具韋伯壽命分佈之串聯系統在隱蔽資料加速壽命實驗下之可靠度分析

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姓名

彭冠榕(Kuan-Jung Peng) 查詢紙本館藏

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統計研究所

論文名稱

具韋伯壽命分佈之串聯系統在隱蔽資料加速壽命實驗下之可靠度分析
(Reliability Analysis of a Series System on Weibull Step-stress Accelerated Life Tests with Masked Data)

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摘要(中)

本文主要探討在物件壽命為韋伯分佈之串聯系統的可靠度分析。對高可靠度產品，時常無法在正常環境下蒐集足夠的資料，因此常採用設限階段應力加速實驗。而在串聯系統中，一般常常只觀察到系統失效的時間，至於真正造成系統失效的物件卻不得而知，只知道可能引起系統失效之物件集合，這樣的資料稱為隱蔽資料。一般常假設隱蔽的發生具對稱性假設，即系統產生隱蔽的機率與物件無關。本文將分別使用貝氏方法與最大概似法在串聯物件壽命具韋伯分佈且其尺度參數與應力具對數線性關係之階段加速實驗下，分別討論在對稱和非對稱線性隱蔽模型下之可靠度分析，其中貝氏方法將以馬可夫鏈蒙地卡羅演算法模擬後驗分佈及其推論，而最大概似法將使用期望值-最大化演算法求其參數之最大概似估計，並以有母數拔靴法估計其標準誤差。最後以模擬研究及闡述舉例來說明所提方法之可行性。

摘要(英)

In this thesis, reliability analysis of a series system consisting of J independent Weibull lifetime components is the main purpose. Due to high reliability product, we can not collect enough data under normal environment. A step-stress accelerated life test is employed for K-stage and M-stress variables under Type-I censoring scheme. In reality, not only the system lifetimes but also the sets containing the possible causes of failure are observed since the failure cause of the system may be lost. Such data are called masked. In general, the symmetry assumption for masking probabilities is assumed. We will consider the scale parameters of the Weibull lifetime distributions of the components is of a log-linear relationship with the stress variables. Bayesian approach via the Markov chain Monte Carlo procedure and the maximum likelihood approach with EM-algorithm and parametric bootstrap method are both developed for reliability analyses of the components as well as the system. Simulation studies and illustrative examples are presented.

關鍵字(中)

★ 加速壽命實驗
★ 期望值-最大化演算法
★ 馬可夫鏈蒙地卡羅
★ 隱蔽資料
★ 對稱性假設
★ 有母數拔靴法

關鍵字(英)

★ accelerated life testing
★ masked data
★ symmetry assumption
★ Markov chain Monte Carlo
★ EM-algorithm
★ parametric bootstrap method

論文目次

摘要 .....................i
Abstract .....................ii
誌謝 .....................iii
Table of Contents .....................v
List of Figures .....................vii
List of Tables .....................viii
1. Introduction .....................1
1.1 Motivation and Background .....................1
1.2 Proposed Methods .....................4
2. Bayesian Approach .....................7
2.1 Model Description and Notation .....................7
2.2 Posterior Inference with Symmetry Assumption .....................10
2.3 Posterior Inference without Symmetry Assumption .....................15
3. Maximum Likelihood Approach .....................19
3.1 MLE with Symmetry Assumption .....................19
3.2 Parametric Bootstrapping of the Standard Errors .....................20
3.3 ML Inference without Symmetry Assumption .....................23
4. Simulation Study .....................25
4.1 Simulation Study with Symmetry Assumption .....................25
4.2 Illustrative Example for ALT Model with Symmetry Assumption .....................31
4.3 Simulation Study without Symmetry Assumption .....................36
4.4 Illustrative Example for ALT Model without Symmetry Assumption .....................39
5. Concluding Remarks .....................43
Reference .....................44

參考文獻

[1] Bagdonavicius, V. and Nikulin, M.S. (2002). Accelerated Life Models: Modeling and Statistical Analysis. Boca Raton, FL: Chapman & Hall/CRC.
[2] Bai, D.S., Kim, M.S., and Lee, S.H. (1989). Optimum simple step-stress accelerated life tests with censoring. IEEE Transactions on Reliability, 38, 528-532.
[3] Balakrishnan, N. and Han, D. (2009). Optimal step-stress testing for progressively Type-I censored data from exponential distribution. Journal of Statistical Planning and Inference, 139, 1782-1798.
[4] Balakrishnan, N., Kundu, D., Ng, H.K.T., and Kannan, N. (2007). Point and interval estimation for a simple step-stress model with Type-II censoring. Journal of Quality Technology, 39, 35-47.
[5] Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag.
[6] Berger, J.O. and Sun, D. (1993). Bayesian analysis for the poly-Weibull distribution. Journal of the American Statistical Association, 88, 1412-1418.
[7] Chung, S.W. and Bai, D.S. (1993). Optimal designs of simple step-stress accelerated life tests for lognormal lifetime distributions. International Journal of Reliability, Quality and Safety Engineering., 5, 315-336.
[8] Dempster, A., Laird, N., and Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B, 39, 1-38.
[9] Efron, B. (1979). Bootstrap method: another look at the jacknife. Annals of Statistics, 17, 1-26.
[10] Escobar, L.A. and Meeker, W.Q. (2006). A review of accelerated test models. Statistical Science, 21, 552-577.
[11] Fan, T.H., Wang, W.L., and Balakrishnan, N. (2008). Exponential progressive stepstress life-testing with link function based on Box-Cox transformation. Journal of Statistical Planning and Inference, 138, 2340-2354.
[12] Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
[13] Guess, F.M., Usher, J.S., and Hodgson, T.J. (1991). Estimating system and component reliabilities under partial information on cause of failure. Journal of Statistical Planning and Inference, 29, 75-85.
[14] 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.
[15] Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
[16] Khamis, I.H. (1997). Optimum M-step, step-stress design with K stress variables. Communications in Statistics - Simulation and Computation, 26, 1301-1313.
[17] Khamis, I.H. and Higgins, J.J. (1996). Optimum 3-step step-stress tests. IEEE Transactions on Reliability, 45, 341-345.
[18] Kuo, L. and Yang, T. (2000). Bayesian reliability modeling for masked system lifetime data. Statistics and Probability Letters, 47, 229-241.
[19] Lin, D.K.J. and Guess, F.M. (1994). System life data analysis with dependent partial knowledge on the exact cause of system failure. Microelectronics and Reliability, 34, 535-544.
[20] Lin, D.K.J., Usher, J.S., and Guess, F.M. (1993). Exact maximum likelihood estimation using masked system data. IEEE Transactions on Reliability, 42, 631-635.
[21] Lin, D.K.J., Usher, J.S., and Guess, F.M. (1996). Bayes estimation of componentreliability from masked system-life data. IEEE Transactions on Reliability, 45, 233-237.
[22] Meeker, W.Q. and Escobar, L.A. (1998). Statistical Methods for Reliability Data.. New York: John Wiley & Sons.
[23] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1092.
[24] Miller, R. and Nelson, W.B. (1983). Optimum simple step-stress plans for accelerated life testing. IEEE Transactions on Reliability, 32, 59-65.
[25] Miyakawa, M. (1984). Analysis of incomplete data in competing risk model. IEEE Transactions on Reliability, 33, 293-296.
[26] Mukhopadhyay, C. (2006). Maximum likelihood analysis of masked series system lifetime data. Journal of Statistical Planning and Inference, 136, 803-838.
[27] Nelson, W. (1980). Accelerated life testing - step-stress model and data analysis. IEEE Transactions on Reliability, 29, 103-108.
[28] Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis. New York: John Wiley & Sons.
[29] Sarhan, A.M. (2001). Reliability estimations of components from masked system life data. Reliability Engineering and System Safety, 74, 107-113.
[30] Sarhan, A.M. (2003). Estimation of system components reliabilities using masked data. Applied Mathematics and Computation, 136, 79-92.
[31] Tanner, M.A., Wong, W.H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528-550.
[32] Teng, S.L. and Yeo, K.P. (2002). A least-squares approach to analyzing life-stress relationship in step-stress accelerated life tests. IEEE Transactions on Reliability, 51, 177-182.
[33] Usher, J.S. (1996).Weibull component reliability-prediction in the presence of masked data. IEEE Transactions on Reliability, 45, 229-232.
[34] Usher, J.S. and Hodgson, T.J. (1988). Maximum likelihood analysis of component reliability using masked system life-test data.. IEEE Transactions on Reliability, 37, 550-555.
[35] van Dorp, J.R. and Mazzuchi, T.A. (2004). A general Bayes exponential inference model for accelerated life testing. Journal of Statistical Planning and Inference, 119, 55-74.
[36] van Dorp, J.R., Mazzuchi, T.A., Fornell, G.E., and Pollock, L.R. (1996). A bayes approach to step-stress acclerated life testing. IEEE Transactions on Reliability, 45, 491-498.
[37] Wang, W. and Kececioglu, D.B. (2000). Fitting the Weibull log-linear model to accelerated life-test data. IEEE Transactions on Reliability, 49, 217-223.
[38] Watkins, A.J. (1994). Review: Likelihood method for fittingWeibull log-linear models to accelerated life-test data. IEEE Transactions on Reliability, 43, 361-365.
[39] Xiong, C. (1998). Inferences on a simple step-stress model with Type-II censored exponential data. IEEE Transactions on Reliability, 47, 142-146.
[40] Xiong, C. and Milliken, G.A (1999). Step-stress life testing with random stress-change times for exponential data. IEEE Transactions on Reliability, 48, 141-148.
[41] Zhao W, Elsayed E. (2005). A general accelerated life model for step-stress testing. IIE Transactions, 37, 1059-1069. 48

指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2010-7-2

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