論文使用權限 Thesis access permission:校內公開,校外永不公開 restricted
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus:永不公開 not available
論文名稱 Title |
I(d)過程的統計管制圖
Statistical Control Charts of I(d) processes |
||
系所名稱 Department |
|||
畢業學年期 Year, semester |
語文別 Language |
||
學位類別 Degree |
頁數 Number of pages |
77 |
|
研究生 Author |
|||
指導教授 Advisor |
|||
召集委員 Convenor |
|||
口試委員 Advisory Committee |
|||
口試日期 Date of Exam |
2002-05-31 |
繳交日期 Date of Submission |
2002-07-10 |
關鍵字 Keywords |
EWMA管制圖、長相關過程、EWRMS管制圖、長記憶過程 ARFIMA process, long-memory process, EWRMS, I(d) process, EWMA |
||
統計 Statistics |
本論文已被瀏覽 5759 次,被下載 28 次 The thesis/dissertation has been browsed 5759 times, has been downloaded 28 times. |
中文摘要 |
本文主要在建立監控長相關過程 ( I(d) process ) 的管制圖,包含EWMA及EWRMS管制圖。論文中推導出與超幾何函數相關的EWMA準確(exact)漸近管制線。對於EWRMS則推導出Box及Pearson的逼近管制界線。並且利用蒙地卡羅模擬方法探討此管制圖的偵錯能力,如其ARL值。此管制圖可廣泛應用在具有長相關特性過程的監控,例如:河流年最低水位、空氣污染、臭氧含量監控等。 |
Abstract |
Long range dependent processes occur in many fields, it is important to monitor these processes to early detect their shifts. This paper considers the problem of detecting changes in an I(d) process or an ARFIMA(p,d,q) process by statistical control charts. The control limits of EWMA and EWRMS control charts of I(d) processes are established and analytic forms are derived. The average run lengths of these control charts are estimated by Monte Carlo simulations. In addition, we illustrate the performance of the control charts by empirical examples of I(d) processes and ARFIMA(1,d,1) processes. |
目次 Table of Contents |
Contents 1 Introduction 1 2 Preliminaries 3 2.1 The ARFIMA(p; d; q) Process . . . . . . . . . . . . . . . . 3 2.2 Generalized Hypergeometric Function . . . . . . . . . . . . 5 2.3 Control Charts . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Control Charts for I(d) Processes 9 3.1 EWMA Control Chart (The Exponentially Weighted Moving Average Control Chart) 9 3.2 EWRMS Control Chart (Expontentially Weighted Root Mean Square) . . . . . . . 12 3.3 Control Charts for ARFIMA(p; d; q) Processes . . . . . . . 17 4 Simulation Results 18 4.1 Detecting Mean Shift . . . . . . . . . . . . . . . . . . . . . 18 4.2 Detecting Variance Change . . . . . . . . . . . . . . . . . . 19 4.3 Pre-I(d)ing Procedure . . . . . . . . . . . . . . . . . . . . 20 5 Examples 22 5.1 The Nile River's Annual Lowest Water Level . . . . . . . 22 5.2 Monitoring Air Pollution . . . . . . . . . . . . . . . . . . . 23 5.3 Monitoring Ozone . . . . . . . . . . . . . . . . . . . . . . . 24 6 Conclusions and Further Study 27 A Appendix A 30 B Appendix B 34 B.1 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 B.2 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 |
參考文獻 References |
References [1] Montogmery, D.C. (1997) Introduction to statistical quality control. John Wiley & Sons, Inc. [2] Imhof, J.P.(1961) Computing the distribution of quadratic forms in normal variables. Biometrika 148, pp.419-426. [3] Pearson, E.S. Note on an approximation to the distribution of non-central ˜ 2 . Biometrika 146, pp.364. [4] Anderson, T.W. (1971) The statistical analysis of time series. John Wiley & Sons, Inc. [5] Box, G.E.P. (1953) Some theorems on quadratic forms applied in the study of analysis of variance problems. (I) Eect of inequallity ofvariance in the one-way classication. Annals of Mathematical statistic 125, pp.290-302. [6] Macgregor, J.F. & Harris, T.J. (1993) The exponentially weighted moving variance. Journal of Quality Technology 25, pp.106-117. [7] Seaborn, J.B. (1991) Hypergeometric functions and their applications. Springer- Verlag New York, Inc. [8] Brockwell, P.J. & Davis, R.A. (1991) Time Series: Theory and Methods. Springer- Verlag New York, Inc. [9] Wei, William W.S. (1994) Time series analysis. Addison-Wesley, Inc. [10] Lu, C.W. & Reynolds, M.R., JR. (1993) Control charts for monitoring the mean and variance of autocorrelated processes. Journal of Quality Technology 31, pp.259-274. [11] Lu, C.W. & Reynolds, M.R., JR. (1993) EWMA control charts for monitoring the mean of autocorrelated processes. Journal of Quality Technology 31, pp.166-188. |
電子全文 Fulltext |
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。 論文使用權限 Thesis access permission:校內公開,校外永不公開 restricted 開放時間 Available: 校內 Campus: 已公開 available 校外 Off-campus:永不公開 not available 您的 IP(校外) 位址是 54.236.245.71 論文開放下載的時間是 校外不公開 Your IP address is 54.236.245.71 This thesis will be available to you on Indicate off-campus access is not available. |
紙本論文 Printed copies |
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。 開放時間 available 已公開 available |
QR Code |