Missing information principle of the use-rate accelerated test for a series system under type-I censoring

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：34

、訪客IP：3.133.134.121

姓名

尤家祥(Chia-hsiang Yu) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Missing information principle of the use-rate accelerated test for a series system under type-I censoring)

相關論文

★ 具Box-Cox轉換之逐步加速壽命實驗的指數推論模型	★ 多元反應變數長期資料之多變量線性混合模型
★ 多重型 I 設限下串聯系統之可靠度分析與最佳化設計	★ 應用累積暴露模式至單調過程之加速衰變模型
★ 串聯系統加速壽命試驗之最佳樣本數配置	★ 破壞性加速衰變試驗之適合度檢定
★ 串聯系統加速壽命試驗之最佳妥協設計	★ 加速破壞性衰變模型之貝氏適合度檢定
★ 加速破壞性衰變模型之最佳實驗配置	★ 累積暴露模式之單調加速衰變試驗
★ 具ED過程之兩因子加速衰退試驗建模研究	★ 逆高斯過程之完整貝氏衰變分析
★ 加速不變原則之偏斜-t過程	★ 花蓮地區地震資料改變點之貝氏模型選擇
★ 颱風降雨量之統計迴歸預測	★ 花蓮地區地震資料之長時期相關性及時間-空間模型之可行性

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

在傳統的可靠度研究中常見的資料為測試物件的壽命或設限時
間。然而大部份的可靠度實驗並沒有考慮到現實生活中的某些變數，
例如系統使用率、系統負荷、使用環境溫度、溼度等條件。隨著科技
的進步，現今我們已可以在許多的產品上安裝感應元件或晶片，如此
我們將可輕易的收集到上述的變數資料。我們在這篇論文中主要考慮
串聯系統的實驗，若系統是有安裝感應元件或晶片則我們可以收集到
這些系統的使用次數和使用率等資訊；反之，若系統沒有安裝感應元
件或晶片，則我們只能觀測到系統的壽命。模型中的最大概似估計量
主要是透過最大期望演算法求得，再透過遺失資訊法則算出觀測資訊
矩陣進一步求得估計量其對應的標準差。透過上述的方法證明了我們
不僅可以得到較準確的估計結果而且比起一般的方法還節省了大量的
運算時間。

摘要(英)

In traditional reliability life test, usually the data are the failure (censored) times of the test units. However, most of the analyses do not consider the variabilities in the real life, such as the use-rate, load, temperature, humidity, etc. With new technology, we can install sensors or smart chips in many products so that the variabilities of
the above characteristics can be collected. In this thesis, we consider the life test of multi-components series systems, when the cycles-to-failure and use-rate information are available for those systems with censors (chips). On the other hand, only the times-to-failure can be collected from the systems without censors (chips). EM-algorithm is employed to obtain the MLEs along with their estimated standard errors computed based on the observed information matrix via the missing information principle. It turns out that the proposed method not only provides accurate results but also saves much computing time than the existing method.

關鍵字(中)

★ 串聯系統
★ 使用率
★ 使用次數
★ 遺失資訊法則

關鍵字(英)

★ Multi-components series system
★ Use-rate
★ Cycles-to-failure
★ Missing information principle

論文目次

1 Introduction.............................................1
2 Maximum Likelihood Estimates for Censored Data...........5
2.1 The Likelihood Function of the Connected Group.........6
2.2 The Likelihood Function of the Not-Connected Group.....8
2.3 The Full Likelihood Function..........................10
2.4 The EM-Algorithm......................................11
2.5 The Information Matrix................................16
2.6 Reliability Inference.................................20
2.7 The Experimental Results..............................22
2.7.1 Simulation of censored data under theta_T=(5,2,4,3,0.8)’............................................23
2.7.2 Simulation of censored data under theta_T=(5,2,4,3,1)’..............................................29
2.7.3 Simulation of censored data under theta_T=(5,2,4,3,1.2)’............................................34
3 Maximum Likelihood Inference for Masked Data............39
3.1 Likelihood for Imputed Components in the Not-Connected Group.....................................................40
3.2 EM-algorithm in Masked Data...........................41
3.3 The Information Matrix in Masked Data.................43
3.4 The Experimental Results with Masked Data.............45
3.4.1 Simulation of masked data under theta_T=(5,2,4,3,0.8)’............................................45
3.4.2 Simulation of masked data under theta_T=(5,2,4,3,1)’..............................................50
3.4.3 Simulation of masked data under theta_T=(5,2,4,3,1.2)’............................................54
4 Identification of the Masking Component.................59
4.1 Support Vector Classification.........................59
4.2 Identification for the Masked Data Using SVM..........65
4.3 Using Maximum Probability as a Classifier.............66
4.4 Comparison............................................70
5 Conclusions and Future Work.............................72
Bibliography..............................................74
Appendices................................................78
A. The Iterative Formulas in the EM-Algorithm for Unmasked Data......................................................78
B. Derivation of the Complete Information.................80
C. Derivation the Missing Information.....................81
D. Derivation the Missing Information in Masked Data......85

參考文獻

[1] Balakrishnan N. and Kateri M. (2008) "On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data". Statistics and Probability Letters, Vol. 78, pp. 2971-2975.
[2] Balakrishnan N. and Mitra D. (2011) "Likelihood inference for lognormal data with left truncation and right censoring with an illustration". Journal of Statistical Planning and Inference, Vol. 141, pp. 3536-3553.
[3] Boser B. E., Guyon I. M. and Vapnik V. (1992) "A training algorithm for optimal margin classifiers". In Proceedings of the Fifth Annual Workshop of Computational Learning Theory, Pittsburgh.
[4] Burges C. J. C. (1998) "A tutorial on support vector machines for pattern recognition". Data Mining and Knowledge Discovery, Vol 2, pp. 121-167.
[5] Chang C. C. and Lin C. J. (2011) "LIBSVM: a library for support vector machines". ACM Transactions on Intelligent Systems and Technology, Vol. 2, pp. 27:1-27:27.
[6] Cortes C. and Vapnik V. (1995) "Support-vector Networks". Machine Learning, Vol. 20, pp. 273-297.
[7] Cristianini N. and Taylor J. S. (2000) An introduction to support vector machines. Cambridge University Press, Cambridge, UK.
[8] Efron B. (1979) "Bootstrap method: another look at the jackknife". Annals of Statistics, Vol. 17, pp. 1-26.
[9] Fan T. H. and Hsu T. M. (2012) "Accelerated life tests of a series system with masked interval data under exponential lifetime distributions". IEEE Transactions on Reliability, Vol. 61, pp. 798-808.
[10] Fan T. H. and Wang W. L. (2011) "Accelerated life tests for Weibull series systems with masked data". IEEE Transactions on Reliability, Vol. 60, pp. 557-569.
[11] Friedman J. H. (1996) Another approach to polychotomous classification. Technical report, Stanford Department of Statistics. http://www-stat.stanford.edu/jhf/ftp/poly.ps.Z.
[12] 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, Vol. 29, pp. 75-85.
[13] Hong Y. and Meeker W. Q. (2010) "Field-failure and warranty prediction based on auxiliary use-rate information". Technometrics, Vol. 52, pp. 148-159.
[14] Huang C. M., Lee Y. J., Lin D. K. J. and Huang S. Y. (2007) "Model selection for support vector machine via uniform design". Computational Statistics and Data Analysis, Vol. 52, pp. 335-346.
[15] Kreßel U. (1999) "Pairwise classification and support vector machines". Advances in Kernel Methods - Support Vector Learning, Schölkopf B., Burges C. J. C. and Smola A. J., editors. pp. 255-268, Cambridge, MA, MIT Press.
[16] Knerr S., Personnaz L. and Dreyfus G. (1990) "Single-layer learning revisited: A stepwise procedure for building and training a neural network". Neurocomputing: Algorithms, Architectures and Applications, Fogelman-Soulie and Herault, editors. NATO ASI Series, Springer.
[17] Louis T. A. (1982) "Finding the observed information matrix when using the EM algorithm". Journal of the Royal Statistical Society, Series B, Vol. 44, pp. 226-233.
[18] Meeker W. Q. and Escobar L. A. (1998) Statistical methods for reliability data. New York: Wiley.
[19] Meeker W. Q., Escobar L. A. and Hong Y. (2009) "Using accelerated life test results to predict product field reliability". Technometrics, Vol. 51, pp. 146-161.
[20] Miyakawa M. (1984) "Analysis of incomplete data in competing risk model". IEEE Transactions on Reliability, Vol. R-33, pp. 293-296.
[21] Mukhopadhyay C. (2006) "Maximum likelihood analysis of masked series system lifetime data". Journal of Statistical Planning and Inference, Vol. 136, pp. 803-838.
[22] Newton M. A. and Raftery A. E. (1994) "Approximate bayesian inference with the weighted likelihood bootstrap". Journal of the Royal Statistical Society, Series B, Vol. 56, pp. 3-48.
[23] Ng H. K. T. and Wang Z. (2009) "Statistical estimation for the parameters of Weibull distribution based on progressively type-I interval censored sample". Journal of Statistical Computation and Simulation, Vol. 79, pp. 145-159.
[24] Ng H. K. T., Chan P. S. and Balakrishnan N. (2002) "Estimation of parameters from progressively censored data using EM algorithm". Computational Statistics and Data Analysis, Vol. 39, pp. 371-386.
[25] Pal M. (2005) "Multiclass approaches for support vector machine based land cover classification". Proceedings of the 8th Annual International Conference, Map India.
[26] Sarhan A. M. (2001) "Reliability estimations of components from masked system life data". Reliability Engineering and System Safety, Vol. 74, pp.107-113.
[27] Sarhan A. M. (2003) "Estimation of system components reliabilities using masked data". Applied Mathematics and Computation, Vol. 136, pp. 79-92.
[28] Stacy E. W. (1962) "A generalization of the gamma distribution". The Annals of Mathematical Statistics, Vol. 33, pp. 1187-1192.
[29] Usher J. S. (1996) "Weibull component reliability-prediction in the presence of masked data". IEEE Transactions on Reliability, Vol. 45, pp. 229-232.
[30] Usher J. S. and Hodgson T. J. (1988) "Maximum likelihood analysis of component reliability using masked system life-test data". IEEE Transactions on Reliability, Vol. 37, pp. 550-555.
[31] Vapnik V. (1998) Statistical learning theory. New York: Wiley.
[32] Yang G. (2007) Life cycle reliability engineering. New Jersey: Wiley.

指導教授

樊采虹(Tsai-hung Fan)

審核日期

2013-7-29

推文