隨著蓬勃發展的塑膠光電產業，塑膠光學鏡片具輕、薄、耐衝擊及可撓曲的優勢下逐步取代了玻璃鏡片，佔據了國內外大部分的市場，光學鏡片的產品品質被嚴苛的要求，但由於硬度低，耐磨損性較差，必需在其表面加工強硬膜層，以達到耐衝擊、抗磨損之效果。
本研究探討光學塑膠鏡片的表面精度與強化製程條件間的關係，結合了柏拉圖最佳解的概念和渴望函數來處理多目標實驗設計的問題，同時考量成本因素與有限制的實驗次數，找出一個近似D-optimal的實驗設計，並依此就光學塑膠鏡片強化工程來進行實驗並且分析，根據實驗結果找出位在柏拉圖前緣上的設計點，計算出未執行實驗的設計點之反應變數預測值後再更新柏拉圖前緣上的設計點，並透過渴望函數進行反應變數的轉換，最終考量製造成本，以效用成本比最大作為最佳設計點。並以實例來驗證本研究方法，討論變異數-共變異數矩陣對前緣的影響。預期在考量製造成本的多目標實驗設計下，實驗結果能提供決策者一個較為彈性的最佳解集合，提高決策者對品質特性預測上的準確性和可信度。

Plastic optical lenses replace the glass lens gradually with the rapid development of plastic photovoltaic industry, and occupy most of the global markets.Optical lenses product quality is required strictly.To achieve impact resistance and anti-wear effect, plastic optical lenses are required coatinghard film layers on its surface because of the low hardness and poor wear resistance. This study is to investigate the relationship between the surface of plastic lenses and precision optics hard coating process conditions. This is a multiple response optimization problem.
This study combines the Pareto frontier, the desirability function,and cost factor to deal with multiple objective experimental designssubjected to a limited number of experiments.The design is approximated bya D-optimal algorithm. According to this design matrix, optical plastic lenses hard coating experiments were performed and analyzed. We thenidentify the design points ofPareto frontier,build approximating models of responses, and predict the responses of unexecuted design points. If fitted unexecuted design points are not dominated, we then addthem to thePareto frontier.Multiple objectives are converted to a value through desirability function and then divided by the manufacturing cost of each design points. An optimum design is the one with the maximum ratio. An optical plastic lens hard coating example is performed and presented. Our results provide decision makers a more flexible set of optimal solutions to improve the accuracy and reliability of the prediction.

中文文獻
潘姝吟(2005)，「應用柏拉圖式與使用者偏好的多目標基因演算法來解決產能批量問題－以光學鏡片產業為例」，國立高雄第一科技大學運籌管理研究所碩士論文。
簡仲廷(2014)，「考慮效用成本比最大化之限制條件下多目標實驗設計」，國立成功大學工業與資訊管理研究所碩士論文。
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