穩定過程之衰變分析;Stable Processes for Degradation Analysis

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题名:	穩定過程之衰變分析;Stable Processes for Degradation Analysis
作者:	林祐頡;Lin, Yu-Chieh
贡献者:	統計研究所
关键词:	Birnbaum-Saunders分配;首次通過門檻值之時間點;非奇異第二型渥爾特拉積分方程式;厚尾特徵;學生-t 過程;Birnbaum-Saunders distribution;first passage time;heavy-tail;non-singular second-kind Volterra integral equation;Student’s t process
日期:	2020-08-11
上传时间:	2020-09-02 17:04:12 (UTC+8)
出版者:	國立中央大學
摘要:	對於高可靠度產品的壽命推論, 衰變分析已成為建立統計模型之最有效和最重要的技術。隨機過程則廣泛應用於衰變資料之分析, 然而對於具有厚尾特徵的衰變路徑, 文獻上則是付之闕如。本文提出涵蓋常見的維納與柯西過程為特例的非線性穩定過程, 配適具厚尾性質之衰變資料, 建立具有隨機效應之(加速) 衰變模型, 以評估產品壽命分配之相關資訊。關於首次通過門檻值之時間分配(即壽命分配) 的估計, 則以兩近似公式為猜想, 並與以模擬為驗證基礎的產品壽命分配做比較。佐以三組實例分析呈現產品壽命的百分位數估計、相對應的逐點拔靴法信賴區間及模型的適合度檢定等。;Degradation analysis has become the most effective and important technique for establishing statistical models to draw lifetime inference of highly reliable products. Stochastic processes are widely used to analyze degradation tests data. However, there is relatively few literature on degradation paths with heavy-tailed characteristics. This thesis proposes a non-linear stable process, which not only has heavy-tail but also covers the common Wiener and Cauchy processes as special cases, to establish degradation model with possibly random effects to assess the information of product’s lifetime distribution. Two conjecturable formulas are used to approximate the distribution function of the first passage time (product’s lifetime) which are also compared with the estimated life time distribution based on Monte-Carlo simulation. The proposed model is applied to three real datasets in which the estimation of the quantiles of the products lifetime distribution along with the corresponding pointwise bootstrap confidence intervals and the goodnessof-fit tests are demonstrated.
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