加速不變原則之偏斜-t過程;Skew-t Processes Based on the Acceleration Invariance Principle

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/86318

Title:	加速不變原則之偏斜-t過程;Skew-t Processes Based on the Acceleration Invariance Principle
Authors:	黃鴻緒;Huang, Hung-Hsu
Contributors:	統計研究所
Keywords:	拔靴法;共軛分布;逆高斯分布;積分方程式;隨機效應;bootstrap;conjugate distribution;inverse Gaussian distribution;integral equation;random effects
Date:	2021-08-10
Issue Date:	2021-12-07 12:31:39 (UTC+8)
Publisher:	國立中央大學
Abstract:	衰變試驗常用於推論高可靠度產品之壽命資訊，其中隨機過程因具有物理/化學的機制及工程上的解釋，從而廣泛地使用在衰變模型的建構上。本研究提出一非線性偏斜-t過程，可描述產品間變異、量測誤差、偏斜及厚尾特徵之衰變路徑，將文獻上常見的維納、偏斜維納及學生-t等過程涵蓋為特例。本文詳細探討此過程首次通過門檻值之產品壽命分布，並提供計算其機率密度函數之演算法的收斂性。在線性偏斜-t過程假設下，可推導出產品壽命之機率密度函數、累積分布函數與平均失效時間的解析式。除此之外，藉由加速不變原則理論分析所提過程之加速衰變模型中，加速變數與模型參數之間的關聯性。進而論敘此加速衰變模型之可辨別性，並提供參數估計之演算法。最後輔以兩組實際例子驗證所提模型之可行性。;Degradation tests are often used to assess the lifetime of highly reliable products. Stochastic processes are widely used in the construction of degradation models due to the physical/chemical mechanisms and engineering interpretation. This research proposes a non-linear skew-t process, including Wiener, skew-Wiener and Student-t processes as special cases, under consideration for modelling the between-unit variability, measurement errors, skewed and heavy-tailed degradation paths. The first-passage-time distribution of the skew-t degradation-based process is discussed in detail, along with the convergence of an algorithm for calculating its density function. Under the assumption of linear skew-t process, the product′s lifetime probability density function, cumulative distribution function and mean-time-to-failure are derived in closed forms. In addition, the relationship between the accelerated variables and model parameters of the accelerated degradation model is obtained by using the acceleration invariance principle. The identifiability of the accelerated degradation model is investigated and two EM-type algorithms are proposed for the parameter estimation. Finally, the proposed accelerated degradation model is verified by two real datasets.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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