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系統識別號 U0026-2506201400574300
論文名稱(中文) 應用虛擬變數於多重實驗環境下辨別異質因子效果之最佳受限制實驗設計
論文名稱(英文) Applying indicator variable to the constrained optimization of experimental designs to identify heterogeneous treatment effects under multiple experimental environments
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系
系所名稱(英) Department of Industrial and Information Management
學年度 102
學期 2
出版年 103
研究生(中文) 林裕昌
研究生(英文) Yu-Chang Lin
學號 R36011115
學位類別 碩士
語文別 中文
論文頁數 50頁
口試委員 指導教授-張裕清
口試委員-王泰裕
口試委員-蔡青志
中文關鍵字 實驗設計  區集  虛擬變數  多重實驗環境  最佳設計  品質管理 
英文關鍵字 block  indicator variable  multiple experimental environments  optimal design  quality management 
學科別分類
中文摘要 目前的實驗設計方法大多需要在同一個實驗環境下進行,但多重實驗環境在現實世界中是一個容易遭遇到的情境,本研究的多重實驗環境是指在不同實驗環境下進行相同的實驗,例如一家公司的某樣產品由母工廠與子工廠同時生產製造,其中母廠與子廠的製程相同。然而多重實驗環境若以企業的角度則可能會造成品質相關的問題,如前述例子中母工廠與子工廠的生廠良有可能會有明顯差異。實驗設計方法現今已經被廣泛使用來處理品質相關的問題,而在多重實驗環境的部分大多是以區集設計來處理,區集設計估計出來的區集效應是一個整體的效應,無法估計因子與個別實驗環境的效應,然而這些效應卻是極為重要的資訊,企業能使用這些資訊來管理產品的品質,故本研究希望以實驗設計的方法來估計多重實驗環境的表現。本研究在模型中導入虛擬變數,以虛擬變數的交互作用估計不同實驗環境的效應,並且修改Fedorov的D-optimal演算法,加入多重實驗環境的情境與實驗資源的限制,讓演算法更貼近實務,在最後將會有一個實際的個案,個案中使用修改過後的演算法產生最佳設計,並以最佳設計執行實驗獲取實驗資料,再依照模型做各項迴歸分析,從分析結果可以發現,若使用本研究的方法來估計多重實驗環境可以得到良好的效果,實驗者可以區隔出不同實驗環境的效應,這些資訊可以提供給管理者作為品質管理的依據。
英文摘要 Applying indicator variable to the constrained optimization of experimental designs to identify heterogeneous treatment effects under multiple experimental environments

Author: Yu-Chang Lin
Advisor: Yu-Ching Chang

Key words: block, indicator variable, multiple experimental environments, optimal design, quality management

National Cheng Kung University
Department of Industrial and Information Management

SUMMARY

In this article, we offer a Design of Experiments (DOE) method to model the performance of multiple experimental environments. Indicator variables are used in the regression model to represent different experimental environments, and we modify the Fedorov’s D-optimal algorithm to find the optimal experiment design under the multiple experimental environments situation. There is a case study in chapter 4, which we can confirm the validity of this method. Above all, the analysis of the data can be valuable to improve the product quality for that managers can take advantage of the results to manage the product quality under different experimental environments.

INTRODUCTION

Today, it is common to see multiple experimental environments situation. We define multiple experimental environments as doing same experiments under different environments, like a company has mother factor and subsidiary factor which produce same product. This situation can increase the reliability and flex of companies, but it also increases the difficulty of quality management. Because of the difference between these experimental environments, it brings quality problems as well. It is impossible for environments to have same experimental conditions, such as material, equipment, operators and so on, then companies may produce with big variance. It will lead to inconsistency of product. As far as quality management and quality engineering are concerned, DOE has been an important tool. In the field of DOE, blocking is a common method which is used to deal with different experimental environments. However, it can estimate only overall effects of environments, but experimenters usually want to know more details about the difference of environments. On the other hand, there may not be equal experimental resource between environments. So experimenters have to do experiment under this restriction. In order to find the best design of experiment with constrained experimental resource, there are several optimal designs using mathematical method. They can help experimenter get information without doing a full experiment. This implies that experimenters can reduce cost at the same time, since every single experiment represents money and time, which may be heavy burden for experimenters or company. In this article, we provide a DOE method which can estimate the difference of suppliers for the same factor. After getting these details, it is expected to be the important information for manager to solve quality problems.

MATERIALS AND METHOD

Assume that there are two environments, and they have the same environmental process which contains several important factors. The responses of the observation are not consistent. In this situation, managers would want to know where the problem is. If we use blocking to deal with environments, we could only estimate the overall effects of environments. In order to find where the problem is, we build a model which can do what blocking can’t. Indicator variables are used in the regression model to represent different environments, and the coefficients of interaction between factors and indicator variables are used to estimate the difference of environments for the same factor. Because the resource is not same between environments, experimenters may not be able do the full experiment. In order to find the optimal experiment design under the multiple experimental environments and constrained resource, we modify the Fedorov’s D-optimal algorithm, adding restriction to the original algorithm, so the modified algorithm can fit the real problem. The D-criterion can minimize the estimate of variance, it makes experiments more precise. After actually doing the experiment based on the optimal design, we can get response variables, and analyze the data. Due to the response variables of the case study are in the interval (0, 1), it is obvious that the response variables are not normal distribution. To avoid violating normal assumption, we use beta regression to analyze the data. In the case study, beta regression is definitely better than linear regression.

RESULTS AND DISCUSSION

According to the result of case study, the method we provide can model the multiple experimental environments situations well. We can estimate the difference of environments for the same factor by using the model in this article. And the modified algorithm can be practically run to find the optimal design under multiple experimental environments situations. Finally, the result of analysis will provide manager important information to improve product quality. From the case study of this study, we can conclude that the performance of supplier 1 is much better than supplier 2 and supplier 3 by analyzing the data. Managers can formulate a strategy like increasing the proportion of orders of supplier 1 or asking supplier 2 and supplier 3 to use equipment as same as supplier 1 etc. In conclusion, our research builds a method to get more detail about multiple experimental environments, and this brings contribution to managers in quality management.
論文目次 目錄
摘要 I
Abstract II
誌謝 IV
表目錄 VII
圖目錄 VIII
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究價值 3
1.4 研究假設 3
1.5 研究架構 3
第二章 文獻回顧 5
2.1 實驗設計 5
2.1.1 因子實驗(factorial experiments) 5
2.1.2 飽和設計(saturated design) 7
2.2 區集設計(block design)與裂區設計(split-plot design) 7
2.2.1 區集設計 7
2.2.2 裂區設計 9
2.3 虛擬變數(indicator variable) 11
2.3.1 對虛擬變數的誤解 12
2.4 最佳設計(optimal designs) 12
2.4.1 D-optimal 13
2.4.2 D-optimal演算法 14
第三章 研究方法 18
3.1 建立模型 19
3.1.1 建立實驗環境的虛擬變數 19
3.1.2 建立迴歸模型 19
3.1.3 模型解釋 20
3.2 演算法 23
3.2.1 原始設計矩陣 23
3.2.2 分配實驗環境的實驗次數 24
3.2.3 修改演算法 24
3.3 顯著性檢定 29
3.3.1 估計 29
3.3.2 檢定顯著性 29
第四章 實證分析 31
4.1 資料來源 31
4.2 個案分析 32
4.2.1 實驗的反應值與因子 32
4.2.2 建立模型 33
4.2.3 實驗限制 33
4.2.4 產生最佳設計 35
4.2.5 分析實驗數據 36
第五章 結論與未來研究建議 44
5.1 結論 44
5.2 未來研究建議 44
參考文獻 45
附錄 48

表目錄
表3.1 原始設計矩陣 23
表4.1 站點介紹 31
表4.2 因子介紹 32
表4.3 個案的虛擬變數 32
表4.4 原始的模型配適結果 36
表4.5 貝他迴歸的模型配適結果 38
表4.6 不同迴歸比較 41
表4.7 貝他迴歸分析結果的意義 43

圖目錄
圖1.1 研究流程圖 4
圖2.1 Fedorov演算法流程圖 17
圖3.1 修改過後的演算法流程圖 28
圖4.1 原始的殘差分析 37
圖4.2 貝他迴歸的殘差分析 39
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