淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-2706200611213300
中文論文名稱 在逐步型一區間設限下建立指數分配的壽命檢驗計畫
英文論文名稱 Exponential Life Test Plans 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 94
學期 2
出版年 95
研究生中文姓名 范曉菁
研究生英文姓名 Hsaio-Ching Fan
學號 693460072
學位類別 碩士
語文別 中文
口試日期 2006-06-23
論文頁數 35頁
口試委員 指導教授-蔡宗儒
委員-廖敏治
委員-蘇懿
委員-蘇聖珠
中文關鍵字 壽命檢驗計畫  逐步設限  型一設限  區間設限 
英文關鍵字 Life test plan  Progressive censoring  Type I censoring  Interval censoring 
學科別分類 學科別自然科學統計
中文摘要 傳統的壽命檢驗計畫,通常採用型一或型二設限方法來蒐集資料,但傳統的設限方法不允許在實驗中移除存活的實驗單位,且必須連續地監控產品,當我們因故或基於實驗上的方便無法連續檢驗產品,且在實驗中對存活的產品做移除時,就必須採用逐步區間設限方法進行實驗,本論文結合型一設限、區間設限及逐步設限方法,探討當產品壽命服從指數分配時,如何建立壽命檢驗計畫,在給定生產者風險與消費者風險下,求出壽命檢驗計畫所需的最小樣本數,以及檢定壽命的臨界值,並將以上結果編製成表,以利實務界使用。
英文摘要 Traditional life tests are often established based on the type I or type II censoring schemes, moreover, the survival units can not be removed during the test. In practice, we may not inspect the experiment units continuously due to some accidents or just for convenience so that some survive units needed to be removed. In the thesis, we combine type I censoring, interval censoring, and progressive censoring to develop life test plans under exponential distribution. The minimum sample sizes and the critical values of lifetime needed for life test plans are found under some removal schemes. Some tables are provided here to help the use of the proposed life test plans for practitioners.
論文目次 目錄

第一章 緒論 1
1.1 研究動機與目的 1
1.2 論文架構 2
第二章 文獻探討 4
2.1 區間設限資料之壽命檢驗計畫 4
2.2 逐步設限資料之壽命檢驗計畫 5
第三章 逐步型一區間設限下之指數分配壽命檢驗計畫 7
3.1 模式與假設 7
3.2 壽命檢驗計畫 12
第四章 數值模擬與例題 15
4.1 數值結果分析 15
4.2 數值實例探討 18
第五章 結論 32
參考文獻 32
圖形目錄
4.1 實驗為平均移除時,不同條件下所需抽取的樣本數,(a)t=1/3;(b)t=1/5;(c)t=1/10 -------------------------------------------------------------------------------20
4.2 實驗為第一階段移除時,不同條件下所需抽取的樣本數,(a)t=1/3;(b)t=1/5;(c)t=1/10----------------------------------------------------------------------------21
4.3 實驗為最後階段移除時,不同條件下所需抽取的樣本數,(a)t=1/3;(b)t=1/5;(c)t=1/10----------------------------------------------------------------------------22
4.4 實驗為平均移除時,不同條件下檢定的臨界值,(a)t=1/3;(b)t=1/5;(c)t=1/10------------------------------------------------------------------------------------23
4.5 實驗為第一階段移除時,不同條件下檢定的臨界值,(a)t=1/3;(b)t=1/5;(c)t=1/10--------------------------------------------------------------------------------24
4.6 實驗為最後階段移除時,不同條件下檢定的臨界值,(a)t=1/3;(b)t=1/5;(c)t=1/10--------------------------------------------------------------------------------25
4.7 m=3時,不同移除情況所需抽取的樣本數,group=1,2,3,4表示移除比例為(1,0,0),(0.5,1,0),(0,0.5,1),(0,0,1),(a)θa=1/10;(b) θa=1/2;(c) θa=2/3---26

表格目錄
4.1 n=4,m=2,p=(0.5,1),t=1/3,θa=1/10, a=0:05,β=0.1--------------------27
4.2 m=2,P=(0.5,1);m=3,P=(0.5,0.5,1);m=4,P=(0.5,0.5,0.5,1)---------------28
4.3 m=2,P=(1,0);m=3,P=(1,0,0);m=4,P=(1,0,0,0)---------------------------29
4.4 m=2,P=(0,1);m=3,P=(0,0,1);m=4,P=(0,0,0,1)---------------------------30
4.5 m=3,P=(0,0.5,1)-----------------------------------------------------31
4.6 m=3,P=(0.5,1,0)-----------------------------------------------------31

參考文獻 參考文獻

Aggarwala, R. (2001), Pregressive interval censoring: some mathematical results with applications to inference. Communications in Statistics - Theory Methods, 30, 1921-1935.

Balasooriya, U. and Saw, S.L.C. (1998), Reliability sampling plans for the two-parameter
exponential distribution under progressive censoring. Journal of Applied Statistics, 25, 707-714.

Balakrishnan, N. and Aggarwala, R. (2000), Progressive Censoring - Theory, Methods, and Applications. Boston: Birkhäuser.

Cohen, A.C. (1963), Pregressive censored samples in life testing. Technometrics, 5, 327-329.

Epstein, B. (1954), Truncated life tests in the exponential case. Annals of Mathematical
Statistics, 25, 555-564.

Kemp, C.D. and Kemp, W. (1987), Rapid generation of frequency tables. Applied
Statistics, 36, 277-282.

Kim, S.H. and Yum, B.J. (2000), Comparisons of exponential life test plans with intermittent inspections. Journal of Quality Technology, 32, 217-230.

Lindsey, J.C. and Ryan, L.M. (1985), Tutorial in biostatistics methods for interval-censored data. Statistics in Medicine, 17, 219-238.

Lui, K.J. Steffey, D. and Pugh, J.K. (1993), Sample size determination for grouped exponential observations: a cost function approach. Biometrical Journal, 35, 677-688.

Ng, H.K.T. Chan, P.S. and Balakrishnan, N. (2004), Optimal progressive censoring plans for the Weibull distribution. Technometrics, 46, 470-481.

Patel, M.N. and Gajjar, A.V. (1995), Some results on maximum likelihood estimators of parameters of exponential distribution under type I progressive censoring with changing failure rates. Communications in Statistics - Theory Methods, 24, 2421-2435.

Rao, M.B. (1998), Interval-censored type-II plan - a knell of the traditional type-II pkan?. In IISA International Conference 1998 Abstracts, McMaster University, p. 55.

Shapiro, S.S. and Gulati, S. (1996), Selecting failure monitoring times for an exponential life distribution. Journal of Quality Technology, 28, 429-438.

Sun, J. (1997), Regression analysis of interval-censored failure time data. Statistics in Medicine, 16, 497-504.
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2006-06-30公開。
  • 同意授權瀏覽/列印電子全文服務,於2006-06-30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 2281 或 來信