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 U0002-1706200500334200
中文論文名稱 在保證政策下當檢驗設備的個數受限時對韋伯壽命資料的貝氏抽樣計畫
英文論文名稱 Bayesian Sampling Plan for Weibull Lifetime Data under Warranty Policy with Limited Size on Test Equipment
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 93
學期 2
出版年 94
研究生中文姓名 呂玉婷
研究生英文姓名 Yu-Ting Lu
學號 692460511
學位類別 碩士
語文別 英文
口試日期 2005-05-27
論文頁數 31頁
口試委員 指導教授-蔡宗儒
委員-吳碩傑
委員-蘇聖珠
委員-蘇懿
委員-廖敏治
中文關鍵字 指數分配  先驗分配  驗收抽樣計劃  保證政策  韋伯分配 
英文關鍵字 Exponential distribution  Prior distribution  Sampling plan  Warranty policy  Weibull distribuion 
學科別分類 學科別自然科學統計
中文摘要 在本篇論文中,我們在形狀參數己知的韋伯壽命分配之下,根據不同的貨批大小去檢驗貝氏單次抽樣計畫。我們更進一步的假設尺度參數是隨機的,它是根據每批不同的先驗分配而有所變動。若產品是在保證政策下出售, 而且檢驗設備的個數受限時,考慮成本函數的模型包含檢驗成本, 接受成本和拒絕成本,本論文提出了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,並且根據此程序對產品壽命和先驗分配的參數做敏感度分析。
英文摘要 In this thesis, we examine a Bayesian single sampling plan for lot by lot sampling under Weibull lifetime istribution with known shape parameter; moreover it is assumed that the scale parameter is random and varies from lot to lot according to a predetermined prior distribution. If products are sold under a warranty policy and the size of test equipments is limited. A cost model is established which involves test cost, accept cost, and reject cost. An algorithm of finding the optimal sampling plans with minimizing the expected average cost per lot is provided, and sensitivity analyses for the parameters of the lifetime and prior distributions are conducted.
論文目次 Contents
1 Introduction 1
2 The Sampling Plan 6
3 Numerical Study and Sensitivity Analysis 16
4 Conclusions 27
Bibliography 28
List of Figures
1 Flowchart of finding the optimal sampling plans. . . . . . . . . . . . . . 15
2 Percentage errors in using incorrect values of β, a, and b when true
values are β = 0.8, a = 3, b=875 . . . . . . . . . . . . . . . . . . . . . 25
3 Percentage errors for different values of β, when true values are β = 0.6,
1.0, and 1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
List of Tables
1 Optimal Sampling Plan for β = 0.8, a = 3.0, b = 875, w1 = 180,
cs = 2.8, ct = 0.8, cp = 2.5 and ca = 9.5. . . . . . . . . . . . . . . . . . 19
2 Searching Procedures for the proposed sampling plan with β = 0.8,
a = 3.0, b = 875, w1 = 180, w2 = 360, cs = 2.8, ct = 0.8, cp = 2.5 and
ca = 9.5 under nL =70. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Optimal Sampling Plan for selected combinations of parameters β, a
and b under nL = 70 when N = 600. . . . . . . . . . . . . . . . . . . . 24

參考文獻 Aroian, L. A. (1964), Some comments on truncated sequential tests for the exponential distribution. Industrial Quality Control, 21, 309-312.
Balasooriya, U. (1995), Failure-censored reliability sampling plans for the exponential distribution. Journal of Statistical Computation and Simulation. 52 337-349.
Bulgren, W. and Hewette, J. (1973), Double sample test for hypotheses about the mean of an exponential distribution. Technometrics, 15, 187-190.
Calvin, T. W. (1983), How and When to Perform Bayesian Acceptance Sampling.The ASQC Basic References in Quality Control: Statistical Techniques. Volume7. Milwaukee, WI, American Society for Quality.
Epstein, B. (1954), Trucated life tests in the exponential case. Annals of Mathematical Statistics, 25, 555-564.
Epstein, B. and Sobel, M. (1955), Sequential life test in the exponential case. Annals of Mathematical Statistics, 26, 82-93.Bibliography 29
Fairbanks, K. (1988), A two stage life test for the exponential parameter. Technometrics,30, 175-180.
Fertig, K. W. and Mann, N. R. (1974). A decision-theoretic approach to defning variables sampling plans for finite lots: single sampling for exponential and Gaussian
process. Journal of the American Statistical Association, 69, 665-671.
Fertig, K. W. and Mann, N. R. (1980), Life-test sampling plans for two-parameter Weibull population. Technometrics, 22 165-177.
Harter, H. L. and Moore, A. H. (1976), An evaluation of exponential and Weibull test plans. IEEE Transactions on Reliability , 11-25, 100-104.
Hald, A., (1967). Asymptotic properties of Bayesian single sampling plans. Journal of the Royal Statistical Society, Series B, 29, 162-173.
Huang, W.-T., and Lin, Y.-P. (2002), Bayesian sampling plans for exponential distribution based on Type I censoring data. The Institute of Statistical Mathematics,
54, 100-113.
Huang, W.-T., and Lin, Y.-P. (2004), Bayesian sampling plans for exponential distribution based on uniform random censored data. Computational Statistics and Data Analysis, 44, 669-691.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994), Continuous Univariate Distributions,Volume 1, 2nd edition. John Wiley and Sons, New York.Bibliography 30
Kwon, Y. I. (1996), A Bayesian life test sampling plan for products withWeibull lifetime distribution sold under warranty. Reliability Engineering and System Safety, 53,
61-66.
Lam, Y. (1998a), A decision theory approach to variable sampling plans. Scienta Sinica Ser. A 31, 129-140.
Lam, Y. (1998b), Bayesian approach to single variable sampling plans. Biometrika, 75,387-391.
Lam, Y. and Lau, L. C. (1993), Optimal single variable sampling plans. Communications in statistics : Simulation and Computation, 22, 371-386.
Nelson, W. (1982), Applied Life Data Analysis. Wiley, New York Soland, R. M.(1968), Bayesian analysis of the Weibull process with unknown scale parameter and its application to acceptance sampling. IEEE Transactions on Reliability,
R-17, 84-90.
TR-3 (1961), Sampling Procedures and Tables for Life and Reliability Testing Basedon Weibull Distribution(Mean Life Criterion), US Department of Defense, Washington,D.C.,.
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.,.Bibliography 31
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.
Thyregod, P. (1975), Bayesian single sampling plans for life testing with truncation of the number of failures. Scandinavian Journal of Statistics, 2, 61-70.
Waller, R. A., Johnson, M. M., Waterman, M. S. and Martz, H. F.(1977), Gamma prior distribution selection for Bayesian analysis of failure rate and reliability. Nuclear
Systems Reliab. Engng and Risk Assessment, X, 584-606.
Wetherill, G. B. and K‥ollerstr‥om, J. (1979). A review of acceptance sampling schemes with emphasis on the economic aspect. International Statistics Review. 43, 191-
210.
Wetherill, G. B. and Chiu, W. K. (1975). Sampling inspection simplified. Journal of the Royal Statistical Society, Series A, 142, 1-32 (with discussion).
Wu, J. W. and Tsai, W. L. (2000), Failure-censored sampling plan for the Weibull population. Information and Management Sciences, 2, 13-25.

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2006-06-23公開。
  • 同意授權瀏覽/列印電子全文服務,於2005-06-23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