行政院國家科學委員會專題研究計畫 成果報告

行政院國家科學委員會專題研究計畫 成果報告

兩階段最佳化系統應用於導光板模仁微影製程之研究 研究成果報告(精簡版)

計 畫 類 別 ： 個別型

計 畫 編 號 ： NSC 99-2221-E-216-034-

執 行 期 間 ： 99 年 08 月 01 日至 100 年 07 月 31 日 執 行 單 位 ： 中華大學工業管理學系

計 畫 主 持 人 ： 陳文欽

計畫參與人員： 碩士班研究生-兼任助理人員：邱世傑 碩士班研究生-兼任助理人員：許勝超 碩士班研究生-兼任助理人員：林蔚廷 碩士班研究生-兼任助理人員：丹尼 博士班研究生-兼任助理人員：麥僑芯

報 告 附 件 ： 出席國際會議研究心得報告及發表論文

處 理 方 式 ： 本計畫涉及專利或其他智慧財產權，2 年後可公開查詢

中 華 民 國 100 年 10 月 13 日

行政院國家科學委員會補助專題研究計畫 ■成果報告

□期中進度報告

題目:(中文) 兩階段最佳化系統應用於導光板模仁微影製程之研究

(英文)A two-stage optimization system for the photolithography process of LGP stamper

計畫類別：■個別型計畫 □整合型計畫

計畫編號：NSC 99 － 2221 － E － 216 － 034－

執行期間：

99 年 8 月 1 日 至 100 年 7 月 31 日

執行機構及系所：

中華大學工業管理學系

計畫主持人：

陳文欽

計畫參與人員：蔡翔丞、邱世傑、丹尼、許勝超、林蔚廷、麥僑芯

成果報告類型(依經費核定清單規定繳交)：■精簡報告 □完整報告

本計畫除繳交成果報告外，另須繳交以下出國心得報告：

□赴國外出差或研習心得報告

□赴大陸地區出差或研習心得報告

■出席國際學術會議心得報告

□國際合作研究計畫國外研究報告

處理方式：除列管計畫及下列情形者外，得立即公開查詢

□涉及專利或其他智慧財產權，□一年■二年後可公開查詢

中 華 民 國 100 年 10 月 13 日

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摘 要

在目前薄膜電晶體液晶顯示器(Thin Film Transistor Liquid Crystal Display, TFT-LCD)產業中，導光 板微影製程參數設定時，往往需要依靠工程師之經驗，經由試誤法與實驗設計且需經過多次測試才能 夠找出適合之參數組合，須花費大量時間、人力及成本。故本研究針對微影製程部分提出了兩階段最 佳化之系統，對多品質特性之導光板模仁，進行微影製程參數最佳化研究，其中導光板模仁品質特性 分別為微結構之直徑及微結構整體之均勻性，製程之控制因子為烤箱溫度、烤箱時間、滾輪溫度、曝 光能量、顯影速度。

本微影製程參數最佳化系統分為兩個階段，第一階段S/N 比最佳化，將依田口直交表進行微影製 程之微結構成形實驗，以實驗數據計算S/N 比值，利用倒傳遞類神經網路建構 S/N 比預測器與品質預 測器，結合S/N 比預測器與基因演算法(GA)進行全域搜尋，找出最佳製程參數組合，使各品質特性之 S/N 比值都最大化，此階段將使製程變異降至最低；第二階段品質最佳化，將品質逼近目標規格，運 用ANOVA 找出控制因子，結合品質預測器與粒子群演算法(PSO)進行搜尋，以微結構之直徑及均勻性 為品質特性，找出最符合品質規格且製程最為穩定之最佳製程參數組合。以本研究所提出之兩階段最 佳化系統所找出之製程參數組合，不僅整個製程更為穩定且微結構直徑符合尺寸規格，同時也有效降 低重工次數及有效的提升均勻性以及降低成本，提升整體微影製程之製程穩定度及提高產品品質特性。

關鍵字: 導光板模仁、微影製程、田口方法、倒傳遞類神經網路、基因演算法、ANOVA、粒子群演算 法

Abstract

In the current thin film transistor liquid crystal display (TFT-LCD) industry, the LGP process parameter setting of the photolithography process still relies on the engineers’ experience and intuition, and they often use trial-and-error and numerous design of experiment (DOE) to obtain a suitable and more reliable parameter settings, which leads to spend a large amount of time, manpower and cost. In this research, the two-stage optimization system for photolithography process can be proposed in terms of multi-quality characteristics of the light guide plate mold: the diameter of the micro-structure and the uniformity of the whole micro-structure.

The control factors of photolithography process are oven temperature, oven time, hoop temperature, exposure energy and development speed.

The study is divided into two phases: signal-to-noise (S/N) ratio optimization and quality characteristic optimization. In the first phase, S/N ratio optimization can be achieved using the Taguchi orthogonal array to conduct the combinational experiment for the lithography process of micro-structure molding, and figure out S/N ratio via experiment data. In addition, S/N ratio and the other quality characteristics predictors can be created by training the former experimental data through back-propagation neural network (BPNN), and coming up with the initial process parameters settings using the main-effect plot and ANOVA analysis. Then applying the genetic algorithms (GA) with S/N ratio predictor execute the global search to find out the optimal parameter settings, which maximizes the S/N ratio and can reduce the process variance to a minimum.

In the second phase, quality characteristics optimization- to meet the target under the adjustment

of control factors’ levels via ANOVA analysis, and using the quality characteristic predictors for the diameter

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of the micro-structure and the uniformity of the whole micro-structure with particle swarm algorithm (PSO) to carry out the global search, which can come out the optimal parameter settings to meet the approximation value of the target and develop the most stable process. The proposed two-stage optimization system can effectively identify the best process parameter settings. It not only allows the whole process to become more stable and meet the target specification for micro-structure in diameter, but also effectively reduces the number of reworks, improves the uniformity of photolithography process, and cuts down the cost, and further enhances the process stability and product quality.

Keywords: Light guide plate mold, Photolithography process, Taguchi orthogonal array,

back-propagation neural network, Genetic algorithm, Particle swarm optimization

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第一章 文獻探討

微影製程(photolithography process)早期被應用在半導體製程。目前在導光板(light guide plate, LGP) 模仁製程中stamper)也被廣泛應用，以製作導光板模仁之微影製程技術來說，整個微影技術流程需要六 道步驟：清洗原材、預烤、光阻塗佈、曝光、顯影和硬烤，影響微影製程參數眾多且彼此間呈現非線 性關係，其製程控制參數更直接影響產品的品質與成本，以往大多憑藉著經驗與試誤法或田口實驗的 非連續式最佳化設計所決定製程參數及控制因子。通常LGP之微影製程參數控制不佳時則會造成圖形 轉寫失敗、轉寫率不佳及尺寸變異過大等成形缺陷，就必須重工把光阻剝除，再不斷的重覆之前的流 程直到通過檢查為止。為了能夠降低重工的步驟及減少成本，因此在微影製程中控制因子之參數設定 就更加重要。在過去研究中很多學者探討微影製程參數對於微影製程的影響，Huang et al. (2009)應用 UV-LIGA製程製作精密之電鑄鎳齒輪模具，其中微影製程之控制因子為：光阻厚度、軟烤時間、曝光 能量、曝光後烘烤時間、顯影時間、硬烤時間、及電鑄鎳材料，這些因子對於精密成形模具之圖案轉 移皆有影響，由於微影製程好壞將會影響後續的模具好壞。Pal and Sato(2009)提出一種暫存製造方法，

利用微影技術應用於矽微通道和各種形狀的顯微所需的矽片上。在製造方法中使用晶片鍵合的氮化矽 (Si3N4 陶 瓷 ) 作 為 中 間 層 ， 局 部 使 用 氧 化 矽 ， 和 金 屬 氧 化 物 半 導 體 (Complementary metal–oxide–semiconductor, CMOS)技術建立所需要的微結構圖形，並結合非等向性的濕蝕刻技術來製 作模具，此種方法可在矽晶圓內部製作出各種不同角度的微結構。Huang et al. (2009)提出了新型的mask structure (Γ-shape) 並結合了shadow mask 技術，應用在更薄的版片上進行加工，此法可以提高微結構 的開孔率以及降低光蝕刻過程中所不需要的成本，此法證實可成功的應用於OLED被動式陣列設備上。

Jang et al. (2008)等人提出，導光板模仁使用噴砂製程時，必需先建立微影製程實驗參數才能夠有效的 將微結構圖形轉移到模仁上，然而其中又以微影製程為重要關鍵，實驗之關鍵控制因子分別為，去水 烘烤、壓模溫度、曝光能量與顯影速度，關於上述之實驗因子皆對於導光板微結構轉寫率的品質佔有 絕對之因素，如無法有效的建立此製程參數將對於導光板模仁在後續的射出上會有極大的影響。Mert et al. (2006)利用微影技術並搭配SU-8光阻劑，進行微矩陣列結構模具製造，利用此技術可以輕易的將所 需要的微結構圖形進而轉寫至基材上以利後續製造模仁或是模具，但在微影製程中之各個控制因子及 參數範圍都會直接與間接的影響微結構圖形的尺寸，所以在進行此微矩陣列結構模具製造時，必須經 由實驗才得以確定其最佳製作參數範圍。由文獻得知大多數的製程都必須藉由微影製程來當作圖像轉 移的工具，且這項製程技術是目前產業中不可或缺的一環，不管從TFT-LCD、半導體、太陽能等等產 業都必須仰賴微影技術，由此可見其製程之重要性。且從文獻得知大部分之微影製程參數重要因子為，

光阻厚度、軟烤時間、曝光能量、曝光後烘烤時間、顯影時間、硬烤時間等等。

雖可從上述文獻中可得知導光板模仁微影製程參數的重要因子，大多都藉由經驗或試誤法以求得 參數重要因子。在製程參數最佳化方面，徐瑞富(2004)利用田口方法改善金線偏移之銲線製程問題，利 用田口方法建構一組最佳的製程參數組合，來降低IC(Integrated Circuit)封裝時的金線偏移。楊國榮(2005) 利用田口方法分析電漿參數對IC晶粒導線接合的影響，並找出一組最佳製程參數經過確認實驗結果顯 示電漿製程確實能改善並增加金線的拉力。游昇鑫(2006)在探討BGA(Ball Grid Array)構裝技術中，因 錫球的三維尺寸誤差較大時，將會影響錫球和線路板接觸不良，進而影響IC(Integrated Circuit)晶片的 可靠度，故利用田口方法改善現況並得到一组最佳參數使錫球尺寸的誤差在範圍內。楊明棋(2007)利用 田口方法探討微電化學加工參數對於製作微圓柱電極刀具和金屬移除量的影響程度且加以評估設計最 佳參數組合，並以變異數分析法(Analysis of variance, ANOVA)加以分析發現敏感因子，且順利取得一 组最佳參數。吳志政(2008)以RGB三原色之發光二極體 ( Light Emitting Diode, LED)為燈源之背光模組 結構進行最佳化設計，並且利用田口方法針對混光區及導光板微結構進行最佳化效能設計，同時使得 整體背光模組之輝度與均齊度達到最適化。Chen et al. (2009)探討導光板成型模仁(Stamper)之微影製程 最佳化，其中提到在進行導光板模仁製程中之重要控制因子為，烤箱溫度、烤箱時間、滾輪溫度、曝

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光能量、顯影速度等，利用田口直交表實驗，找出符合品質特性目標之製程參數組合，經實驗結果顯 示可得到一組最佳參數組合能同時滿足直徑與均勻性之需求。

然而田口方法是從直交表水準值中找出最好之製程參數組合，但此最佳組合為離散型之組合，未 能找出最佳化之製程參數，若使用不適當之製程參數組合將會導致產品缺陷的產生，製程不穩定等現 象。要解決上述問題，許多學者應用類神經網路、田口方法、與相關之最佳化理論， Su and Wong(2007) 利用粒子群演算法(PSO)結合類神經網路建構一個多個輸入/輸出的控制器，研究結果顯示此方法更能 將品質特性更準確的逼近目標值，大幅降低誤差。Li(2008)針對LGP網點的最佳化進行研究，利用類神 經網路搭配基因演算法求取最佳化成果，其成果得到90%的均勻度。Chen et al.(2010)對塑膠射出製程 參數最佳化進行探討，將田口實驗法所得之數據資料經由倒傳遞類神經網路建立品質預測器，結合基 因演算法與於塑膠射出成形製程參數最佳化，從實驗中得知限定製程參數範圍落於最佳S/N 比之±1/2 個田口實驗水準時，基因演算法所搜尋之解優於田口實驗計畫所找出之製程參數組合。Chen et al.(2011) 針對LGP網點的最佳化進行研究，運用TracePro光學模擬軟體來進行二次光學分析，利用倒傳遞神經網 路建立光學透鏡之品質預測器，有效預測LED光學透鏡的發光型態，節省後續光學分析所需花費之時 間，並結合基因演算法與倒傳遞神經網路求出全域最佳解。

規納過去文獻，可將以往研究分成三大類，第一類用過往經驗及試誤法進行實驗；第二類運用田 口方法從直交表水準值中找出最好之製程參數組合，但此最佳組合為離散型之組合，未能找出最佳化 之製程參數；第三類運用品質預測器搭配最佳化手法(GA or PSO)針對品質進行改善。其中第一類運用 試誤法搭配經驗值的作法，容易造成不必要的錯誤，且參數如設錯方向將導致整體實驗處於無效之狀 態，而第二類未能找出最佳化之製程參數，若使用不適當之製程參數組合將會導致產品缺陷的產生，

製程不穩定等現象，第三類未考慮產品之穩定性。因此本研究將建構一套兩階段最佳化系統，第一階 段為S/N比最佳化穩定製程為目標，以S/N比預測器結合基因演算法搜尋最佳組合，藉以穩定產品之穩 定性；第二階段為品質最佳化以逼近目標值為目的，以品質預測器結合粒子群演算法搜尋最佳參數組 合，藉此達到符合品質的規格。本研究所提出之兩階段最佳化系統所找出之製程參數組合，不僅整個 製程更為穩定且微結構直徑符合尺寸規格，同時也有效降低重工次數及有效的提升均勻性以及降低成 本，提升整體微影製程之製程穩定度及提高產品品質特性。

第二章 研究方法

本研究目的在於建立一套完整的微影製程參數設定及最佳化技術，並同時找出符合多目標品質之 產品品質且品質變異最小之最佳製程參數組合，使得成品品質能夠維持在所設定的品質可接受範圍 內，產品更趨穩定。本研究整合了田口實驗設計法、倒傳遞類神經網路、基因演算法及粒子群演算法 等相關技術，運用在多目標兩階微影成形製程參數最佳化，第一階段最佳化目的在於降低產品品質變 異並使製程穩定為目標，第二階段最佳化目的將產品品質逼近目標值，符合產品規格。本研究期望微 影製程參數最佳化後，微結構網直徑介於45μm~50μm之間，而後之蝕刻製程(etching process) 將微結構 網直徑逼近50μm，主要是在蝕刻製程中，蝕刻方向包含深度與徑向擴孔。

首先使用田口直交表，針對微影成形製程參數進行實際機台之實驗計畫，利用Tamarack Model 161C曝光機、志聖 CSL-M25E 乾膜機配合資騰 DEP-M400 顯影機等進行實驗， 由於本實驗工件為 導光板模仁，其產品用途為背光模組導光板之主要結構工件，因光學特性特別靈敏，只要導光板模仁 稍有微結構脫落及均勻性不佳便會導致產品無法使用進而成為不良品，根據廠商所提供之規範，進而 將規格選定為直徑與均勻性兩種。首先利用田口實驗設計法取得實驗數據，其中導光板模仁品質特性 分別為微結構之直徑及微結構整體之均勻性，針對品質特性直徑選用望目特性第三型公式，用於必須 同時考慮品質特性的平均值與其變異情況；對於品質直徑則使用望目第三型公式，製程之控制因子為 烤箱溫度、烤箱時間、滾輪溫度、曝光能量、顯影速度，並計算各組之S/N 比值及靈敏度，並將其S/N 比數據運用MATLAB之類神經網路模組建構S/N 比預測器並結合基因演算法，作為第一階段製程參數

3

組合最佳化系統，並得一組參數組合，此組參數將使品質變異降到最低。但本階段僅針對S/N 比進行 最佳化，對於品質特性直徑與均勻性還未能達到最佳目標值。因此本實驗將針對品質特性規格進行第 二階段最佳化，並將產品品質逼近目標值，符合產品規格。為了能夠更快速的搜尋到最佳參數組合，

對其靈敏度與品質特性進行ANOVA 分析，此目的在找出品質特性較為靈敏且顯著之控參數，並作為 第二階段最佳化之調整因子，以實驗數據利用倒傳遞類神經網路建構品質預測器並結合粒子群演算 法，以第一階段最佳化做為初始值，搜尋本研究之最佳化參數組合，此組合不僅符合品質規格且品質 變異達到最小。其中導光板模仁尺寸為450*520mm，微結構直徑量測方式共分為八大區域如圖1，每區 域的量測點數各為一萬點取平均值，這樣的量測方式更能確定導光板模仁上整體微結構直徑的均勻 性，其計算導光板模仁均勻性公式如下所示。

∑

∑

= =

−

×

= ¹⁰⁰⁰⁰

1 8

10000 1

* 8

1

j

t ij i

D D

U

其中Dij是導光板模仁微結構之直徑，Dt是導光板模品質特性之目標值直徑，i為量測區域，j為量測 點數。本研究最佳化參數流程圖如圖2所示。

圖 1 導光板模仁量測示意圖 圖 2 最佳化參數流程圖

第三章 實驗建構與結果分析

第一節實驗機台與實驗材料

本研究之實驗機台設備規格如表1所示，本實驗運用材料為SUS 430BA不銹鋼板、光阻劑為日本旭 化成AQ-2058負型乾式光阻、顯影藥品為碳酸鈉，此外所使用之SUS 430BA不銹鋼板及碳酸鈉，直徑的 量測使用MAHR非接觸3D影像檢測設備量測平台範圍為650*600mm、精確度至±1μm，。

表 1 實驗設備規格

儀器名稱 設備規格

電解脫脂槽 可處理試片 600mmx450 mm，PP材料槽體，耐溫80~90℃.，定電壓或定電流200A，0~18V。

烤箱 可烘烤範圍 450*500mm,最高溫度0~250℃。

乾膜機 可壓印範圍 450*600mm,最高溫度0~250℃,壓力0~9 kg/cm²。

曝光機 曝光機：8KW功率,雙面曝光,450x600 mm面積。

顯 影 機 顯 影 機：水平雙面式、PVC槽體，顯影壓力0~2.0Kg/cm²，顯影壓力0~2.80min/m，最大工件範圍600 x600x0.5 mm。

光學檢測設備 非接觸3D影像檢測設備：具有Z軸量測功能，具XY平台600mm×600 mm，位置測量精度XY軸[1.5+(L/300mm)]m。

一、田口實驗討論

將控制因子及範圍設定值，平均分配成五個水準，如表2。並將設定值套用於L²⁵(5⁶)直交表中，實 驗參數組合。進行田口直交實驗，其中No.1~No.25為田口實驗數據，No.26~No.30為田口範圍內亂數產 生測試用數據，均勻性及微結構直徑實驗結果如表3及表4所示，經過L²⁵(5⁶)田口直交實驗由表3及表4

4

可知，對於品質特性質直徑最佳組合為第十六組，對於品質特性均勻性最佳組合為第二十四組，如表5 所示。

表 2 因子水準設定表 烤箱溫度

(℃)

烤箱時間

(Min)

滾輪溫度

(℃)

曝光能量

(mJ/cm

²

)

顯影時間

(min/m)

水準一 80 10 90 80 0.3

水準二 85 15 95 90 0.4

水準三 90 20 100 100 0.5

水準四 95 25 105 110 0.6

水準五 100 30 110 120 0.7

表 3 直徑(Diameter)實驗結果

No Y1 Y2 Y3 平均 直徑 S/N 比 標準差 靈敏度

1 44.987 45.885 45.625 45.499 39.866 0.462 33.089

2 44.237 45.164 44.216 44.539 38.305 0.541 32.877

3 41.712 41.186 41.216 41.371 42.926 0.295 32.305

4 38.806 39.209 39.778 39.264 38.105 0.488 31.800

5 36.364 36.388 36.144 36.299 48.625 0.134 31.192

6 38.095 38.165 38.044 38.101 55.948 0.061 31.618

7 38.030 38.405 38.014 38.150 44.731 0.221 31.613

8 44.417 43.838 42.939 43.731 35.376 0.745 32.631

9 43.905 43.318 42.724 43.316 37.308 0.591 32.617

10 40.114 40.467 40.678 40.420 43.040 0.285 32.105

11 42.895 42.455 41.716 42.355 37.036 0.596 32.420

12 41.298 40.962 41.491 41.250 43.756 0.268 32.285

13 38.636 38.171 38.446 38.418 44.314 0.234 31.672

14 37.255 37.056 36.833 37.048 44.885 0.211 31.360

15 44.167 44.133 44.038 44.113 56.388 0.067 32.890

16 37.710 37.757 37.786 37.751 59.862 0.038 31.538

17 43.893 42.934 43.359 43.395 39.114 0.481 32.672

18 43.421 43.975 42.881 43.426 37.995 0.547 32.655

19 42.654 41.784 43.453 42.630 34.163 0.835 32.362

20 37.881 36.797 37.948 37.542 35.285 0.646 31.351

21 41.806 42.106 41.507 41.806 42.897 0.300 32.395

22 38.236 37.678 37.567 37.827 40.466 0.359 31.513

23 37.661 37.465 37.148 37.425 43.202 0.259 31.441

24 35.925 36.465 37.023 36.471 36.447 0.549 31.138

25 45.387 45.295 45.835 45.506 43.946 0.289 33.133

五組測試組

*1 37.463 36.505 36.296 38.031 35.723 0.622 31.474

*2 38.117 37.418 37.836 37.312 40.513 0.352 31.396

*3 36.915 35.465 37.023 36.468 32.448 0.870 30.986

*4 40.603 40.529 39.454 41.576 36.212 0.643 32.239

5

*5 39.109 39.412 38.581 38.521 39.238 0.421 31.655

表 4 均勻性(Uniformity)實驗結果

No Y1 Y2 Y3 均勻性 S/N 比 標準差 靈敏度

1 4.300 4.700 4.500 4.500 13.064 0.200 13.051

2 5.370 5.650 5.360 5.460 14.744 0.165 14.735

3 8.850 8.640 8.400 8.630 18.720 0.225 18.703

4 10.440 10.940 10.840 10.740 20.620 0.265 20.597

5 12.010 12.030 12.050 12.030 21.605 0.020 21.605

6 11.770 12.400 11.530 11.900 21.511 0.449 21.444

7 11.630 11.980 11.940 11.850 21.474 0.192 21.462

8 6.340 6.140 6.330 6.270 15.945 0.113 15.941

9 6.390 6.760 6.890 6.680 16.496 0.259 16.473

10 9.580 9.580 9.580 9.580 19.627 0.000 19.627

11 7.870 7.520 7.530 7.640 17.662 0.199 17.649

12 8.980 8.540 8.730 8.750 18.840 0.221 18.824

13 11.320 11.880 11.540 11.580 21.274 0.282 21.248

14 12.860 12.860 13.130 12.950 22.245 0.156 22.237

15 6.030 5.530 6.110 5.890 15.402 0.314 15.369

16 12.450 12.150 12.150 12.250 21.763 0.173 21.753

17 6.810 6.340 6.830 6.660 16.469 0.277 16.444

18 12.130 11.890 12.070 12.030 21.605 0.125 21.600

19 7.690 7.290 7.190 7.390 17.373 0.265 17.350

20 12.270 12.680 12.430 12.460 21.910 0.207 21.896

21 8.310 8.040 8.220 8.190 18.266 0.137 18.259

22 12.010 12.230 12.300 12.180 21.713 0.151 21.705

23 12.310 12.660 12.770 12.580 21.994 0.240 21.974

24 13.130 13.760 13.700 13.530 22.626 0.348 22.586

25 4.370 4.680 4.480 4.510 13.084 0.157 13.075

五組測試組

*1 13.010 13.320 13.390 13.240 22.438 0.202 22.424

*2 11.980 12.330 12.320 12.210 21.734 0.199 21.721

*3 4.520 4.030 4.200 4.250 12.568 0.249 12.547

*4 9.930 9.740 9.730 9.800 19.825 0.113 19.820

*5 10.940 10.960 11.010 10.970 20.804 0.036 20.804

表 5 直徑及均勻性最高 S/N 比之參數表 烤箱溫

度(℃)

烤箱時間

(min)

滾輪溫 度(℃)

曝光能量

(mJ/cm

²

)

顯影速度

(m/min)

平均(um) 標準差 最高

S/N Ratio 直徑 95 10 95 120 0.5 37.75 0.04 59.862 均勻性 100 25 95 80 0.7 13.530 0.34 22.626 由於本研究為多目標品質特性製程參數最佳化，故利用田口實驗所得之數據分別針對直徑與均勻 性進行ANOVA分析，分別找出對直徑及均勻性有顯著影響之控制因子，再利用其貢獻度挑選出田口最佳 參數組合。如表6及表7所示

6

表 6 品質特性-直徑-ANOVA 表

Source DF Seq SS Adj MS F P

烤箱溫度 4 0.294 0.074 0.05 0.994

烤箱時間 4 0.315 0.079 0.05 0.993

滾輪溫度 4 0.268 0.067 0.04 0.995

曝光能量 4 139.702 29.925 23.48 0.002 顯影速度 4 60.077 20.019 10.01 0.031

Error

4 5.964 1.491

Total

24 206.619

S = 1.22109 R-Sq = 97.11% R-Sq(adj) = 82.68%

表7 品質特性-均勻性-ANOVA 表

Source DF Seq SS Adj MS F P

烤箱溫度 4 7.6002 1.9 12.58 0.015

烤箱時間 4 1.9578 0.4895 3.24 0.141

滾輪溫度 4 7.8984 1.9746 13.07 0.014 曝光能量 4 7.947 1.9868 13.15 0.014 顯影速度 4 4.872 1.218 8.06 0.034

Error

4 0.6042 0.151

Total

24 30.8796

S = 0.388648 R-Sq = 98.04% R-Sq(adj) = 88.26%

由表6及表7可知，以P值小於0.05為門檻，故曝光能量、顯影速度對於品質特性直徑貢獻度較大(較 有顯著影響)。烤箱溫度、滾輪溫度、曝光能量、顯影速度對於品質特性均勻性貢獻度較大(較有顯著影 響)。根據ANOVA表得知因子對於品質特性之間的顯著性，對於品質都同時顯著與不顯著之因子採用 平均值的方式取出為田口最佳因子水準，而因子對於其中一個品質為顯著與不顯著則取顯著的水準值 為田口最佳因子。如表8所示：

表 8 直徑及均勻性最高 S/N 比之參數組合表

烤箱溫度 烤箱時間 滾輪溫度 曝光能量 顯影速度

直徑 95 10 95 120* 0.5*

均勻性 100* 25 95* 80* 0.7*

田口最佳參數組合 100 17.5 95 100 0.6

二、第一階段最佳化-S/N 比最佳化

本階段使用MATLAB程式進行類神經網路建構出S/N比預測器(BPNNS/N)，將田口式直交表L25(5⁶)之實 驗做為類神經網路之訓練資料，以五個控制因子的資料作為輸入，以田口實驗25組之S/N比作為輸出。

經過4282個世代的訓練類神經網路的訓練與測試誤差RMSE為0.0095與0.031，因此後續之最佳製程參數 所產生之誤差也在可接受範圍之內，應用在S/N比預測上將會有良好的效果。運用MATLAB之基因演算法 結合S/N比預測器，進行第一階段微影製程參數最佳化，將田口最佳參數組合設為製程參數初始值，範 圍的設定是製程參數初始值之S/N比之組合中最大值加1/2水準，如為最小值減1/2水準，如最大值或最 小值為田口直交表中之最高水準值或最低水準值，則為其水準值。正規化範圍為0.1~0.9，交配池大小 為100，交配方式則使用單點交配的方式，交配率則為0.8，另外突變的方式使用單點突變，突變率為 0.3，收斂門檻為1.000e-004或 迭代100000世代。參數設定範圍如表9所示：

表 9 基因演算法之參數設定範圍

設定範圍 烤箱溫度 烤箱時間 滾輪溫度 曝光能量 顯影速度

7

上界 100 27.5 97.5 120 0.7

下界 92.5 10 92.5 80 0.45

適應函數如下：Min

( )

2 ²

2

1 59.862) ( 22.626)

( − + −

= y_o y_o

X

F s.t.

7 . 0 45

. 0

20 1 80

5 . 97 5

. 92

5 . 27 10

5 . 102 5

. 92

≤

≤

≤

≤

≤

≤

≤

≤

≤

≤

E D

C B

A

其中y_o1為類神經網路所預測品質特性直徑之S/N比值；y_o2為類神經網路所預測品質特性均勻性之 S/N比值；59.862為品質特性直徑S/N比最大值；22.626為品質特性均勻性S/N比值最大值；A為烤箱溫 度；B為烤箱時間;C滾輪溫度；D為曝光能量；E為顯影速度。經由第一階段最佳化，最佳化參數如表 10所示，所得製程參數以小數點下第三位四捨五入方式表示。

表10第一階段最佳化參數

烤箱溫度 烤箱時間 滾輪溫度 曝光能量 顯影速度 BPNNS/N+GA

最佳化參數 95.974 10.131 94.823 119.639 0.488

機台設定值 96 10 95 120 0.49

三、第二階段最佳化-品質特性最佳化

將田口直交表L²⁵(5⁶)之實驗做為類神經網路之訓練資料，以五個控制因子作為輸入，經過1717個 世代的訓練類神經網路的訓練與測試誤差RMSE為0.0016與0.011，因此在後續最佳製程參數之誤差在可 接受範圍之內，應用在品質預測上會有良好的效果。經由上述之最佳化過程已將製程調整至穩定狀態，

故本階段分別針對直徑及均勻性進行ANOVA分析，選出貢獻度較高之因子進行此階段所需調整之因子。

從表中可看出，曝光能量及顯影速度對於直徑貢獻度較高，另外烤箱溫度、滾輪溫度、曝光能量、顯 影速度等對於均勻性貢獻度較高，故在本階段將只針對箱溫度、滾輪溫度、曝光能量、顯影速度進行 第二階段之調整，使品質更逼近我們的目標。運用粒子群演算法結合品質預測器，進行第二階段微影 製程參數最佳化，將第一階段最佳化參數組合設為粒子群演算法之初始值。ANOVA分析可知各因子對於 值徑及均勻性重要性，曝光能量及顯影速度對於直徑較有顯著影響；烤箱溫度、滾輪溫度、曝光能量、

顯影速度等對於均勻性有顯著影響。由於本研究將烤箱時間固定，就實務經驗來看，將此因子固定住 對於品質特性影響不大，對於品質特性(直徑與均勻性)影響之因子為烤箱溫度、滾輪溫度、曝光能量、

顯影速度，與本研究之ANOVA分析相符合，故在第二階段最佳化中將烤箱時間固定，只針對烤箱溫度、

滾輪溫度、曝光能量、顯影速度進行調整。其粒子群演算法之初始值如表11所示。根據田口直交表L²⁵(5⁶) 之實驗結果，本研究將微影製程參數最佳化後，微結構網直徑設定為45μm，而後之蝕刻製程(Etching process) 將微結構網直徑逼近50μm，均勻性門檻值設定為4.5。

表 11 粒子群演算法之參數設定初始值

烤箱溫度 烤箱時間 滾輪溫度 曝光能量 顯影速度

95.974 10.131 94.823 119.639 0.488 其目標函數如下：Min G

( ) (

X = y_o1−45

)

²

s.t.

8 7

. 0 3

. 0

120 80

110 90

100 80

2 4.5

≤

≤

≤

≤

≤

≤

≤

≤

≤

E D C A y_o

其中y_o1為類神經網路品質預測器所預測品質特性之直徑值；y_o2為類神經網路品質預測器所預測 品質特性均勻性之值；45為品質特性直徑目標值；4.5為均勻性之門檻值；A為烤箱溫度；C為滾輪溫度；

D為曝光能量；E為顯影速度。經由類神經網路及粒子群演算法，可得一組第二階段最佳化參數，如表 12所示，所得製程參數以小數點下第三位四捨五入方式表示。

表 12 第二階段最佳化參數

烤箱溫度 烤箱時間 滾輪溫度 曝光能量 顯影時間

BPNN

PQ

+PSO

最佳化參數 95.7218 10.5 103.8858 82.2233 0.4042

機台設定值 96 11 104 82 0.4

第二節結果與討論

由於因子具有交互作用之關係，不能只靠單一因子的變動來決定所變動之因子，因此透過所建立 好的BPNN品質預測器，藉由ANOVA分析可得知靈敏因子(曝光能量、顯影速度)。藉由同時變動時對於直 徑及均勻性的趨勢加以預測，如圖3及圖4所示，由趨勢得知，曝光能量與顯影速度這兩因子特性剛好 相反。

圖 3 曝光能量與顯影速度對於直徑趨勢分佈圖 圖 4曝光能量與顯影速度對於均勻性趨勢分佈圖 第三節確認實驗

經過本研究之兩階段微影成形最佳化方法後，將分別針對田口方法、第一階段最佳化及第二階段 最佳化所得之值分別進行確認實驗，所得之製程參數四捨五入至小數點下三位表示，但由於機台所能 設定之準確度有限，故最佳化參數值須依照機台所能設定之限制以四捨五入之方式進行設定，如表 13 所示：

表 13 參數搜尋值與參數設定值

烤箱溫度 烤箱時間 滾輪溫度 曝光能量 顯影速度

田口方法最佳化參數 100 17.5 95 100 0.6

機台設定參數 100 18 95 100 0.6

第一階段最佳化參數 95.974 10.131 94.823 119.639 0.488

機台設定參數 96 10 95 120 0.49

第二階段最佳化參數 95.7218 10.5 103.8858 82.2233 0.4042

機台設定參數 96 11 104 82 0.4

以表14中三個階段之最佳化方法所找出之機台設定參數，各進行微影實驗製程30次，並量測其直 徑及均勻性。並依照三組最佳化參數所得之直徑與均勻性繪製出折線圖作比較，如圖5及圖6所示：

9

圖 5 品質特性(直徑)製程參數最佳化方法比較圖 圖 6 品質特性(均勻性)製程參數最佳化方法比較圖 製程能力綜合指標(Cpk)是一個評估製程穩定度重要的指標，在微影製程中設定最低Cpk值基本門檻 為1.5，若Cpk值小於1.5，則無法有較高效益的產出且可能會生產出許多不良品。因此針對直徑以製程 綜合能力指標Cpk值作為分析此三組最佳參數之製程能力指標。而本研究產品規格是依照業者所給予產 品均勻性之水準 4±1做為品質特性之規格。經由實際實驗30次量測及計算後整理出表14及表15。由表 14可知，對於品質特性均勻性而言，經過第二階段最佳化之均勻性明顯優於田口方法，平均均勻性值 由11.08降低至4.03且摽準差也由1.17降至0.17，均勻性值大提升了63.62%。

表 14 最佳化結果分析比較表(均勻性)

翹曲 平均值(μm) 標準差

田口方法最佳參數 11.08 1.17

第一階段最佳化

BPNN

S/N

+GA

8.69 0.82

第二階段最佳化

BPNN

PQ

+PSO

4.03 0.17

由表14可知，對於品質特性直徑而言，經過第二階段最佳化之直徑平均值44.7較田口方法之直徑 平均值38.14更逼近目標值且Cpk值也從1.033提升至3.448，標準差從1.17降至0.17，表示經過兩階段最 佳化不僅使直徑更逼近目標值、均勻性也較高，製程也更為穩定。

表15最佳化結果分析比較表(直徑)

直徑 平均值(um) 標準差 C^pk值

田口方法最佳參數 38.14 0.6 1.033

第一階段最佳化 BPNN^S/N+GA 42.42 0.40 2.059 第二階段最佳化 BPNNPQ+PSO 44.70 0.29 3.448

第四章 結論

一、結論

導光板模仁的生產成本會直接影響微影參數設定之決策，尤其生產前之參數設定往往需要具有大 量經驗之現場工程師，根據以往的經驗法則或利用試誤法，尋找可用之製程參數，不過此種方法浪費 過多時間及成本，且尋找到之製程參數也非最佳組合，不符合經濟效益。由於田口方法之搜尋方式為 一個非連續型離散式最佳化，故本研究針對直徑及均勻性兩種品質特性，使用田口實驗法進行微影實 驗，找出最初製程參數組合，並運用田口實驗數據建構S/N比預測器並結合基因演算法使製程趨於穩 定，之後再建立品質預測器同時結合粒子群演算法，搜尋出第二階段最佳化製成，有效的找出可同時 符合品質特性且穩定之製程最佳參數組合。經過本研究之兩階段最佳化搜尋得到參數組合進行實際微 影製程實驗。結果顯示，兩階段最佳化之參數組合針對直徑Cpk值3.448較高於田口方法最佳參數Cpk 值1.033，針對均勻性標準差也從原本的1.17降低至0.17整體均勻性標準差提升了63.62%。

10

參 考 文 獻

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Abstract - This study proposes an optimization approach to generate the optimal process parameterʳ settings of multi- response quality characteristics in the plastic injection molding (PIM) products. Taguchi method was employed to arrange the experimental work and to calculate the S/N ratio to determine the initial process parameter settings. The back-propagation neural network (BPNN) was employed to construct an S/N ratio predictor and a quality predictor. The S/N ratio predictor was along with genetic algorithms (GA) to generate the first optimal parameter combination for multiple-input multiple-output (MIMO) plastic injection molding. Besides, the afore-mentioned BPNN quality predictor was combined with GA to find the second optimal parameter settings. The quality characteristics, product length and warpage, were dedicated to finding the optimal process parameter settings for the best quality specification.

The significant control factors of optimization process influencing the product quality and S/N ratio were determined using experimental data based on analysis of variance (ANOVA). Experimental results show that the proposed approach can create the best process parameter settings which not only meet the quality specification, but also effectively enhance the PIM product quality and reduce cost.

Keywords - Plastic injection molding; Taguchi method, Back- propagation neural network; Genetic algorithms; Analysis of variance

I. INTRODUCTION

Manufacturing of high quality products with effective quality control is one of keys to industry competitiveness.

In the current plastic injection molding (PIM) industry, most products have been full of diversified and variety.

Every product, however, has its own process parameter settings created by engineers relying on their previous experiences or trial-and-error processes, which results in doing numerous tests and wasting much time. In industry applications, Taguchi method is frequently employed to determine the initial process parameter settings. Taguchi optimization methodology is to use the S/N ratio approach for finding the initial process parameter settings. Lin [1]

has examined the effectiveness of the Taguchi technique with regard to multiple performance characteristics by employing cutting parameters. Shiou and Chen [2]

examined optimal process factors as related to a Taguchi orthogonal array in the finishing operation of a freeform surface plastic injection molding. Yang et al. [3]

employed the Taguchi method to arrange sixteen experimental runs. Melting temperature, injection velocity, and injection pressure were adopted as process control factors, and the contour distortions are utilized as the

product’s quality. However, Taguchi’s parameter design method can only discover the best set of specified factor level combinations which is the discrete setting values.

An improper process parameter setting can induce many defective products and unstable product quality during the PIM process. Therefore, an effective methodology is necessary to efficiently and rapidly analyze process parameters and control the product quality.

To deal with these problems, many researchers have investigate optimization of PIM. Shi et al. [4] presented an improved hybrid strategy for optimizing a plastic injection molding process. Numerical simulation software, GA, and back-propagation neural network (BPNN) were employed to optimize process parameters. Costly numerical calculations were avoided by creating a BPNN quality predictor. Kurtaran and Erzurumlu [5] integrated finite element (FE) analysis, design of experimental method, response surface methodology (RSM), and GA to effectively optimize warpage of thin-shell plastic parts. In considering product warpage, ANOVA analysis was used to determine the most significant process parameters.

Optimum values for those process parameters can be determined through a predictive response surface model in conjunction with GA. However, there is an error from 10% to 30% existing in the setting value of control parameters due to interference from an injection molding process’s noise factors neglected by CAE simulations.

CAE simulations are not practical since the molding environments creates another noises to the parts quality, beside the controllability, repeatability, and the precision of molding machines provide more noises that contribute to part quality in real injections molding. To solve the above mentioned problems, Chen, et al. [6] integrated Taguchi method, back-propagation neural networks, and genetic algorithms to optimize the MIMO process parameters. A real-world plastic injection molding experiment was performed. The experimental results show that the optimization approach can effectively help engineers determine optimal process parameter settings.

Deng et al. [7] adopting the Taguchi orthogonal arrays calculated the S/N ratios to find an initial combination of process parameters. Regression analysis and the Davidon- Fletcher-Powell method were used to determine the optimal process parameter settings of plastic injection molding under single quality characteristic considerations.

II. PROPOSED APPROACH

This section presents the proposed process parameter optimization approach for multiple-input multiple-output (MIMO) plastic injection molding process under five

Optimization of MIMO Plastic Injection Molding Using DOE, BPNN, and GA

W. C. Chen, H. C. Tsai, T. T. Lai

Department of Industrial management, Chung Hua University, Hsinchu, Taiwan wenchin@chu.edu.tw

676 ___________________________________

978-1-4244-6482-1/10/$26.00 ©2010 IEEE

control factors, and two quality responses. The proposed approach integrates Taguchi method, BPNN, and GA to obtain the optimal process parameter settings. Taguchi method was used to arrange an L25(5⁶)orthogonal array experiment and to reduce the number of set-test cycles.

Subsequently, the signal-to-noise ratio (S/N ratio) method was employed to determine the initial process parameter settings that have minimal sensitivity to noise with the consideration for the major quality characteristic. The injection pressure, injection velocity, melt temperature, packing pressure and packing time were selected as process control factors, and warpage and length were employed as the quality responses. The back-propagation neural network (BPNN) was employed to construct an S/N ratio predictor and a quality predictor. The S/N ratio predictor was along with genetic algorithms (GA) to generate the first optimal parameter combination for multiple-input multiple-output (MIMO) plastic injection molding. This optimization methodology will significantly reduce variance of the PIM process. Besides, the afore-mentioned BPNN quality predictor was combined with GA to find the second optimal parameter settings. The quality characteristics, product length and warpage, were dedicated to finding the optimal process parameter settings for the best quality specification. The significant control factors of optimization process influencing the product quality and S/N ratio were determined using experimental data based on analysis of variance (ANOVA). Finally, three confirmation experiments are performed to confirm the effectiveness of final optimal process parameter settings.

A. Experimental Equipments

In this study, the experimental material used is PA-765 fireproof plastic material. The injection molding machine is a V i c t o r T a i c h u n g V s - 1 0 0 . P r o d u c t w a r p a g e a n d l e n g t h a r e me a s u r e d u s i n g a n e l e c t r i c c a l i p e r w h i c h h a s a p r e c i s i o n o f 0 . 0 1 m m. The product in this illustrative example is an ADSL modem which is shown in Fig. 1.

Fig. 1 Illustrated component

B. Implementation of Taguchi method and BPNN This research applies L25(5⁶⁾ orthogonal array to assign five factors into the rows, with melt temperature (MT), injection velocity (IV), injection pressure (IP), packing pressure (PP) and packing time (PT) assigned to rows A,

B, C, D and E respectively. Table 1 shows the five process control factors and parameter setting range.

Experimental control factors and the setting of level are shown in Table 2. There are in total twenty-five treatments with different level combinations of four factors. Five replications are taken to increase analytical data amount, for adding sensitivity to statistical analysis.

In total one hundred twenty-five sample data were collected. During the collection of samples, ten shots of each treatment were made before the official sample collecting job started to ensure that the injection molding process was operations stably. Since the responses of the experiment are warpage and length, and the target product length is 124 mm. The nominal-the-best was applied to calculate S/N ratio for each treatment. In addition, the company’s production consulting team had concluded that the target warpage must be less than 0.25 mm and smaller-the-best was applied to calculate S/N ratio for each treatment.

From the experimental treatments, response statistics, and the S/N ratio, the average and standard deviation of each treatment with five replications and the S/N ratio were obtained. Table 3 shows the process parameter combinations of highest S/N ratio under different responses. Table 4 shows the ANOVA results of length and indicates that D and E were significant. Table 5 also reveals that D and E were significant for warpage.

Therefore, the control factors in optimization of the product quality model only employed packing pressure and packing time. Furthermore, the experimental data of Taguchi method were used for effectively training and testing BPNN quality predictor (BPNNPQ) and S/N ratio predictor (BPNNSN). The training performance (RMSE) of BPNNSN is up to 0.007, the testing performance amounts to 0.035. The training performance (RMSE) of BPNNPQ is up to 0.0065, the testing performance amounts to 0.0228.

TABLE 2

CONTROL FACTORS AND THE SETTING OF LEVEL LEVEL VARIABLE

NOTATION

CONTROL

PARAMETERS 1 2 3 4 5

A Melt Temperature 195 197 199 201 203 B Injection Velocity 30 32 34 36 38 C Injection pressure 60 62 64 66 68 D Packing Pressure 50 52 54 56 58 E Packing time 1 1.3 1.6 1.9 2.2

TABLE 1.

PRODUCT PARAMETER SETTING RANGE

CONTROL PARAMETERS SETTING RANGE Melt Temperature 195 ~ 203 ć

Injection Velocity 30 ~ 38 mm/s Injection pressure 60 ~ 68 MPa Packing Pressure 50 ~ 58 MPa Packing Time 1 ~ 2.2 sec

677

C. Hybrid BPNNSN-GA and BPNNPQ-GA search approaches

To optimize the process parameter settings of the proposed optimization approach, hybrid BPNNSN-GA and BPNNPQGA search approaches were adopted to yield two global optimal solutions. In the experiment, Taguchi method was employed to arrange the experiment.

Subsequently, the S/N ratio was used to determine the initial process parameter settings that had minimal sensitivity of noise with the consideration for the major quality characteristic. Melt temperature (MT), injection velocity (IV), injection pressure (IP), packing pressure (PP) and packing time (PT) were selected as process control factors. Two highest S/N ratios for length and warpage were selected by the case study as the responses.

Then, BPNNSN was employed as an S/N ratio predictor and combined with GA to search for the optimal process parameter settings. To identify optimal parameter settings of the proposed hybrid BPNNSN-GA search approach, the fitness function of GA is given as follows:

5 , 2 , 1 .

.

) 65 . 16 ( ) 75 . 34 ( )

( ^{2 2}

 d

d







i USR x LSR t

s

y y

X F Min

i i i

ow ol

where X = (x1, x2, x3, x4, x5) is the process control parameters, y_olis the predicted S/N ratio value (length)

of BPNNSN, y_ow is the predicted S/N ratio value (warpage) of BPNNSN, x_i is the notation of process parameter

i

. LSR_i and USR_i are lower and upper search range of process parameter

i

, respectively. The setting method of LSR_i andUSR_i is listed as follows:

2

i ni i

PS D

LSR 

2

i ni i

PS D

USR 

where _PSni is the process parameter setting value of parameter

i

which let the S/N ratio of response n be highest, _Di is the factor level’s equal range of parameter

i

in Taguchi experiment. The process parameter setting values_PSni are shown in the Table 3.

In addition, BPNNPQ was employed as a quality predictor and combined with GA to search for the optimal process parameter settings. According to the ANOVA results, the control factors in the optimization model only employed packing pressure and packing time. Then, the fitness function of the proposed hybrid BPNNPQ-GA search approach is given as follows:

TABLE5

ANOVA FOR PRODUCT WARPAGE

SOURCE OF VARIANCE SUM OF SQUARES DEGREES OF FREEDOM MEAN SQUARE F0 PERCENT CONTRIBUTION

A 0.006 4 0.00149 3.429 0.38%

B 0.0216 4 0.00539 12.409 1.78%

C 0.0189 4 0.00473 10.887 1.54%

D 0.6271 4 0.15679 360.703 55.93%

E 0.3884 4 0.09710 223.392 34.58%

ERROR 0.0561 129 0.00043 5.09%

TOTAL 1.1181 149 TABLE 3

THE PROCESS PARAMETER SETTINGS OF HIGHEST S/N RATION UNDER DIFFERENT RESPONSE

RESPONSE MELT

TEMPERATURE

INJECTION VELOCITY

INJECTION PRESSURE

PACKING PRESSURE

PACKING

TIME AVERAGE STANDARD DEVIATION

HIGHEST S/N RATIO

LENGTH 197 30 62 54 1.9 123.985 0.0105 34.75

WARPAGE 197 36 68 50 1.3 0.147 0.0103 16.65

TABLE4

ANOVA FOR PRODUCT LENGTH

SOURCE OF VARIANCE SUM OF SQUARES DEGREES OF FREEDOM MEAN SQUARE F0 PERCENT CONTRIBUTION

A 0.0289 4 0.00722 13.673 4.71%

B 0.0023 4 0.000566 1.072 0.03%

C 0.0084 4 0.002096 3.970 1.11%

D 0.4171 4 0.104272 197.493 72.96%

E 0.0441 4 0.011017 20.867 7.38%

ERROR 0.0681 129 0.000528 12.16%

TOTAL 0.5688 149

678

2 , 1 25

. 0 .

.

) 124 (

)

( ²

d d d



i USR x LSR y t s

y X F Min

i i i ow

ol

where ^X



^{x1, x2}



is the process control parameters,

y

olis the predicted value (length) of BPNNPQ,

y

_owis the predicted value (warpage),

x

_i is the notation of process parameter

i

. LSR_i and USR_i are lower and upper search range of process parameter

i

, respectively. The setting method of LSR_i andUSR_i is listed as follows:

2

i ni i

PS D

LSR 

2

i ni i

PS D

USR 

where _PSni is the process parameter setting value of parameter

i

which let the S/N ratio of response n be highest, D_i is the factor level’s equal range of parameter

i

in Taguchi experiment.

III. RESULTS AND DISCUSSION

Following the hybrid BPNNSN-GA and BPNNPQ- GA search approaches, the final optimal process settings are shown in Table 6. To demonstrate the effectiveness of the proposed optimization system, this research performed three confirmation experiments. One experiment utilized preliminary initial process parameter settings obtained from the Taguchi method. The other two experiments utilized the final optimal initial process parameter settings obtained from the hybrid BPNNSN-GA and BPNNPQ-GA search approaches, respectively. Each experiment produced 30 product samples. The statistical averages, standard deviations, and process capability indices of all three methods were compared in order to judge the best approach for determining the final optimal process parameter settings. Comparisons of quality statistics between the Taguchi, BPNNSN-GA and BPNNPQ-GA search approaches are shown in Table 7 and Table 8, respectively. In addition, comparisons of quality characteristics (length and warpage) between the Taguchi, BPNNSN-GA and BPNNPQ-GA search approaches are shown in Fig. 2 and Fig. 3, respectively. According to the experimental results, the standard deviation of the Taguchi approach was 0.0152. That is approximately two times that of the BPNNSN-GA approach (0.0076). In the practical assessment, the process capability index is a major criterion for assessing the ability of a production process to make products that meet specifications. The practical minimum process capability index (Cpk) is 1.33 in many manufacturing industries. As the results in Table 8 show, the Cpk of Taguchi’s approach was 1.274; which

is roughly one half that of the BPNNSN-GA approach (2.592) and BPNNPQ-GA approach (2.221). Consequently, the optimal process parameter settings generated by the proposed two approaches definitely produced better performances than the Taguchi method. Experimental results also revealed that the BPNNSN-GA approach produced the highest Cpk value and the best quality products. The BPNNPQ-GA search approach did not perform quite as well, but was still better than the Taguchi method.

Fig. 2 Comparisons of quality characteristics (length) between the Taguchi, BPNNSN-GA and BPNNPQ-GA search approaches

TABLE6

OPTIMAL PROCESS PARAMETERS FOR BPNNSN-GA AND BPNNPQ-GA SEARCH APPROACHES

Melt Temperature

Injection Velocity

Injection pressure

Packing Pressure

Packing time BPNNSN

-GA 197.44 34.86 61.13 51.94 1.23 BPNNPQ

-GA 197 36 65 52.39 1.53

TABLE8

COMPARISONS OF LENGTH QUALITY STATISTICS AMONG THE TAGUCHI, BPNNSN-GA, AND BPNNPQ-GA APPROACHES

LENGTH AVERAGE STANDARD DEVIATION CPK

TAGUCHI 123.958 0.0152 1.274

BPNNSN-GA 123.969 0.0076 2.592 BPNNPQ-GA 124.003 0.0146 2.221

TABLE7

COMPARISONS OF WARPAGE QUALITY STATISTICS AMONG THE TAGUCHI,BPNNSN-GA, AND BPNNPQ-GA APPROACHES WARPAGE AVERAGE STANDARD DEVIATION

TAGUCHI 0.2202 0.0080

BPNNSN-GA 0.1545 0.0063 BPNNPQ-GA 0.1906 0.0072

679

Fig. 2 Comparisons of quality characteristics (warpage) between the Taguchi, BPNNSN-GA and BPNNPQ-GA search approaches

IV. CONCLUSION

The application of Taguchi method is unreasonable when process parameters are continuous and have a nonlinear relationship. It cannot help engineers obtain optimal process parameter settings. This research employs Taguchi method, analysis of variance, back- propagation neural networks, and genetic algorithms to assist engineers in determining the final optimal process parameter settings for PIM product production in a complex environment. The results of the tests performed using the proposed approach show that the machine parameter settings not only produced measurably better performance than the Taguchi method alone but also can produce better performance. Thus, the proposed approach is a feasible and effective method for process parameter optimization in MIMO plastic injection molding and can result in significant quality and cost advantages.

ACKNOWLEDGMENT

The research was conducted as part of a project sponsored by Polyprecision Industrial Co. Ltd., Hsin-chu, Taiwan.

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國科會補助計畫衍生研發成果推廣資料表

日期:2011/10/08

國科會補助計畫

計畫名稱: 兩階段最佳化系統應用於導光板模仁微影製程之研究 計畫主持人: 陳文欽

計畫編號: 99-2221-E-216-034- 學門領域: 自動化製程技術

無研發成果推廣資料