          系統識別號 U0002-2007202011333500 中文論文名稱 線上壽命時間離群值之檢測 英文論文名稱 OLT Web Interface: Outlier Testing in Lifetime Data 校院名稱 淡江大學 系所名稱(中) 數學學系數學與數據科學碩士班 系所名稱(英) Master's Program, Department of Mathematics 學年度 108 學期 2 出版年 109 研究生中文姓名 伍聿男 研究生英文姓名 Yu-Nan Wu 學號 607190104 學位類別 碩士 語文別 英文 口試日期 2020-06-17 論文頁數 34頁 口試委員 指導教授-林千代委員-陳麗霞委員-吳碩傑 中文關鍵字 臨界值  離群值檢定  間隔  使用者介面 英文關鍵字 Critical values  Discordancy test  Spacings  User interface. 學科別分類 中文摘要 我們利用R統計軟體中的 Shiny 套件開發出一套網路介面 OTL (Outlier Testing in Lifetime Data) 來檢測指數、Weibull、對數常態或對數Laplace分配的資料是否有較大或較小離群值。在許多文獻中，虛無假設下區塊或連續檢定程序之檢定統計量的機率分配計算通常是需要用到非常複雜的積分，而且論文所提供的表格數據都是有限的。因此，我們利用Huffer and Lin (2001)的演算法和Iliopoulos and Balakrishnan (2009)的定理讓OTL 介面可以精確地計算出指數與對數 Laplace 模式之檢定統計量的機率分配。而對於 Weibull 與對數常態模式之檢定統計量的機率分配，我們則用 Monte Carlo 模擬方法取得其機率分配之逼近值，並且將所得數據儲存於資料庫，再與 OTL 介面連結以供使用者可以快速取得並做出判斷。使用OTL 介面不但可以節省搜尋表格的時間，也能擴大使用的數據範圍，更可以直接從介面上看到多個檢定統計量離群值檢測之结果，所以OTL 介面對於研究學者、決策者和企業使用者是一個相當有效且方便判斷檢測壽命時間離群值的線上工具。 英文摘要 A web interface, named OTL, is developed to conduct outlier analysis in exponential, Weibull, Lognormal, and Log-Laplace samples online over the Internet through Shiny and R. It is a tool to evaluate the exact or approximate distributions of block and consecutive test statistics on outliers which have been discussed over the years in the literature. Since it allows for identifying outliers without using the classical extensive tables, OTL can be very useful to academics, policy-makers and businesses to compare and understand the results of outlier testing procedures more efficiently. 論文目次 1 Introduction 1 2 Main Tools for Evaluating the Null Distributions of Test Statistics from Exponential and Laplace Samples 7 2.1 Conditional Independence of Blocked Order Statistics 8 2.2 Recursions 8 3 The OTL User Interface 10 4 Demonstration with Known Data Sets 13 Example 1 13 Block Tests 13 Consecutive Tests 15 Example 2 17 Example 3 18 Example 4 19 5 Concluding Remarks and Possible Future Directions 21 References 22 Appendix A 27 Appendix B 29 參考文獻 Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H. and Tukey, J. W. (1972). 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Exact inference for Laplace quantile, reliability, and cumulative hazard functions based on Type-II censored data. IEEE Transactions on Reliability, 65 164–178. 論文使用權限 同意紙本無償授權給館內讀者為學術之目的重製使用，於2022-08-01公開。同意授權瀏覽/列印電子全文服務，於2022-08-01起公開。 若您有任何疑問，請與我們聯絡！圖書館： 請來電 (02)2621-5656 轉 2486 或 來信 