各式模型的變異數成份管制

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陳佩伶(Pei-Ling Chen) 查詢紙本館藏

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工業管理研究所

論文名稱

各式模型的變異數成份管制
(Monitoring Variance Components in Various Models)

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摘要(中)

監控製程的變異對於確保品質的一致是非常重要的。在很多製程上，尤其是半導體生產製程中，製程的總變異通常是由很多原因造成的，因此僅使用一簡單統計量來衡量整體之製程變異常常無法確認變異的來源。
然而，若製程之總變異可分解成由不同的特殊原因所造成的變異數成份(Variance Components)，則管制已分解的變異數成份比管制整體的變異來的更為適當與有效率，因為造成變異的原因不同，不應該放在一起計算，如此將無法知道究竟是哪個主因造成變異的，故應分開來看。
在Nelson(1995)中所提出的，巢式設計(Nested Design)下其變異數經過特殊轉換後，若會服從F分配，則可獲得該變異數之信賴區間的作法，故本研究主要運用此概念探討在單因子隨機效應模型(One-Factor Random Effects Model)、二個隨機因子模型(Two-Factor Random Effects Model)、二因子混合效應模型(Two-Factor Mixed Effects Model)以及巢式與分裂區集模型(Nested and Split-Plot Design Model)下之變異數成份的信賴區間為何以達到管制製程變異的目的。

摘要(英)

Monitoring the variances of processes is important to ensure the consistence of quality. In many processes, especially for those in the semiconductor industry, several factors would lead to the variance of overall process. Thus, it is difficult to identify the origin of variances by using one simple statistics to measure the overall process variance.
However, it is more effective and more appropriate to monitor the decomposed variance components rather than the overall variance, if the overall process variance can be decomposed into variance components with associated special causes. Since the causes of variance are different, we cannot calculate the variances as a whole; otherwise, we cannot identify the major cause contributing to the variance, so we should do separately.
Nelson (1995) addressed that with Nested Design, if the variance follows F- statistics after being specially transformed, we can get the confidence intervals of variance. Hence, this study mainly applies this idea to discuss how the confidence interval of variance components with One-Factor Random Effects Model, Two-Factor Random Effects Model, Two-Factor Mixed Effects Mode and Nested and Split-Plot Design Model can reach the goal of controlling the variance of process.

關鍵字(中)

★ 單因子隨機效應模型
★ 變異數成份
★ 信賴區間
★ 二個隨機因子模型
★ 巢式與分裂區集設計模型
★ 二因子混合效應模型

關鍵字(英)

★ One-Factor Random Effects Model
★ Confidence Intervals
★ Variance Components
★ Two-Factor Mixed Effects Model
★ Two-Factor Random Effects Model
★ Nested and Split-Plot Design Model

論文目次

目錄 I
表目錄 III
第一章緒論 1
第二章文獻回顧 4
2.1 有隨機因子模型 5
2.2 巢式及分裂區集設計模型 9
2.3 信賴區間的估計 13
第三章各式模型的變異數成份管制 15
3.1 有隨機因子模型之變異數成份分析 16
3.1.1 單因子隨機效應模型 16
3.1.2 二個隨機因子的模型 17
3.1.3 二因子混合效應模型 19
3.2 巢式與分裂區集設計模型 24
3.2.1 二因子巢式隨機效應模型 24
3.2.2 三因子分裂區集設計模型 26
3.3 實例分析 29
3.3.1 單因子隨機效應模型實例分析 29
3.3.2 二個隨機因子的模型實例分析 31
3.3.3 二因子混合效應模型實例分析 34
3.3.4 二因子巢式隨機效應模型實例分析 36
3.3.5 三因子分裂區集設計模型實例分析 39
第四章結論 44
參考文獻 46
附錄 48
附錄A：單因子隨機效應模型變異數成份信賴區間之推導 48
附錄B：二個隨機因子模型變異數成份信賴區間之推導 50
附錄C：二因子混合效應模型變異數成份信賴區間之推導(無重複測量) 53
附錄D：二因子混合效應模型固定因子處理效應信賴區間推導(無重複測量) 55
附錄E：二因子混合效應模型變異數成份信賴區間之推導(重複測量) 57
附錄F：二因子混合效應模型固定因子處理效應信賴區間之推導(重複測量) 59
附錄G：二因子巢式隨機效應模型變異數成份信賴區間之推導 60
附錄H：三因子分裂區集設計模型之變異數分析 62
附錄I：三因子分裂區集設計模型變異數成份信賴區間之推導 68
附錄J：三因子分裂區集設計模型中固定因子處理效應信賴區間之推導 71

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指導教授

王丕承(Pe-Cheng Wang)

審核日期

2006-7-10

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