以迴歸模型與混整數規劃最佳化機台參數

Abstract

在許多產業的產品製程中，一般有著大量的機台影響成品品質的優劣，如半導體製造或紡織業等。因此，如何有效的調整機台參數以達到控制項的目標就成為了相當重要的議題，稱之為參數調整(parameter tuning)。實務上常以實驗設計(DOE, design of experiment)的方式找出機台參數與控制項之間的關係用於調機時的依據，並以混整數規劃(Mixed-Integer Linear Programming; MILP)求解最佳調機策略；然而，此類型的問題複雜度會隨著機台參數及控制項的數量上升而呈指數成長，僅憑實驗結果與過往經驗的決策仍會有許多潛在的因子沒有被考慮到。本研究先利用歷史資料進行分析，找出較具指標性的調機策略作為資料分類的依據後，根據不同類別的資料各自進行迴歸分析(regression analysis)，並透過最佳化模型即時針對機台現況給予最佳的調機策略。

There are generally a large number of machines that affect the quality of products in the manufacturing processes. Therefore, how to effectively tune the parameters of the machine to achieve the target of the control items has become a very important issue, called parameter tuning. In practice, the relationship between machine parameters and control items is often determined by the design of experiment. The parameter tuning is solved by Mixed-Integer Linear Programming (MILP). However, the complexity of this type of problem exponentially grows as the number of machine parameters and control items increases. This study first uses historical data to find out the tuning pattern for data classification. The regression analysis is performed on the basis of the classification results followed by an optimization model to determine tuning parameters.