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研究生： Berihun Bizuneh Tegegne
Berihun Bizuneh Tegegne
論文名稱： 改善監控Weibull過程的管制圖
Improved Control cahrts for Monitoring Weibull Processes
指導教授： 王福琨
Fu-Kwun Wang
口試委員: 林則孟
James T. Lin
Houn-Gee Chen
Houn-Gee Chen
蒂莫
Timon Du
王孔政
Kung-Jeng Wang
學位類別： 博士
Doctor
系所名稱： 管理學院 - 工業管理系
Department of Industrial Management
論文出版年： 2018
畢業學年度： 107
語文別： 英文
論文頁數： 156
中文關鍵詞： 韋伯分配 、事件之間的時間 、型Ⅰ設限 、型Ⅱ設限 、指數加權移動平均 、累積和
外文關鍵詞： Weibull, time between events, type-I censoring, type-II censoring, EWMA, CUSUM
相關次數： 點閱：391  下載：14 
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    • 透過管制圖監控可靠度資料，可以控制和改善製程品質，在高科技製造過程中，當不良發生率較少時，監控兩個相鄰不良發生的時間是合適的。因此，本論文提出一個改善管制圖監控韋伯分配(Weibull distribution)可靠度資料和相鄰兩個事件的發生時間，所採用的方法包括對現有方法做全面比較，以探索不同情況下的替代方案並提出新方法。此篇考慮單雙尾舒華特(Shewhart)、指數加權移動平均(EWMA)及累積和管制圖(CUSUM) ，以監控韋伯資料，並轉換成常態、指數、最小極值分配。平均運串長度(ARL)、運算長度標準差(SDRL)和相對平均指標(RMI)用作績效測量。蒙特卡羅模擬方法用於第2、3、4章，另外在第4章和第5章使用積分方程和馬可夫鏈方法來計算績效測量。第2章中提出Weibull-EWMA及 mixed CUSUM-EWMA圖表對現有的Weibull CUSUM及mixed EWMA-CUSUM圖表進行全面比較，用比較結果監控相鄰兩個事件發生的時間。第3章和第4章內容主要是關於監控Weibull製程中型Ｉ設限的管制圖，第3章進行研究比較，第4章為其改善方法。第2章、第3章、第4章描述監控Weibull製程的參數，第5章和第6章中，採用了基於輔助統計數據的關鍵數量的監控統計量，並提出了EWMA和CUSUM圖表。在所有的章節中，所提出的管制圖在大多數情況下檢測出小幅度的績效改善，此外，文中提供示範說明基於已發表論文真實數據及模擬數。

    Process quality can be controlled and improved by monitoring reliability data using control charts. When there are fewer failures, for example, in high-tech manufacturing processes, monitoring the time between failures is preferable. With these objectives, this dissertation presents improved control charts for monitoring Weibull-distributed reliability data and time between events. The approaches followed include comprehensive comparisons of existing methods to explore alternatives in different situations and proposing new methods. One-sided and two-sided Shewhart-type, exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts for monitoring Weibull data transformed into the normal, exponential and smallest extreme value distributions are considered. The average run length (ARL), standard deviation of run lengths (SDRL) and relative mean index (RMI) are used as performance measures. While the Monte Carlo simulation approach is used in chapters 2, 3 and 4, the integral equation and Markov chain approaches are utilized in chapters 4 and 5 to compute the performance measures. The proposed Weibull EWMA and mixed CUSUM-EWMA charts along with a comprehensive comparison with the existing Weibull CUSUM and mixed EWMA-CUSUM charts for monitoring time between events are presented in chapter 2. Chapters 3 and 4 deal with control charts for monitoring a Weibull process with type-I censoring. Chapter 3 is a comparison study and chapter 4 is an improvement. While chapters 2, 3 and 4 deal with monitoring the scale parameter of a Weibull process, chapters 5 and 6 consider monitoring Weibull percentiles. In chapters 5 and 6, a monitoring statistic based on a pivotal quantity conditioned on ancillary statistics is employed, and EWMA and CUSUM charts are proposed. In all chapters, the proposed control charts have shown improved performances in detecting smaller shifts in most cases. Illustrative examples based on real data from published papers and simulated data are provided in all chapters.

    摘要…………………………………………………………………………………………………………………….………………. ii Abstract iii Acknowledgment iv Table of contents v List of figures ix List of tables xi Chapter One 1 Introduction 1 1.1. Background 1 1.1.1. Performance measures of control charts 5 1.1.2. Computation methods 5 1.2. Statement of the problem 9 1.3. Objectives of the study 9 1.4. Organization of the dissertation 10 Chapter Two 12 A comparison study of control charts for Weibull distributed time between events 12 2.1. Introduction 12 2.2. Four control charts 14 2.2.1. Two existing control charts 15 2.2.2. Two new control charts 17 2.3. ARL and SDRL 19 2.3.1. Performance evaluation 19 2.3.2. Optimal design parameters of the MCE chart 23 2.4. Comparison study 24 2.5. Illustrative examples 28 2.6. Conclusions 34 Chapter Three 35 Comparison of different control charts for a Weibull process with type-I censoring 35 3.1. Introduction 35 3.2. Control charts under comparison 36 3.2.1. Shewhart-type control charts 38 3.2.2. EWMA chart 41 3.2.3. CUSUM chart 42 3.3. Comparison study 43 3.3.1. Computation of control limits 43 3.3.2. Performance Evaluation 46 3.4. Illustrative Example 51 3.5. Conclusions 53 Chapter Four 54 A mixed CUSUM-EWMA chart for monitoring a Weibull process with type-I censoring 54 4.1. Introduction 54 4.2. Proposed control chart 55 4.3. Comparison study 58 4.4. Illustrative example 61 4.5. Conclusions 62 Chapter Five 63 New control charts for monitoring Weibull percentiles under complete data and type-II censoring 63 5.1. Introduction 63 5.2. Existing control charts 66 5.2.1. Weibull percentiles 66 5.2.2. Existing control charts for complete data and Type-II censoring 69 5.3. Three new control charts 75 5.3.1. A new control chart for complete data and Type-II censoring 75 5.3.2. Two new control charts for complete data 76 5.3.3. Computation of the ARLs of the proposed control charts 78 5.3.4. Optimal design parameters for the EWMA-SEV-Q and proposed control charts ………………………………………………………………………………….80 5.4. Comparison study 83 5.5. Numerical examples 88 5.6. Conclusions 93 Chapter Six 95 EWMA chart based on Bayes-conditional pivotal quantity for Weibull percentiles under complete data and type-II censoring 95 6.1. Introduction 95 6.2. Existing control charts and proposed control chart 97 6.2.1. Existing Shewhart-SEV- and bootstrap control charts 98 6.2.2. EWMA-SEV- chart 105 6.3. Comparison study 106 6.4. Numerical examples 112 6.5. Conclusions 115 Chapter Seven 117 Conclusions and future study 117 7.1. Conclusions 117 7.2. Applications 119 7.3. Future study 120 Appendices 121 Appendix I. R-code for ARL and SDRL compuation of the WEWMA chart 121 Appendix II. R-code for ARL compuation of the EWMA-CEV chart 122 Appendix III. R-code for ARL and SDRL compuation of the MCE chart 123 Appendix IV (a). R-code for ARL compuation of the EWMA-SEV-Q chart 125 Appendix IV (b). R-code for ARL compuation of the CUSUM-SEV-Q chart 127 Appendix IV (c). R-code for ARL compuation of the EWMA-YP chart 128 Appendix IV (d). R-code for ARL compuation of the CUSUM-YP chart 129 Appendix V. R-code for ARL and SDRL compuation of the EWMA-SEV- chart 130 References 133

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