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 U0002-0607200714430200
中文論文名稱 逐步型一區間設限下的最佳設計與允收抽樣計畫
英文論文名稱 Optimal Design and Acceptance Sampling Plan 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 95
學期 2
出版年 96
研究生中文姓名 黃炫融
研究生英文姓名 Syuan-Rong Huang
學號 694460311
學位類別 碩士
語文別 中文
口試日期 2007-06-22
論文頁數 41頁
口試委員 指導教授-吳碩傑
委員-蔡宗儒
委員-陳麗霞
中文關鍵字 預算  最小化成本  指數分配  最大概似法  敏感度分析;變異數最佳化 
英文關鍵字 Budget  Cost minimization  Exponential distribution  Maximum likelihood method  Sensitivity analysis  Variance optimality 
學科別分類 學科別自然科學統計
中文摘要 一般傳統的設限試驗都是在實驗最後才能移除存活元件,然而在實務上,我們有時需要在實驗進行中提早移除部份存活元件,此類型的試驗稱之為逐步設限。除此之外,因為成本或實驗操作上的限制,某些壽命試驗只能在固定時點觀察元件故障與否,以此方式所收集到的資料稱為分群資料。本篇論文我們將逐步型一設限與分群資料結合,
以逐步型一區間設限方法收集指數壽命分配下元件的壽命資料做相關的參數估計,並討論以下兩個主題:

在可靠度的壽命試驗中,收集越多關於產品的資訊對我們評估產品可靠度越有幫助。然而,為了得到更多關於產品的壽命資訊,往往需要增加實驗成本,而實驗成本常會影響整個實驗的規模。為了同時兼顧評估產品可靠度的精確度與實驗成本的大小,我們給定實驗成本與實驗預算限制,以非線性混合整數規劃方法,找出使得最大概似估計量的漸近變異數最小且不超過實驗預算限制的實驗配置,並舉例做敏感度分析。

抽樣檢查是品質管制問題中主要研究的議題,如何決定壽命實驗的配置與允收臨界值將會影響整個抽樣實驗的結果,我們將在給定生產者風險與消費者風險下,建立一允收抽樣計畫使得整個實驗總成本小,並做數值的模擬分析與討論。
英文摘要 In traditional censoring schemes, surviving units can only be removed at the end of the life tests. However, in some practical situations, one has to remove surviving units at the points other than the final termination point. A life test of this type is called progressive censoring. Besides, in some life tests, we can only record whether a test unit fails in an interval instead of measuring failure time exactly. Hence, the test units are inspected intermittently. This type of inspection is called interval censoring. In this thesis, we combine progressive censoring and interval censoring to develop a progressive type-I interval-censoring scheme. We will focus on two designing problems of progressive type-I interval-censoring life test with exponential failure time distribution.

The first problem is how to design an appropriate life test that would result in the optimal estimation of the mean life. Simply put, more test units, more test time, and more number of inspections will generate more information, which improves the precision of estimates. However, one practical problem arising from designing a life test is the restricted budget of experiment. The size of budget always affects the decisions of number of test units, number of inspections and length of inspection intervals and hence, affects the precision of estimation. In this study, we will use the nonlinear mixed integer programming to obtain the optimal settings of a progressive type-I interval-censored life test by minimizing the asymptotic variance of mean life under the constraint that the total experimental cost does not exceed a pre-determined budget. An example is discussed to illustrate the proposed method and sensitivity analysis is also studied.

The second problem is to establish the acceptance sampling plans with cost consideration. We will construct acceptance sampling plans which have the minimum experimental cost under given consumer's and producer's risks. Some numerical examples and studies are performed to illustrate the proposed approach.
論文目次 目錄
1 緒論...........................................................................................................................1
1.1 研究目的與動機..................................................................................................1
1.2 文獻探討..............................................................................................................4
1.3 本文架構............................................................................................................. 6
2 逐步型一區間設限........................................................................................................7
2.1 實驗方式............................................................................................................. 7
2.2 參數估計..............................................................................................................8
3 逐步型一區間設限在成本限制下的最佳設計..............................................................13
3.1 成本限制下的最佳設計................................................................................... 13
3.2 數值實例............................................................................................................15
3.3 敏感度分析........................................................................................................17
3.3.1 壽命分配參數對最佳解的影響...................................................................17
3.3.2 移除比例對最佳解的影響...........................................................................19
3.3.3 成本參數對最佳解的影響...........................................................................19
3.4 總實驗時間限制下的最佳設計........................................................................23
4 逐步型一區間設限在成本限制下的允收抽樣計畫 25
4.1 允收抽樣計畫....................................................................................................25
4.2 成本限制下的允收抽樣計畫..................................................................................27
4.3 數值分析............................................................................................................29
4.4 固定總實驗時間下的允收抽樣計畫........................................................................30
5 結論 ....................................................................................................................36
參考文獻 38

表格目錄
3.1 逐步型一區間設限樣本......................................................................................16
3.2 不同的theta與p下最佳的(n,k,tau)組合................................................................18
3.3 不同成本參數組合下的最佳(n,k,tau)設計,theta=4.9326與p=0.05.........................20
3.4 不同成本參數組合下的最佳(n,k,tau)設計,theta=4.9326與p=0.1..........................21
3.5 不同成本參數組合下的最佳(n,k,tau)設計,theta=4.9326與p=0.25.........................22
4.1 使總成本最小的允收臨界c值與實驗配置(n,k,tau),alpha=0.05,beta=0.05............31
4.2 使總成本最小的允收臨界c值與實驗配置(n,k,tau),alpha=0.05,beta=0.1..............32
4.3 使總成本最小的允收臨界c值與實驗配置(n,k,tau),alpha=0.1,beta=0.05..............33
4.4 使總成本最小的允收臨界c值與實驗配置(n,k,tau),alpha=0.1,beta=0.1................34

圖形目錄
2.1 逐步型一區間設限計畫........................................................................................8



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

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

Balakrishnan, N., Kannan, N., Lin, C. T. and Ng, H. K. T. (2003). Point and interval estimation for Gaussian distribution, based on progressively type-II censored samples, IEEE Transactions on Reliability, 52, 90-95.

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

Chang, Y.-C. (2003). Accelerated life test for Weibull grouped experiment: A cost function approach, Master thesis, Tamkang University, Department of Statistics (in Chinese).

Chen, J., Chou, W., Wu, H. and Zhou, H. (2004). Designing acceptance sampling schemes for life testing with mixed censoring, Naval Research Logistics, 51, 597-612.

Chen, J., Li, K. H. and Lam, Y. (2007). Bayesian signal and double variable sampling plans for the Weibull distribution with censoring, European Journal of Operational Research, 177, 1062-1073.

Chung, S. W. and Seo, Y. S. (2006). Acceptance sampling plans based on failure-censored step-stress accelerated tests for Weibull distribtution, Journal of Quality in Maintenance Engineering, 12, 373-396.

Fernández, A. J. (2005). Progressive censored variables sampling plans for two-parameter exponential distribution, Journal of Applied Statistics, 32, 823-829.

Fertig, K. W. and Mann, N. R. (1980). Life-test sampling plans for two-parameter Weibull population, Technometrics, 22, 165-177.

Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data, 2nd edition, New York: Wiley.

Liao, H.-C. (2000). Sample size determination for grouped Weibull experiment: A cost function approach, Master thesis, Tamkang University, Department of Statistics (in Chinese).

Lui, K. J., Steffey, D. and Pugh, J. K. (1993). Sample size determination for grouped exponential observation observation: A cost function approach, Biometrical Journal, 34, 667-688.

Montgomery, D. C. (2005). Introduction to Statistical Quality Control, 5th edition, New York: Wiley.

Schneider, H. (1989). Failure-censored variables-sampling plans for lognormal and Weibull distribution, Technometrics, 31, 199-206.

Soliman, A. A. (2005). Estimation of parameters of life from progressively censored data using Burr-XII model, IEEE Transactions on Reliability, 54, 34-42.

Tse, S. K. and Yang, C. (2003). Reliability sampling plans for the Weibull distribution under type II progressive censoring with binomial removals, Journal of Applied Statistics, 30, 709-718.

Tse, S. K., Yang, C. and Yuen, H. K. (2002a). Design and analysis of survival data under an integrated type-II interval censoring scheme, Journal of Biopharmaceutical Statistics, 12, 333-345.

Tse, S. K., Yung, H. K. and Yang, C. (2002b). Statistical analysis of exponential lifetimes under an integrated type-II interval censoring scheme, Journal of Statistical Computation and Simulation, 72, 461-471.

Wu, S.-J. (2003). Estimation for the two-parameter Pareto distribution under progressive censoring with uniform removals, Journal of Statistical Computation and Simulation, 73, 125-134.

Wu, S.-J., Lin, Y.-P. and Chen, Y.-J. (2006). Planning step-stress life test with progressively type I group-censored exponential data, Statistica Neerlandica, 60, 46-56.

Xiong, C. and Ming, J. (2004). Analysis of grouped and censored data from step-stress life test, IEEE Transactions on Reliability, 53, 22-28.
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2008-07-17公開。
  • 同意授權瀏覽/列印電子全文服務,於2008-03-24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