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系統識別號 U0002-2907201301215300
中文論文名稱 韋伯型I混合設限資料之加速壽命試驗的推論
英文論文名稱 Inference for a Simple Step-Stress Model with Type-I Hybrid Censored Data from the Weibull Distribution
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 101
學期 2
出版年 102
研究生中文姓名 洪紹媛
研究生英文姓名 Shao-Yuan Hung
學號 600190242
學位類別 碩士
語文別 英文
口試日期 2013-07-04
論文頁數 22頁
口試委員 指導教授-林千代
委員-陳麗霞
委員-蔡志群
中文關鍵字 加速壽命試驗  累積暴露模型  混合設限 
英文關鍵字 Accelerated life test  Cumulative exposure model  Hybrid Censoring 
學科別分類 學科別自然科學數學
中文摘要 本論文首先討論簡單逐步應力加速壽命試驗在型I混合設限策略下韋伯分配參數的點估計與區間估計。 利用最大概似法與牛頓數值法,我們先求得模型中參數的最大概似估計值與其相對應之觀察的費雪情報矩陣。 之後,再用蒙地卡羅模擬的方法來計算參數估計值的平均偏差值與均方誤差值以評估參數估計值的精確程度。此外,所得的參數估計結果更進一步分別代入最大概似估計量之常態近似分配 、 概似比檢定法和兩種有母數拔靴反覆抽樣法以建構模型參數之信賴區間。 最後,在成本限制條件下,我們討論最佳化設計,亦即,最佳的樣本個數、失敗個數、以及逐步之檢測時間的配置,以使得在無加應力情況下所估計的第p個百分位數的一般訊息的測量值為最大。
英文摘要 The simple step-stress model with lifetimes being Weibull distributed under Type-I hybrid censoring, which provides a more flexible model than the exponential model, is considered in this thesis. For this model, the maximum likelihood estimates of its parameters, as well as the corresponding observed Fisher information matrix, are derived. We then evaluate the bias and mean square error of these estimates, and provide the confidence intervals for the parameters using asymptotic distributions, a likelihood ratio test, and two parametric bootstrap resampling methods. Finally, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal test plan for the estimated 100pth percentile at the use condition is determined.
論文目次 Contents
1 Introduction 1
2 Model Assumptions 3
3 Likelihood Estimation of Model Parameters 5
4 Estimations of Model Parameters 6
4.1 Asymptotic Confidence Interval . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.2 Likelihood Ratio-Based Confidence Interval . . . . . . . . . . . . . . . . . . . 7
4.3 Bootstrap Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.3.1 Bootstrap-t Confidence Interval . . . . . . . . . . . . . . . . . . . . . 9
4.3.2 Percentile Bootstrap Confidence Interval . . . . . . . . . . . . . . . . 9
4.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5 Optimal Test Plan 10
6 CONCLUDING REMARKS 16
Appendix 16
References 18

List of Tables
Table 1 Estimated biases, MSE, and coverage probabilities of 90% and 95% confidence intervals for n = 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Table 2 Estimated biases, MSE, and coverage probabilities of 90% and 95% confidence intervals for n = 100 and r = 80 . . . . . . . . . . . . . . . . . . . . . 12
Table 3 Information measure I(n, rn, τ1n, τ2n) for (n, rn, τ1n, τ2n) when 2 ≤ n ≤ ˜n 15
Table 4 Optimal test plans under various choices of the parameters ((1+ε1)β0, (1+ε2)β1, (1 + ε3)σ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

List of Figures
Figure 1 The relationship of I(no, ro, τ o1 , τ o2 ) with k when τ2 = kτ1. . . . . . . . . 15
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