[Back to Results | New Search]

Student Number 982205005 Author WanJ-Jr Su(蘇岏智) Author's Email Address hellowpdd@hotmail.com Statistics This thesis had been viewed 546 times. Download 325 times. Department Graduate Institute of Statistics Year 2010 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Title The relibility analysis of series system with masked data dash generalized gamma distribution Date of Defense 2011-06-09 Page Count 61 Keyword bayesian factor DIC EM algorithm generalized gamma Markov chain Monte Carlo masked data Abstract In this thesis, we consider a system of independent and non-identical components connected in series, each component having a Weibull life time distribution under Type-I censored. In a series system, the system fails if any of the components fails, and it may only be ascertained that the cause of system failure is due to one of the components in some subset of system components, so called masked data. The maximum likelihood estimates via EM algorithm is developed for the model parameters with the aid of nonparametric bootstrap method to estimate the resulting standard errors of the MLE when the data are masked. Subjective Bayesian inference incorporated with the Markov chain Monte Carlo method is also addressed. Simulation study shows that the Bayesian analysis provides better results than the maximum likelihood approach not only in parameters estimation but also in reliability inference for both the system and components. We also discuss model fitting issue regarding the generalized gamma distribution and Weibull distribution via different model selection criteria. Table of Content 摘要i

Abstract ii

誌謝iii

目錄iv

圖目次vi

表目次vii

第一章緒論1

1.1 研究動機. . . . . . . . . . . . . . . . 1

1.2 研究背景. . . . . . . . . . . . . . . . 3

1.3 研究方法. . . . . . . . . . . . . . . . 4

第二章物件壽命具韋伯分配之串聯系統的壽命試驗6

2.1 模型介紹. . . . . . . . . . . . . . . . 6

2.2 最大概似估計. . . . . . . . . . . . . . 8

2.3 貝氏推論. . . . . . . . . . . . . . . . 13

第三章物件壽命具廣義伽瑪分配之串聯系統的壽命試驗20

3.1 模型介紹與最大概似估計. . . . . . . . . 20

3.2 概似比檢定. . . . . . . . . . . . . . . 23

3.3 貝氏推論. . . . . . . . . . . . . . . . 24

3.4 貝氏模型選擇. . . . . . . . . . . . . . 26

第四章數值分析與模擬研究29

4.1 壽命具韋伯分配之串聯系統模型. . . . . . 29

4.2 壽命具廣義伽瑪分配之串聯系統模型. . . . 33

4.3 模型選擇. . . . . . . . . . . . . . . . 36

第五章結論與展望49

參考文獻50Reference [1] Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Reliab. , 19, 716-723.

[2] Ashkar, F., Bobee, B., Leroux, D. and Morisette. D. (1988). The generalized method of moments as applied to the generalized gamma distribution. Stochastic Hydrology and Hydraulics, 2, 161-174.

[3] Basu S., Basu, A. P., and Mukhopadhyay, C. (1999). Bayesian analysis for masked system failure data using nonidentical weibull models. J. Statist. Plann. Inference, 78, 255–275.

[4] Basu, S., Sen, A. and Banerjee, M. (2003). Bayesian analysis of competing risks with partially masked cause of failure. Appl. Statist., 52, 77–93.

[5] Berger, J. O. and Sun, D. (1993). Bayesian analysis for the Poly-Weibull distribution. J. Amer. Statist. Assoc., 88, 1412–1418.

[6] Cox, C., Chu H., Schneider, M. F. and Munoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in medicine, 26, 4352-4374.

[7] Edwin, M. M., Heleno, B. and Gilberto, A. P. (2003). Influence diagnostics in generalized log-gamma regression models. Computational Statistics and Data Analysis, 42, 165-186.

[8] Edwin, M. M., Vicente, G. and Gilberto, A. (2009). Generalized log-gamma regression models with cure fraction. Lifetime Data Analysis, 15, 79-106.

[9] Efron, B. (1979). Bootstrap method:another look at the jacknife. Annals of Statist., 17, 1–26.

[10] Gomes, O., Combesv, C. and Dussauchoy, A. (2008). Parameter estimation of the generalized gamma distribution. Mathematics and Computers in Simulation, 79, 955-963.

[11] Guttman, I., Lin, D. K. J., Reiser, B. and Usher, J. S. (1995). Dependent Masking and System Life Data Analysis: Bayesian Inference for Two-Component Systems. Lifetime Data Analysis, 1, 87-100.

[12] Jan, M. and Van Noortwijk. (2004). Bayes Estimates of Flood Quantiles using the Generalised Gamma Distribution . System and Bayesian Reliability, 351-374.

[13] Lawless, J. F. (1980). Inference in the Generalized Gamma and Log Gamma Distributions. American Statistical Association and American Society for Quality., 22,409-419.

[14] Lin, D. K. J., Usher, J. S. and Guess, F. M. (1996). Bayes estimation of componentreliability from masked system-life data. IEEE Trans. Reliab., 45, 233–237.

[15] Matz, H. F. and Waller, R. A. (1982), Bayesian Relibility Analysis. New York: John Wiley.

[16] Miyakawa, M. (1984). Analysis of incomplete data in competing risks model. IEEE Trans. Reliab., 33, 293–296.

[17] Mukhopadhyay, C. and Basu, A. P. (1993). Bayesian analysis of competing risks: k independent exponentials. Technical report No.516, Department of Statistics, The Ohio

State University.

[18] Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference with the

weighted likelihood bootstrap. Journal of the Royal Statistical Society Series., 56, 3-48.

[19] Pascoa, M. A. R., Ortega, E. M. M.,Cordeiro, G. M. and Paranaiba, P. F.(2011). The Kumaraswamy generalized gamma distribution with application in survival analysis.

Available online 13 April 2011.

[20] Reiser, B., Guttman, I., Lin, D. K. J., Usher, J. S. and Guess, F. M. (1995). Bayesian inference for masked system lifetime data. Appl. Statist., 44, 79–90.

[21] Saralees, N. and Gupta. A. K. (2007). A generalized gamma distribution with application to drought data. Mathematics and Computers in Simulation, 74, 1-7.

[22] Sarhan, A. M. (2001). Reliability estimation of components from masked system life data. Reliability Engineering and System Safety, 74, 107–113.

[23] Sathit, I. and Nopparat S. (2009). Speckle Filtering by Generalized Gamma Distribution. NCM '09 Proceedings of the 2009 Fifth International Joint Conference on INC, IMS and IDC., 1335-1338.

[24] Spiegelhalter, D. J. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B, 64, 583V639.

[25] Stacy, E. W. (1963). A Generalization of the Gamma Distribution. Ann. Math. Statist., 33, 1187-1192.

[26] Usher, J. S. and Hodgson, T. J. (1988). Maximum likelihood analysis of component reliability using masked system life-test data. IEEE Trans. Reliab., 37, 550–555.

[27] Xie X. and Liu. X. (2009). Analytical three-moment autoconversion parameterization based on generalized gamma distribution. JOURNAL OF GEOPHYSICAL RE-SEARCH, 114, D17201, doi:10.1029/2008JD011633.Advisor Tsai-hung Fan(樊采虹)

Files approve immediately

982205005.pdf Date of Submission 2011-07-15

Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.