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系統識別號 U0002-2206201401030100
中文論文名稱 Burr XII分配產品的壽命績效指標在逐步型I區間設限下之檢定程序
英文論文名稱 A testing procedure for the lifetime performance index of products with Burr XII 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 102
學期 2
出版年 103
研究生中文姓名 陳姿瑾
研究生英文姓名 Tzu-Chin Chen
學號 601650343
學位類別 碩士
語文別 中文
口試日期 2014-06-06
論文頁數 42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  Burr XII分配  最大概似估計量  拔靴法  製程能力指標  檢定程序 
英文關鍵字 progressive type I interval censoring  Burr XII distribution  maximum likelihood estimator  bootstrap  process capability index  testing procedure 
學科別分類
中文摘要 近年來,由於科技的進步,許多高科技產品像是平板電腦、智慧型手機等等,皆很受消費者歡迎,而消費者對於產品的品質要求則更加嚴格,因此提升產品製程的能力是品管上很重要的工作。在實務上,已經發展了很多種方法來評估產品的品質能力,製程能力指標(process capability indices, PCIs)就是其中一種方法。
本研究假設產品的壽命服從Burr XII分配時,在逐步型I區間設限下,計算出壽命績效指標 之最大概似估計量並求得其漸近分配。在規格下限L已知的情形下,使用此估計量及兩種拔靴法發展出三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,我們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, consumers are in the pursuit of more stringent product quality requirements for many high-tech products such as tablet, smart mobile phones, etc. In practice, many researchers have developed a variety of methods to assess the quality of the product and the method of process capability indices (PCIs) is one of them.
This research is focusing on the lifetime of products following the Burr XII distribution. The maximum likelihood estimator is used to estimate the lifetime performance index (CL) based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator and two kinds of bootstrap to develop three kinds of new hypothesis testing algorithmic procedure in the condition of known lower specification limit L. Finally, two practical 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 I
表目錄 III
圖目錄 IV
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻探討 3
1.3 本文架構 8
第二章 壽命績效指標與其估計 9
2.1 產品的壽命績效指標 11
2.2 壽命績效指標的估計量 14
第三章 壽命績效指標的檢定演算程序 19
3.1 壽命績效指標的檢定演算程序 19
3.2 壽命績效指標檢定的檢定力 23
第四章 模擬與數值實例方析 28
4.1 數值實例 28
4.2 模擬範例 33
第五章 結論與未來研究 37
5.1 結論 37
5.2 未來研究 38
參考文獻 39

表目錄
表 2.1 壽命績效指標 值對應之製程良率 13
表 4.1 50位關節炎患者的緩解時間(單位:小時) 28
附表1 當規格下限 ,總觀測時間 ,觀測樣本數 、 、 、 ,設限樣本數 、 及逐步移除率 時,在目標值 和顯著水準 下,檢定力函數 在 的數值 41

圖目錄
圖 1.1 逐步型I區間設限圖 7
圖 2.1 雙參數在 時Burr XII分配之機率密度函數圖 10
圖 2.2 雙參數在 時Burr XII分配之故障率函數圖 10
圖 3.1 當 、 、 及 下,對不同檢定方法的檢定力函數 26
圖 3.2 當 、 及 下,對不同設限樣本 時的檢定力函數 26
圖 3.3 當 、 及 下,對不同總樣本 時的檢定力函數 27
圖 4.1 不同 下之p-value 29
參考文獻 [1] Boyles, R. A. (1991), The Taguchi capability index, Journal of Quality Technology, 23(1), pp. 17–26.
[2] Burr, I.W. (1942), Cumulative frequency function, A. Math. Stat. , 13, pp. 215–232.
[3] 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.
[4] Cohen, A. C. (1963), Progressively censored samples in life testing, Technometrics, 5(3), pp. 327–339.
[5] Cohen, A. C. (1991), Truncated and censored sample, New York : Marcel Dekker.
[6] Efron, B. (1982), The Jackknife, the Bootstrap and other re-sampling plans, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 38, SIAM, Philadelphia, PA.
[7] Hall, P. (1988), Theoretical comparison of bootstrap confidence intervals, Annals of Statistics, vol.16, pp. 927–953.
[8] Hong, C. W., Wu, J. W., and Cheng, C. H. (2008), Computational procedure of performance assessment of lifetime index of Pareto lifetime businesses based on confidence interval, Applied Soft Computing , 8(1), pp. 698–705.
[9] Juran, J. M. (1974), Journal Quality Control Handbook, 3rd Edition,
McGraw-Hill, New York.
[10] Kane, V. E. (1986), Process capability indices, Journal of Quality Technology, 18, pp. 41–52.
[11] Lawless, J. F. (1982), Statistical Methods for Lifetime Data, John Wiley and Sons, New York.
[12] Lawless, J. F. (2003), Statistical Models and Methods for Lifetime Data, (2nded), New York, John Wiley.
[13] Lee, H. M., Wu, J. W., and Lei, C. L. (2013) , Assessing the lifetime performance index of exponential products with step-stress accelerated life-testing data, IEEE, 62, pp. 296–304.
[14] Lee, W. C., Wu, J. W., and Hong, C. W. (2009), Assessing the lifetime performance index of products from progressively type II right censored data using Burr XII model, Mathematics and Computers in Simulation, vol. 79(7), pp. 2167–2179.
[15] Lee, W. C., Wu, J. W., and Lei, C. L. (2010), Evaluating the lifetime performance index for the exponential lifetime products, Applied Mathematical Modelling, 34(5), pp. 1217–1224.
[16] Montgomery, D. C. (1985), Introduction to statistical quality control, John Wiley and Sons, New York.
[17] 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.
[18] 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.
[19] Wingo, D. R. (1983), Maximum likelihood methods for fitting the Burr type XII distribution to life test data, Biometric.J. , 25, pp. 77–84.
[20] 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.
[21] 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.
[22] Wu, J. W., Lee, W. C., Hong, C.W. and Yeh, S.Y. (2013) , Implementing lifetime performance index of Burr XII products with progressively type II right censored sample, ICIC International, pp. 671–693.
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