control factors through ANN, and determined the optimal settings of control factors by using simulated annealing (SA). Accordingly, in this work we propose an integrated data mining approach which extends the previous research presented by Su and Chang (2000) and incorporates exponential desirability functions to model and optimize dynamic multiple response systems. The proposed approach consists of four stages which employ the methodologies of ANN, SA, and desirability functions. First, an ANN is used to construct the response model of a dynamic multiple response system by using the experimental data to train the network. The response model is then used to predict the corresponding responses of the system by inputting specific parameter combinations. Second, each of the predicted multiple responses is evaluated their performance measures (PMs) by using desirability functions. Third, multiple PMs are integrated into an OPI for evaluating a specific parameter combination. Finally, a SA is performed to obtain the optimal parameter combination within experimental region. Applying the proposed approach, the obtained optimal control factor values are no longer restricted to the solution points composed of discrete experimental levels. The proposed approach is illustrated and compared with an example from the literature presented by Chang (2006).

Parameter robust design is at a critical phase in the development new products and processes because of its influence on the total production time, cost, and quality. With regard to the optimization problems of dynamic multiple response systems, it is difficult to determine the optimal parameter settings for all responses. This is because different settings of the same factor could be optimal for responses having different quality characteristics; that is, the goals of different responses are usually in conflict. A common method used for tackling multiple responses is to give a weighted value to each response, which usually depends upon an engineer’s subjective judgment. The desirability function approach proposed here should prove an attractive method to industry in simplifying multiple response problems because it directly employs the LSL and USL of each response without the need for any human judgment. This work proposes a data mining approach based on ANN, desirability functions, and SA to resolve problems of dynamic parameter designs having multiple responses. Improving on an example from the literature that had three dynamic responses confirmed the effectiveness of the proposed approach. The proposed approach can provide the following several merits: 1. The assumption of a linear relationship between responses and signal factor is not required. The approach can effectively deal with non-linear relationship owing to the ANN’s ability of mapping a complex non-linear relationship. 2. Sometimes no adjustment factor exists in a system. The approach can simultaneously optimize dynamic multiple responses without using adjustment factors. 3. By using this approach, the obtained combination can be formed from any values within the upper and lower bounds of control factors. 4. In real applications, the number of signal factors is sometimes more than one. This approach can be directly extended to treat a dynamic multiple response system having double signal factors.