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系統識別號 U0002-2506201314054500
中文論文名稱 在逐步型I區間設限下對Rayleigh分配的壽命績效指標之檢定程序
英文論文名稱 A testing procedure for the lifetime performance index of products with Rayleigh distribution under progressive type I interval censoring
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 101
學期 2
出版年 102
研究生中文姓名 林盈孜
研究生英文姓名 Ying- Tzu Lin
學號 600650039
學位類別 碩士
語文別 中文
口試日期 2013-05-31
論文頁數 40頁
口試委員 指導教授-吳淑妃
委員-王智立
委員-吳錦全
中文關鍵字 逐步型I區間設限;Rayleigh分配;最大概似估計量;製程能力指標;檢定程序 
英文關鍵字 progressive type I interval censored  Rayleigh distribution  maximum likelihood estimator  process capability index  testing procedure 
學科別分類
中文摘要 近年來,由於智慧型手機及平板電腦的盛行等等,在產業高度競爭的時代,消費者對於產品品質要求更加嚴格。在實務上,製程能力指標(process capability indices, PCIs)已經被廣泛地用於評估製程的績效,進而不斷地提升產品品質及製程能力。
本研究假設當產品的壽命服從Rayleigh分配時,在逐步型I區間設限下,求出壽命績效指標C_L之最大概似估計量,並探討其漸近分配與檢定力函數,在規格下限L已知的情形,利用此估計量發展出一個新的假設檢定程序,以判定壽命績效是否達到預定的能力水準。最後,將用兩個數值實例去說明如何使用本研究所提出的檢定程序。
英文摘要 In recent years, due to the prevalence of smart phones and tablet PCs, the consumers require more stringent product quality in the highly competitive commercial market. In practice, process capability indices (PCIs) has been widely used to assess the performance of the process, and then continues to be employed to improve the product quality and process capability.

This research is focusing on the lifetime of products following the Rayleigh distribution. The maximum likelihood estimator is used to estimate the lifetime performance index (C_L) based on the progressive type I interval censored sample. The asymptotic distribution of this estimator and the power function are also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure in the condition of known lower specification limit L. Finally, two numerical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.
論文目次 目 錄
第一章 緒論 1
1.1研究動機和目的 1
1.2文獻探討 3
1.2.1 製程能力指標的發展 3
1.2.2 設限樣本 5
1.3 本文架構 7
第二章 Rayleigh分配之壽命績效指標 8
2.1 產品的壽命績效指標與製程良率 8
2.2 壽命績效指標之估計量 11
第三章 壽命績效指標的檢定演算程序 17
3.1 壽命績效指標的檢定演算程序 17
3.2 壽命績效指標檢定程序的檢定力 19
第四章 模擬與數值實例分析 25
4.1 數值實例 25
4.2 模擬例子 28
第五章 結論與未來研究 30
5.1 結論 30
5.2 未來研究方向 31
參考文獻 32
附 錄 34

表目錄

附表2.1 壽命績效指標C_L值對應之製程良率 34

附表3.1當規格下限L=0.05,總觀測時間T=0.5,設限樣本數m=5(1)8,觀測樣本數n=60(20)100及逐步移除率p=0.05(0.025)0.1時,在目標值c_0=0.8和顯著水準alpha=0.01下, h(c_1)在c_1=0.8,0.825(0.025)0.975檢定力函數的數值 35

附表3.2 當規格下限L=0.05,總觀測時間T=0.5,設限樣本數m=5(1)8,觀測樣本數n=60(20)100及逐步移除率p=0.05(0.025)0.1時,在目標值c_0=0.8和顯著水準alpha=0.05下, h(c_1)在c_1=0.8,0.825(0.025)0.975檢定力函數的數值 37

附表3.3 當規格下限L=0.05,總觀測時間T=0.5,設限樣本數m=5(1)8,觀測樣本數n=60(20)100及逐步移除率p=0.05(0.025)0.1時,在目標值c_0=0.8和顯著水準alpha=0.1下, h(c_1)在c_1=0.8,0.825(0.025)0.975檢定力函數的數值 39

圖目錄

圖1.1 逐步型I區間設限圖 7

圖3.1 當alpha=0.1、m=5及p=0.05下,對不同總樣本n=(60,80,100)時的檢定力函數。 22

圖3.2 當alpha=0.1、n=60及p=0.05下,對不同的設限樣本m=(5,6,7,8)時的檢定力函數。 23

圖3.3 當alpha=0.1、n=60及m=5下,對不同的移除率p=(0.05,0.075,0.1)時的檢定力函數。 23

圖3.4 當n=60、m=5及p=0.05下,對不同顯著水準alpha=(0.01,0.05,0.1) 時的檢定力函數。 24

圖3.5 當n=60、m=5,...,20及p=0.05下,對不同顯著水準 alpha=(0.01,0.05,0.1)時的檢定力函數。 24


參考文獻 參考文獻
[1] Balakrishnan, N. (1989), Approximate MLE of the scale parameter of Rayleigh distribution with censoring, IEEE Transactions On Reliability, 38(3), pp. 355-357.
[2] Boyles, R.A. (1991), The Taguchi capability index, Journal of Quality Technology, 23(1), pp.17-26.
[3] Caroni, C. (2002), The correct “ball bearings” data, Lifetime Data Analysis, 8, pp.395-399.
[4] Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), A new measure of process capability Cpm, Journal of Quality Technology, 20(3), pp.162-175.
[5] Chiou, K. C. and Tong, L. I. (2001), Average type-II censoring times for two-parameter Pareto and Rayleigh distributions, International Journal of Quality and Reliability Management, 18(6), pp.643-656.
[6] Gill, M.H. and Gastwirth J.L. (1978), A sacle-free goodness-of-fit Test for the Exponential Distribution Based on the Gini Statistic, Journal of the Royal Statistical Society, Series B(Methodological), 40, pp.350-357.
[7] Hong, C. W., Wu, J. W. and Cheng, C. H. (2007), Computational procedure of performance assessment of lifetime index of businesses for the pareto lifetime model with the right type II censored sample, Applied Mathematics and Computation , 184, pp.336-350.
[8] Juran, J. M. (1974), Journal Quality Control Handbook, 3rd Edition,
McGraw-Hill, New York.
[9] Kane, V. E. (1986), Process capability indices, Journal of Quality Technology, 18, pp.41-52.
[10] Lawless, J. F. (2003), Statistical Models and Methods for Lifetime Data, (2nded), New York, John Wiley.
[11] Montgomery, D. C. (1985), Introduction to statistical quality control, John Wiley and Sons, New York.
[12] Pearn, W. L., Kotz, S. and Johnson, N. L. (1992), Distributional and inferential properties of process capability indices, Journal of Quality Technology, 24(4), pp.216-231.
[13] Polovko, A. M. (1968), Fundamentals of Reliability Theory, Academic Press.
[14] Tong, L. I. , Chen, K. S. and Chen, H. T. (2002), Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution, International Journal of Quality &Reliability Management, 19(7), pp.812-824.
[15] Wu, J. W., Lee, W. C. and Hou, H. C. (2007), Assessing the performance for the products with Rayleigh lifetime, Journal of Quantitative Management, 4, pp.147-160.
[16] Wu, J. W., Lee, H. M. and Lei, C. L. (2007), Computational testing algorithmic procedure of assessment for lifetime performance index
of products with two-parameter exponential distribution, Applied Mathematics and Computation, 190, pp.116-125.
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