根據關聯結構函數建構的混合EWMA-CUSUM管制圖

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姓名

魏姝姍(Shu-Shan Wei) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

根據關聯結構函數建構的混合EWMA-CUSUM管制圖
(A Copula-based Hybrid EWMA-CUSUM Control Chart)

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至系統瀏覽論文 (2025-8-1以後開放)

摘要(中)

統計管制圖是監控製程中產品品質穩定性的重要工具。隨著現代製程的進步，製程中經常需要監控多個的品質特性，因此多變量統計製程的設計日益重要。為能設計一種穩健且能監測多變量平均向量微量改變的製程管制方法，本文建議混合使用多變量指數加權移動平均(MEWMA)及累和管制圖(MCUSUM)，其中各品質特性之邊際分布為常態分布，但是應用關連結構模型描述品質特性之聯合分布。本文藉由蒙地卡羅模擬比較所提方法與MEWMA及MCUSUM管制圖在品質特性失控時所需的平均連串長度。最後利用一個在計算機製程中的一組真實數據展示所提方法的實際應用。

摘要(英)

Statistical control charts are important tools for monitoring the stability of product quality in manufacturing processes. With advancements in modern processes, it is of increasing importance to monitor more than one quality characteristic simultaneously, hence emphasizing the need for designing multivariate statistical process control methods. To develop a robust method for detecting subtle changes of mean vectors in multivariate processes, this paper proposes a hybrid approach using Multivariate Exponentially Weighted Moving Average (MEWMA) and Multivariate Cumulative Sum (MCUSUM) charts. The marginal distributions of quality characteristics are assumed to be normal distributions, while a structural model is employed to describe the interrelations among quality characteristics. Through Monte Carlo simulations, the performance of the proposed method is compared with that of MEWMA and MCUSUM control charts on the average run length required when multivariate quality characteristics are out-of-control. Finally, the practical application of the proposed method is illustrated by a real-world dataset arising from a computer manufacturing process.

關鍵字(中)

★ 關連結構函數
★ 多維指數加權移動平均管制圖
★ 多維累和管制圖
★ 混合多維指數加權移動平均及累和管制圖

關鍵字(英)

★ Copula function
★ MEWMA control chart
★ MCUSUM control chart
★ MEWMA-MCUSUM control chart

論文目次

Chinese Abstract i
English Abstarct ii
Table of Contents iv
List of Figures vi
List of Tables vii
1. Introduction 1
2. Literature Review 5
2.1 Statistical Control charts 5
2.1.1 Univariate Control Charts 5
2.1.2 Multivariate Control Chatrs 8
2.2 Copula Function and Kendall′s tau 10
2.3 Goodness-of-fit Tests 14
3. Copula-based MEC Control Charts 17
3.1 Algorithm for Finding Control Limits 17
3.2 Simulated Upper Control Limit 18
4. A Simulation Study 21
4.1 Design of Study 21
4.2 Results of Study 22
5 A Real Data Example 24
6 Conclusion and Discussion 31
Bibliography 31
Appendix 35

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指導教授

陳玉英(Yuh-Ing Chen)

審核日期

2024-7-22

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