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系統識別號 U0002-2106200713534400
中文論文名稱 基於貝氏方法在逐步型二設限下對韋伯壽命分配的允收抽樣計畫
英文論文名稱 Acceptance Sampling Plans under Progressive Type-II Censoring for the Weibull Lifetime Distribution Based on Bayesian Method
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 黃思縈
研究生英文姓名 Szu-Ying Huang
電子信箱 starryheavens.tw@yahoo.com.tw
學號 694460014
學位類別 碩士
語文別 英文
口試日期 2007-06-05
論文頁數 32頁
口試委員 指導教授-蔡宗儒
委員-吳碩傑
委員-侯家鼎
中文關鍵字 逆伽瑪分配  壽命檢驗計畫  損失函數  先驗分配  逐步型二設限檢驗 
英文關鍵字 Inverted gamma distribution  Life test plan,  Loss function  Prior distribution  Progressively Type-II censored test 
學科別分類 學科別自然科學統計
中文摘要 本論文以逐步型二設限在韋伯壽命分配下,引用貝氏決策理論建立允收抽樣計畫。假設韋伯分配的形狀參數已知,但尺度參數是隨機的且依照一個已知的先驗分配逐批變動,本論文使用一個包含抽樣成本、檢驗成本以及決策損失的損失函數來描述貝氏風險。此外,本文也提出一個能找出最小化每單位平均成本的最佳貝氏允收抽樣計畫程序,並根據此程序對批量大小、設限計畫表和先驗分配的參數做敏感度分析,進而衡量其影響。
英文摘要 The thesis employs Bayesian decision theory to establish acceptance sampling plans for the Weibull lifetime distribution based upon progressively Type-II censored data. Assume that the shape parameter of the lifetime distribution is known, but the scale parameter is random and varies from lot to lot according to a predetermined prior distribution. A loss function involving sampling cost, test cost and decision loss is proposed to describe the Bayes risk. Moreover, an algorithm is suggested to determine the optimal sampling plans which minimize the expected average cost per lot. A sensitivity analysis study is conducted to evaluate the influences of the lot size, the censoring scheme and the parameter of the prior distribution on the proposed sampling plans.
論文目次 1. Introduction -1-
2. Acceptance Sampling Plans with Progressive Type-II Censoring -6-
3. Numerical Study and Sensitivity Analysis -15-
4. Conclusions -27-
Bibliography -30-

list of figures
2.1 Flowchart of finding the optional sampling plans 14
3.1 The ECPI for different lot sizes with the Schemes I,II
and III for B=0.8, a=4.0,b=1.8 24
3.2 The ECPI v.s. the Schemes I, II and III for different values of a when N=800, B=0.8 and b=1.8 25
3.3 The ECPI v.s. the Schemes I, II and III for different values of b when N=800, B=0.8 and a=4 26

list of tables
3.1 Optional sampling plans for B=0.8, a=4.0, b=1.8, r=0.7, cs=0.7, and ct=8 21
3.2 Sensitivity analysis for the sampling plan as the prior
parameter a changes 22
3.3 Sensitivity analysis for the sampling plan as the prior
parameter b changes 23

參考文獻 1. Aggarwala, R. (2001). Progressive interval censoring: some mathematical results with applications to inference. Communications in Statistics - Theory Methods, 30, 1921-1935.
2. Balakrishnan, N. and Aggarwala, R. (2000). Progressive Censoring - Theory, Methods, and Applications. Boston: Birkhauser.
3. Balakrishnan, N., Chandramouleeswaran, M. P. and Ambagaspitiya, R. S. (1996). BLUEs of location and scale parameters of Laplace distribution based on Type-II censored samples and associated inference. Microelectron reliability, 36, 371-374.
4. Cohen, A. C. (1963). Progressive censored samples in life testing. Technometrics, 5, 327-329.
5. Fertig, K. W. and Mann, N. R. (1974). A decision-theoretic approach to defining variables sampling plans for finite lots: single sampling for exponential and
Gaussian process. Journal of the American Statistical Association, 69, 665-671.
6. Fertig, K. W. and Mann, N. R. (1980). Life-test sampling plans for two-parameter Weibull population. Technometrics, 22, 165-177.
7. Harter, H. L. and Moore, A. H. (1976). An evaluation of exponential and Weibull test plans. IEEE Transactions on Reliability, R-25, 100-104.
8. Lam, Y. (1988a). A decision theory approach to variable sampling plans. Scienta Sinica Ser. A 31, 129-140.
9. Lam, Y. (1988b). Bayesian approach to single variable sampling plans. Biometrika, 75, 387-391.
10. Ng, H. K. T., Chan, P. S. and Balakrishnan, N. (2004). Optimal progressive
censoring plans for the Weibull distribution. Technometrics, 46, 470-481.
11. Nigm, A. M. and Ismail, M. A. (1985). Bayesian life test sampling plans for the two parameter exponential distribution. Communications in Statistics -Simulation and Computation, 14, 691-707.
12. Soland, R. M. (1968). Bayesian analysis of the Weibull process with unknown scale parameter and its application to acceptance sampling. IEEE Transactions on
Reliability, 17, 84-90.
13. Thyregod, P. (1975). Bayesian single sampling plans for life testing with truncation of the number of failures. Scandinavian Journal of Statistics, 2, 61-70.
14. TR-3 (1961). Sampling Procedures and Tables for Life and Reliability Testing Based on Weibull Distribution (Mean Life Criterion), US Department of
Defense, Washington, D.C.
15. TR-4 (1962). Sampling Procedures and Tables for Life and Reliability Testing Based on Weibull Distribution (Hazard Rate Criterion), US Department of Defense, Washington, D.C.
16. TR-6 (1963). Sampling Procedures and Tables for Life and Reliability Testing Based on Weibull Distribution (Reliable Life Criterion), US Department of Defense, Washington, D.C.
17. Tse, S. -K. and Yuen, H. -K. (1998). Expected experiment times for the Weibull distribution under progressive censoring with random removals. Journal of Applied Statistics, 25, 75-83.
18. Wetherill, G. B. and Kollerstom, J. (1979). A review of acceptance sampling schemes with emphasis on the economic aspect. International Statistical Review, 43, 191-210.
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