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研究生：	尤家祥 Chia-hsiang Yu
論文名稱：	Missing information principle of the use-rate accelerated test for a series system under type-I censoring
指導教授：	樊采虹 Tsai-hung Fan
口試委員:
學位類別：	博士 Doctor
系所名稱：	理學院 - 統計研究所 Graduate Institute of Statistics
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	86
中文關鍵詞：	串聯系統、使用率、使用次數、遺失資訊法則
外文關鍵詞：	Multi-components series system, Use-rate, Cycles-to-failure, Missing information principle
相關次數：	點閱：9 下載：0
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查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

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。

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.

Introduction.............................................1
Maximum Likelihood Estimates for Censored Data...........5
1 The Likelihood Function of the Connected Group.........6
2 The Likelihood Function of the Not-Connected Group.....8
3 The Full Likelihood Function..........................10
4 The EM-Algorithm......................................11
5 The Information Matrix................................16
6 Reliability Inference.................................20
7 The Experimental Results..............................22
7.1 Simulation of censored data under theta_T=(5,2,4,3,0.8)'............................................23
7.2 Simulation of censored data under theta_T=(5,2,4,3,1)'..............................................29
7.3 Simulation of censored data under theta_T=(5,2,4,3,1.2)'............................................34
Maximum Likelihood Inference for Masked Data............39
1 Likelihood for Imputed Components in the Not-Connected Group.....................................................40
2 EM-algorithm in Masked Data...........................41
3 The Information Matrix in Masked Data.................43
4 The Experimental Results with Masked Data.............45
4.1 Simulation of masked data under theta_T=(5,2,4,3,0.8)'............................................45
4.2 Simulation of masked data under theta_T=(5,2,4,3,1)'..............................................50
4.3 Simulation of masked data under theta_T=(5,2,4,3,1.2)'............................................54
Identification of the Masking Component.................59
1 Support Vector Classification.........................59
2 Identification for the Masked Data Using SVM..........65
3 Using Maximum Probability as a Classifier.............66
4 Comparison............................................70
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
                                

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