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系統識別號 U0026-2907201417483900
論文名稱(中文) 基於剖面資料進行多階段製程建模之研究
論文名稱(英文) Model Building of Multistage Manufacturing Process with Profile Data
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 102
學期 2
出版年 103
研究生(中文) 張惇皓
研究生(英文) Tun-Hao Chang
學號 R26014048
學位類別 碩士
語文別 英文
論文頁數 107頁
口試委員 指導教授-鄭順林
口試委員-張升懋
口試委員-李水彬
中文關鍵字 多階段製程  根本原因尋找  剖面資料  函數型迴歸模型  交互作用  lasso 
英文關鍵字 multistage manufacturing process  root cause finding  profile data  functional regression model  interaction  lasso 
學科別分類
中文摘要   在現今的工業界中,產出高附加價值產品的多階段製程扮演越來越重要的角色,也因此這種類型的製程分析也獲得越來越多的關注。 在本篇論文中,我們的目標是提供一個模型建立的流程,該模型可以幫助了解製程變數隨著時間變動的影響力,並且能基於該模型 針對不尋常品質產出進行根本原因的尋找。
  在製程中,自動化資料蒐集工具隨著時間量測並記錄了製程變數的數值,這些隨著時間紀錄的資料是以曲線方式呈現且被稱為剖面資料(profile data)。
我們將這些剖面資料視為函數型資料,因此函數型資料分析的技術在這裡可以被應用。為了建立製程剖面資料與最終品質產出的關係,我們應用了函數型迴歸模型。首先是應用了函數型線性模型。對於該模型,最小絕對值壓縮和選取法(lasso)(Tibshirani, 1996)被用來進行變數選擇以及參數估計。
  本論文的主要貢獻在於我們發展了一個可用來描述製程變數間(或變數內)的交互作用模型。且在主效用優先的前提下,對於該模型提供了一套兩階段建模方式。最後,由實際資料分析的結果可得知該模型的估計結果可用來幫助製程分析與對於不尋常品質產出進行根本原因的尋找。
英文摘要 The multistage manufacturing processes with high-value-added products are become gradually important in today's industry thus the process analysis for quality-related problems of this kind of process draw more and more attention. In this thesis, we aim to provide a model building procedure for realizing the temporal influence of the process variables on final quality and for finding the root causes of abnormal quality products.
The automatic data collection tools within the process provide longitudinal measurement data of the process variables, these measurements are in the form of curve to which refer "profile data". We consider the process profile data are of functional nature so that the techniques of functional data analysis can be applied. To relate the functional profile data to the final quality outcome, first we employed the functional linear model. For the functional linear model with multiple functional covariates, the least absolute shrinkage and selection operator (lasso) (Tibshirani, 1996) is introduced for simultaneous variable selection and parameter estimation.
The major contribution of this thesis is in developing a functional regression model which includes the temporal interaction between (and/or within) process profiles. A two-stage modeling approach is also proposed for keeping the "main effect priority". Finally, the property of the proposed model is illustrated through a real data analysis. The result shows that the estimated models from the two-stage modeling approach are helpful for process analysis and root cause finding.
論文目次 1. Introduction 1
1.1 Background and Motivation 1
1.2 Data Description 3
1.2.1 Final Quality Data 5
1.2.2 Process Profile Data 7
1.3 Literature Review 9
1.3.1 Dynamic Time Warping 9
1.3.2 Multistage Manufacturing Process Modeling 9
1.3.3 Functional Regression 11
1.4 Overview 12

2. Methodology 13
2.1 Profile Alignment Technique 13
2.1.1 Problem Formulation 13
2.1.2 Profile Alignment by Dynamic Time Warping (DTW) 14
2.1.3 References for DTW 15
2.1.4 Constant Stage Duration Method (CSD) 16
2.2 Functional Linear Regression Model 17
2.2.1 Functional Principal Component Analysis (FPCA) 17
2.2.2 Model Formulation 19
2.2.3 Model Estimation 21
2.3 Functional Regression with Interactions 23
2.3.1 Model Formulation 23
2.3.2 Two-stage Modeling Approach 25

3. Real Data Analysis 28
3.1 Preprocessing Step of Process Profile 28
3.1.1 Profile Alignments by Stagewise DTW (sDTW) and CSD 28
3.1.2 Comparison of the Alignment Methods 33
3.2 Exploration on Centered Process Profiles 33
3.2.1 Centered Process Profiles 34
3.2.2 FPCA on the Process Profiles 38
3.3 Main Effect Model for a Multistage Process 41
3.3.1 sDTW Based on Mode Time Reference 42
3.3.2 Constant Stage Duration Method 57
3.4 Interaction Effect Model for a Multistage Process 69
3.4.1 sDTW Based on Mode Time Reference 69
3.4.2 Constant Stage Duration Method 76
3.5 Two-stage Modeling Approach 78
3.5.1 Implementation 78
3.5.2 Comparison with Pooled Modeling Approach 83

4. Problems and Discussions 85
4.1 Impact of Profile Alignment Methods 85
4.2 Impact of Cumulative Variance Restriction 86
4.3 Lambda Selection of Lasso 89
4.4 Lambda Allocation in the Two-stage Modeling Approach 89
4.5 Suggestion on Simulation 92

5. Conclusions and Future Work 96
5.1 Conclusions 96
5.2 Future Work 97

Bibliography 100

Appendix A Figures 103
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