Decision AidingDynamic multiple responses by ideal solution analysis
Introduction
Stringent global competition demands continuously elevating product quality. Off-line quality control and robust design have been widely implemented throughout industry to upgrade product quality. As a major proponent of the philosophy of robust design, Taguchi focused on information of both the mean and variability of a quality characteristic using the signal to noise (SN) ratio. In doing so, the optimal factor/level combination obtained from the Taguchi method can be determined to simultaneously reduce the quality variation and bring the mean close to the target value. Despite its widespread industrial applications, the Taguchi method can only be used for optimizing single-response problems. Cases involving dynamic multi-response problems have rarely been seen. However, industry has increasingly emphasized developing procedures capable of simultaneously optimizing the dynamic multi-response problems in light of the increasing complexity of modern product design. Furthermore, moderate or high correlations among these responses may incur difficulty in optimizing multiple responses simultaneously. Accordingly, developing optimization procedure of dynamic multiple responses must consider the correlations among these responses to accurately depict the multi-response performances in a dynamic system.
This study develops a novel multi-response optimization procedure for a dynamic system that can resolve the correlation problems among responses and reduce the computational complexity. The SN ratio and system sensitivity are used to assess the performance of each response. Principal component analysis (PCA) is then performed on SN values and system sensitivity values to obtain a set of uncorrelated principle components, which are linear combinations of the original responses. Additionally, the variation mode chart is plotted to interpret the variation mode (or principal component variation) resulting from PCA. Based on engineering requirements, engineers can determine the optimization direction for each principal component using the variation mode chart. Finally, technique for order preference by similarity to ideal solution (TOPSIS) is adopted to derive the overall performance index (OPI) for multiple responses. The optimal factor/level combination is determined with the maximum OPI value and therefore, simultaneously reduces the quality variation and brings the mean to the target value. Results obtained from the biological reduction of an ethyl acetoacetate process experiment demonstrate the effectiveness of the proposed procedure.
Section snippets
Dynamic system
The feasibility of optimizing a dynamic system has received increasing attention in recent years (Wasserman, 1998). A dynamic system differs from a state system in that the former contains signal factors to achieve the target performance or express the intended output. The response varies with the level of the signal factor. For example, signal factors may be the steering angle in the steering mechanism of an automobile or the speed control setting of a fan. The signal factors are selected by
Proposed procedure
This study proposes an optimization procedure for multiple responses in a dynamic system based on Taguchi’s parameter design. Because multiple responses always contain moderate or high correlations among each other, the PCA is initially performed on the SN values and system sensitivity obtained from each response to integrate the dimension of multiple responses to a smaller number of uncorrelated components. The variation mode charts for components obtained from PCA are then utilized to
Illustrative example
A biological reduction of the ethyl 4-chloro acetoacetate processes for the production of an optically pure compound was used to demonstrate the effectiveness of the proposed optimization method. The Industrial Technology Research Institute at Taiwan performed this illustrative example. S-4-Chloro-3-hydroxybutyric acid ethyl ester (S-CHBE) is a widely used chiral synthon used for synthesizing various optically active compounds such as antihypertensive drugs, HMG-CoA reductase inhibitors and
Conclusion
This study utilizes the PCA to simplify the dynamic multi-response problems and determines the optimization direction by using the variation mode chart. The optimal factor/level combination is also determined based on the OPI for multiple responses obtained from TOPSIS. A case study in which the biological reduction of the ethyl 4-chloro acetoacetate processes for the production of an optically pure compound is optimized confirms the effectiveness of the proposed procedure.
The proposed
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