跳到主要內容

臺灣博碩士論文加值系統

(35.175.191.36) 您好!臺灣時間:2021/07/30 19:56
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:蘇翠淑
研究生(外文):Tsui-Shu Su
論文名稱:EstimatingLifetimeDistributionandItsParametersBasedonIntermediateDatafromaWienerDegradationModel
論文名稱(外文):Estimating Lifetime Distribution and Its Parameters Based on Intermediate Data from a Wiener Degradation Model
指導教授:唐正
指導教授(外文):Jen Tang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:49
中文關鍵詞:Accelerated life testWiener processDegradation dataLifetime distributionMaximum likelihood estimatorUniformly minimum variance unbiased estimatorGoodness-of-fit testInverse Gaussian distribution
相關次數:
  • 被引用被引用:0
  • 點閱點閱:120
  • 評分評分:
  • 下載下載:5
  • 收藏至我的研究室書目清單書目收藏:0
Due to technological advance and high expectation from consumers, many products are now expected to function for a long time before failure. However, during design and manufacturing stages, managers and engineers need failure data much sooner to estimate the lifetime distributions of their products. Accelerated life testing and step-stress life testing, where products are subject to higher-than-normal stresses to accelerate their failures, are standard methods of obtaining timely failure data. In a different approach, one will study the degradation/accumulated decay of a quality characteristic (QC) in case where the product will fail when its QC’s sample degradation path first passes the failure threshold. One advantage is that, if one can model the degradation sample path by, for example, a stochastic process, then it is possible to predict/estimate the lifetime without testing till failure of the product. When assuming a Wiener process with a constant or linear failure threshold, the lifetime distribution is an inverse Gaussian distribution and estimation procedures based on failure data are available. However, since we have a time-continuous degradation process, it is possible to obtain intermediate data before product’s failure and these data may be useful for lifetime estimation and model verification. In this paper, we first propose a simple way of obtaining intermediate data, which are basically boundary-crossing times of the degradation process but over certain boundaries before failure and hence are not actual failure times. Then we obtain various estimators of the lifetime distribution and its parameters based on these intermediate data, with or without the actual failure data. The results for cases without failure data are particularly useful for products that are highly reliable since lifetime could be too long or costly to obtain. In addition to the standard maximum likelihood estimators, we also obtain the uniformly minimum variance unbiased (UMVU) estimators, or mixtures of the two, for various quantities of interest. An example of an electronic product, namely the contact image scanner (CIS), is used to illustrate the proposed method.
1.Introduction 1
2.The Degradation Model and Lifetime Distribution 7
3.The Proposed Sampling Scheme and Intermediate Data 10
4.MLEs and UMVUEs of the Mean and Variance of Lifetime Distribution Based on Intermediate Data 13
4.1.MLE and UMVUE of mu and 1/lambda 13
4.2.MLE and UMVUE of the Variance of the Lifetime Distribution 15
5.Inference on the Lifetime Distribution and Its Percentiles 18
5.1.MLE and Modified MLE of F(t) 18
5.2.An Alternative Estimator of F(t) With Only Intermediate Data 19
5.3.Approximate Confidence Intervals for F(t) and Its Percentiles 22
6.Goodness-of-Fit Test of the Inverse Gaussian Distribution 25
7.An Example and Comparisons 28

8.Conclusions 32
References 34
Appendices A-C 37
[1] W. R. Blischke, and D. N. P. Murthy, Reliability: Modeling, prediction, and optimization, Wiley, New York, 2000.

[2] R. S. Chhikara and L. Folks, Statistical distribution related to the inverse Gaussian, Communication in statistics, 4(12), (1975), 1081-1091.

[3] R. S. Chhikara and L. Folks, The inverse Gaussian distribution: Theory, methodology, and applications, Marcel Dekker, New York, 1989.

[4] K. A. Doksum and A. Hoyland, Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution, Technometrics, 34(1), (1992), 74-82.

[5] K. A. Doksum and S.-L. T. Normand, Gaussian models for degradation processes-Part I: Methods for the analysis of biomarker data, Lifetime Data Analysis, 1 (1995), 131-144.

[6] G. J. Hahn, S. S. Shapiro, Statistical models in engineering, New York: John Wiley and Sons, 1967.

[7] K. Iwase and N. Seto, Uniformly minimum variance unbiased estimation for the inverse Gaussain distribution, Journal of the American Statistical Association, 78 (1983), 660-663.

[8] S. Karlin and H. M. Taylor, A second course in stochastic processes, Academic Press, New York, 1981.

[9] E. L. Lehmann, and G. Casella, Theory of point estimation, Springer-Verlag, New York, 1998.

[10] C. J. Lu, and W. Q. Meeker, Using degradation measures to estimate a time-to-failure distribution, Technometrics, 35 (1993), 161-174.

[11] J. C. Lu, J. Park, and Q. Yang, Statistical inference of a time-to-failure distribution derived from linear degradation data, Technometrics, 39 (1997), 391-400.

[12] Y. L. Luke, The special functions and their approximations, vol. 1, Academic Press, New York, 1969.

[13] W. Q. Meeker and L. A. Escobar, A review of recent research and current issues in accelerated testing, International Statistical Review, 61(1) (1993), 147-168.

[14] W. Q. Meeker and L. A. Escobar, Statistical methods for reliability data, John Wiley and Sons, New York, 1998.

[15] W.Q. Meeker, L. A. Escobar, and C. J. Lu, Accelerated degradation tests: Modeling and analysis, Technometrics, 40 (1998), 89-99.

[16] Nelson, W., Accelerated testing: Statistical models, test plans, and data analysis, Wiley, New York, 1990.

[17] R. J. Pavur, R. L. Edgeman and R. C. Scott, Quadratic statistics for the goodness-of-fit test of the inverse Gaussian distribution, IEEE Trans. on Reliab., R-41(1) (1992), 118-123.

[18] V. Seshadri, The inverse Gaussian distribution: Statistical theory and applications, Springer-Verlag, New York, 1999.

[19] N. D. Singpurwalla, Survival in dynamic environments, Statistical Science, 10 (1995), 86-103.

[20] C. Su, J. C. Lu, D. Chen and J. M. Hughes-Oliver, A random coefficient degradation model with random sample size, Lifetime Data Analysis, 5 (1999), 173-83.

[21] L. C. Tang and D. S. Chang, Reliability prediction using nondestructive accelerated degradation data, IEEE Trans. on Reliab., R-44 (1995), 562-566.

[22] S. T. Tseng, J. Tang, and I. H. Ku, Determination of optimal burn-in parameters and residual life for highly reliable products, Nav. Res. Logistics, 50 (2003), 1-14.

[23] S. T. Tseng and H.F. Yu, A termination rule for degradation experiment, IEEE Trans. Reliab., R-46(1) (1997), 130-133.

[24] M.C.K. Tweedie, Statistical properties of inverse Gaussian distributions I, Ann. Math Statist., 28 (1957), 362-377.

[25] G. A. Whitmore, and F. Schenkelberg, Modelling accelerated degradation data using Wiener diffusion with a time scale transformation, Lifetime Data Analysis, 3(1) (1997), 27-45.

[26] A. J. Wu, and J. Shao, Reliability analysis using the least squares method in nonlinear mixed-effect degradation models, Statistica Sinica, 9 (1999), 855-877.

[27] H. F. Yu and S. T. Tseng, Designing a degradation test, Nav. Res. Logistics, 46 (1999), 699-706.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top