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博碩士論文 etd-0710102-145834 詳細資訊
Title page for etd-0710102-145834
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
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) E ect of inequallity ofvariance in the one-way classi cation.
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.
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