累積暴露模式之單調加速衰變試驗;Monotonic Accelerated Degradation Tests With Cumulative Exposure Law

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/80921

Title:	累積暴露模式之單調加速衰變試驗;Monotonic Accelerated Degradation Tests With Cumulative Exposure Law
Authors:	董奕賢;Dong, Yi-Shian
Contributors:	統計研究所
Keywords:	Hougaard 過程;伽瑪過程;逆高斯過程;拔靴法;模型選擇;Hougaard process;gamma process;inverse Gaussian process;bootstrap;model selection
Date:	2019-06-25
Issue Date:	2019-09-03 15:16:03 (UTC+8)
Publisher:	國立中央大學
Abstract:	加速衰變試驗已廣泛應用於評估高可靠度產品在正常使用條件下的壽命資訊。然而在加速衰變模型與環境變數間的關聯性中，相關的物理化學機制及其統計意義卻較少被探討。因此本文以 Tweedie 過程作為加速衰變模型之基礎，結合物理/化學機制之累積暴露模式，從理論上得到模型中參數與環境變數的關聯性，並賦予其統計/工程意義；此外在加速因子不變原則下，藉由泛函等式推導出隨機過程中時間項函數之充分必要條件，提供非線性時間函數的物理意義。最後以三組實例分析呈現在不同參數與應力關係下，Tweedie 加速衰變模型的優點、壽命推估的精準性、相對應的逐點信賴區間及模型的適合性等。;Accelerated degradation tests (ADTs) are widely used to assess lifetime information under normal use condition for high-reliability products. However, the physical/chemical mechanism as well as the statistical/engineering interpretation between the ADT model with the environmental variables is rarely discussed. In this thesis, we consider the ADT models based on Tweedie process by adopting the assumption of cumulative exposure law, due to the physical/chemical mechanism, to derive the relationship between model parameters and environment variables.Moreover, from the functional equation with the assumption of acceleration factor constant principle, we also obtain the explicit functional form for the time structure of the stochastic process, which gives the physical interpretation of the non-linear function of time. Finally, three datasets are analyzed to show the advantages of the proposed degradation models and the accuracy of product’s lifetime inference, including pointwise confidence intervals and goodness-of-fit tests, under various relationships between model parameters and environment variables.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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