在多組壽命試驗中，為了準確地估計模型的參數，我們必須找出最合適的實驗品數量，以分配給每一個應力水平。近來, Ng, Chan and Balakrishnan(2006)，在完整樣本情況下，利用「極值回歸模型」發展了找尋實驗品數量最合適的分配方法。其後，Ka, Chan, Ng and Balakrishnan (2011)在同一個回歸模型下，研究了對於「II型截尾樣本」最合適的分配方法。因為我們仍未確立對「I型截尾樣本」的最合適分配方法，所以我們將會在本篇論文中探討如何在「I型截尾壽命試驗」中找出最合適的實驗品分配方法。 / 在本論文中，我們會利用最大似然估計的方法去估計模型參數。我們也會計算出「逆費雪訊息矩陣」(「漸近方差協方差矩陣」)I⁻¹，用以量度參數估計值的準確度。以下是三個對最合適分配方法的決定準則: / 1.費雪訊息矩陣的行列式最大化, / 2. ν1估計值的方差最小化, var( ν1)(V -優化準則 ) / 3.漸近方差協方差矩陣的跡最小化, tr(⁻¹)(A-優化準則 ) / 我們也會討論在「極值回歸模型」的特例：「指數回歸模型」之下最合適的分配方法。 / In multi-group life-testing experiment, it is essential to optimize the allocation of the items under test to dierent stress levels in order to estimate the model parameter accurately. Recently Ng, Chan and Balakrishnan(2006) developed the optimal allocation for complete sample case with extreme value regression model, and Ka, Chan, Ng and Balakrishnan (2011) discussed about the optimal allocation for Type -II censoring cases with the same model. The optimal allocation for Type-I censoring scheme has not been established, so in this thesis, we are going to investigate the optimal allocation if Type-I censoring scheme is adopted in life-testing experiment. / Maximum likelihood estimation method will be adopted in this thesis for estimating model parameter. The inverted Fisher information matrix (asymptotic variance -covariance matrix),I⁻¹ , will be derived and used to measure the accuracy of the estimated parameters. The optimal allocation will be determined based on three optimal criteria: / 1. Maximizing the determinant of the expected Fisher Information matrix, / 2. Minimizing the variance of the estimator of ν1, var( ν1) (V -optimality ) / 3. Minimizing the trace of the variance-covariance matrix, tr(I⁻¹) (A-optimality ) / Optimal allocation under the exponential regression model,which is a spe¬cial case of extreme value regression model, will also be discussed. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / So, Hon Yiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 46-48). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.i / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Accelerated Life Test --- p.1 / Chapter 1.2 --- Life-Stress Relationship --- p.1 / Chapter 1.3 --- Type I Censoring --- p.3 / Chapter 1.4 --- Optimal Allocation --- p.3 / Chapter 1.5 --- The Scope of the Thesis --- p.4 / Chapter 2 --- Extreme Value Regression Model --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Model and Maximum Likelihood Estimation --- p.5 / Chapter 2.3 --- Expected Fisher Information --- p.8 / Chapter 3 --- Criteria for Optimization and the Optimal Allocation --- p.12 / Chapter 3.1 --- Introduction --- p.12 / Chapter 3.2 --- Criteria for Optimization --- p.12 / Chapter 3.3 --- Numerical Illustrations and the Optimal Allocation --- p.14 / Chapter 4 --- Sensitivity Analysis --- p.17 / Chapter 4.1 --- Introduction --- p.17 / Chapter 4.2 --- Sensitivity Analysis --- p.17 / Chapter 4.3 --- Numerical Illustrations --- p.19 / Chapter 4.3.1 --- Illustration with McCool (1980) Data --- p.19 / Chapter 4.3.2 --- Further Study --- p.21 / Chapter 5 --- Exponential Regression Estimation --- p.26 / Chapter 5.1 --- Introduction --- p.26 / Chapter 5.2 --- The Model and the Likelihood Inference --- p.27 / Chapter 5.3 --- Optimal Sample Size Allocation for Estimation of Model Pa- rameters --- p.30 / Chapter 5.4 --- Numerical Illustration --- p.33 / Chapter 5.5 --- Sensitivity Analysis --- p.35 / Chapter 5.5.1 --- Parameter Misspeci cation --- p.35 / Chapter 5.5.2 --- Censoring Time --- p.38 / Chapter 5.5.3 --- Further Study --- p.40 / Chapter 6 --- Conclusion and Further Research --- p.44
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328547 |
| Date | January 2012 |
| Contributors | So, Hon Yiu., Chinese University of Hong Kong Graduate School. Division of Risk Management Science. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource ([2], vi, 48 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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