Inference for a simple step-stress model with type-I hybrid censored data from the weibull distribution

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Title:	Inference for a simple step-stress model with type-I hybrid censored data from the weibull distribution
Other Titles:	韋伯型I混合設限資料之加速壽命試驗的推論
Authors:	洪紹媛;Hung, Shao-Yuan
Contributors:	淡江大學數學學系碩士班林千代
Keywords:	加速壽命試驗;累積暴露模型;混合設限;Accelerated life test;Cumulative exposure model;Hybrid Censoring
Date:	2013
Issue Date:	2014-01-23 13:49:25 (UTC+8)
Abstract:	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。 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.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Thesis

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