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研究生:張海飛
研究生(外文):Hafiedza Pradana Rakasiwi
論文名稱:對韋伯分配故障間隔時間的一些管制圖之比較研究
論文名稱(外文):Comparison of some control charts for monitoring Weibull-distributed time between failures
指導教授:王福琨王福琨引用關係
指導教授(外文):Fu-Kwun Wang
口試委員:陳欽雨歐陽超
口試委員(外文):Qin-Yu ChenChao Ou-Yang
口試日期:2017-05-25
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:工業管理系
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:英文
論文頁數:77
中文關鍵詞:CUSUM-TCCEWMA-TCC單次測量NEWMA-TCC串連長度t-chartWeibull分配
外文關鍵詞:CUSUM-TCCEWMA-TCCindividual measurementsNEWMA-TCCrun lengtht-charttime between failuresWeibull distribution
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在可靠度領域中,對於監控元件或系統的失效間隔時間(time between failures)一直是感興趣的。失效間隔時間可以使用Weibull分配進行建模,因為Weibull分配可以更靈活的描述不同形狀的失效時間分配。在失效間隔時間為Weibull分配和單次測量(individual measurements)的情況下,分別使用EWMA-Tukey control chart (EWMA-TCC)、CUSUM-TCC、t-chart與normal-transformed EWMA-TCC (NEWMA-TCC)這四種管制圖(control chart)進行監控與比較。本研究的目的為在不同的Weibull形狀參數 (shape parameter) 以及尺度參數 (scale parameter) 中,監控失效間隔時間的平均偏移。其中三個測量值,像是平均連串長度 (average run length)、串連長度標準差(standard deviation of run length)和中位數串連長度 (median run length),使用〖10〗^5次迭代的蒙地卡羅模擬(Monte-Carlo simulation) 進行計算。相對平均指標(relative mean index)的測量也被用來比較不同管制圖的整體表現。以兩個闡述性範例說明四個管制圖應用於監控失效間隔時間的平均偏移。結果發現當EWMA-TCC的λ=0.25時,在失效間隔時間為Weibull分配且形狀參數固定的情況下檢測平均偏移的表現優於其他管制圖。EWMA-TCC還能夠根據相對平均指標快速檢測出尺度參數與形狀參數的變化,這種情況在業界非常的普遍。另一方面,在監控形狀參數的改變上,t-chart是最有效的管制圖。
In the reliability area, monitoring the time between failures (TBF) of the component or system is often of interest. The TBF can be modeled by using Weibull distribution because it is more flexible to describe the failure time distributions with many different shapes. Four different control charts including EWMA-Tukey control chart (EWMA-TCC), CUSUM-TCC, t-chart, and normal-transformed EWMA-TCC (NEWMA-TCC) are compared to monitor the Weibull-distributed TBF with individual measurements. The objective of this research is to monitor the TBF mean shifts under the different values of the Weibull scale and shape parameters. Three measures such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL) are computed using Monte-Carlo simulation with 105 iterations. Relative mean index (RMI) is also used as a measure for comparing the overall performance of different control charts. Two illustrative examples are provided to show the application of four control charts for monitoring the TBF mean shifts. Based on the results, EWMA-TCC with λ=0.25 performed better than the other control charts for detecting the mean shift of the Weibull-distributed TBF with fixed shape parameter. EWMA-TCC also able to detect the change of the scale and the shape parameter quickly in terms of RMI. These parameter changes are very common in the industry. On the other hand, t-chart is the most effective control chart for monitoring the shape parameter change.
摘要 i
Abstract ii
Acknowledgement iii
Table of contents iv
List of figures v
List of tables vi
Chapter 1: INTRODUCTION 1
1.1 Research background and motivation 1
1.2 Research objective 3
1.3 Research limitations 3
1.4 Research flow 4
Chapter 2: LITERATURE REVIEW 6
2.1 Monitoring Weibull-distributed time between failures 6
2.2 Existing control charts 7
2.3 The other control charts for monitoring Weibull processes 9
Chapter 3: RESEARCH METHODS 11
3.1 EWMA-Tukey control chart and normal-transformed EWMA-TCC 11
3.2 CUSUM-Tukey control chart 13
3.3 Performance evaluation 15
Chapter 4: ILLUSTRATIVE EXAMPLES 31
Chapter 5: CONCLUSIONS 50
References 51
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