伽馬過程之貝氏加速衰變試驗模型與序列分析

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陳稚蕙(Chih-Hui Chen) 查詢紙本館藏

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統計研究所

論文名稱

伽馬過程之貝氏加速衰變試驗模型與序列分析
(Bayesian Accelerated Degradation Models and Sequential Analysis based on Gamma Processes)

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至系統瀏覽論文 (2027-11-5以後開放)

摘要(中)

為了改善產品在正常的環境應力之下衰變速度過於緩慢的問題，可以將產品置於高應力環境下進行加速衰變試驗 (accelerated degradation test)，根據高應力下的衰變資料建構加速衰變模型進而推論產品壽命分布。由於產品之間可能存在些微差異，本文加入隨機效應 (random effect) 以描述產品間的個別差異，並使用貝氏方法分析伽馬隨機過程 (gamma process) 的加速衰變試驗。在模型選擇上，以偏差訊息量準則 (deviance information criterion; DIC) 選擇適當的模型，並藉由馬可夫鍊蒙地卡羅 (MCMC) 演算法得參數近似後驗樣本，從而推導出正常使用狀態下產品的貝氏可靠度推論。本文利用伽馬過程的加速衰變試驗結果作為產品在正常應力條件下的先驗資訊，並透過逐步預測探討正常應力下衰變模型分布改變時的貝氏逐步分析，並在滿足預設的容忍度時決定試驗終止時間。最後以三個實例和模擬資料驗證所提方法的可行性。

摘要(英)

To address the issue of product degradation being too slow under normal environmental stress, the product can be subjected to accelerated degradation tests under high-stress conditions. By constructing an accelerated degradation model based on the degradation data obtained under high-stress conditions, we can infer the product′s lifetime distribution. Considering potential differences between products, this thesis incorporates random effects into the model to describe the heterogeneity of products, and employs Bayesian methods to analyze the gamma process in accelerated degradation tests. For model selection, the deviance information criterion is used to choose an appropriate model, and the Markov Chain Monte Carlo (MCMC) algorithm is employed to obtain approximate posterior samples of the parameters. This allows for the derivation of Bayesian reliability inferences for the product under normal usage conditions.The thesis uses the results of the gamma process accelerated degradation tests as prior information for the product under normal stress conditions. It explores Bayesian sequential analysis when the degradation model distribution changes under normal stress conditions, to determine a the test termination time when a preset tolerance is met. Finally, the feasibility of proposed method is verified through three case studies as well as by simulated data.

關鍵字(中)

★ 伽馬隨機過程
★ 隨機效應
★ DIC 準則
★ 後驗預測 p-值
★ 階層貝氏

關鍵字(英)

★ Gamma process
★ random effect
★ DIC criterion
★ posterior predictive p-value
★ hierarchical Bayesian

論文目次

摘要 i
Abstract ii
目錄 iii
圖目錄 vi
表目錄 vii
第一章緒論 1
1.1研究背景與動機 1
1.2文獻回顧 3
1.3研究方法 5
1.4本文架構 6
第二章伽馬過程之貝氏加速衰變模型 7
2.1伽馬加速衰變模型與加速因子 7
2.1.1伽馬加速衰變模型 7
2.1.2加速應力結構 9
2.1.3加速模式 9
2.2概似函數 10
2.2.1符號定義 10
2.2.2固定效應模型 11
2.2.3隨機效應模型 11
2.3貝氏架構 14
2.3.1固定效應貝氏模型 15
2.3.2隨機效應貝氏模型 17
2.4模型選擇與診斷 21
2.4.1偏差訊息量準則 22
2.4.2貝氏適合度檢定 23
第三章貝氏可靠度推論與序列預測分析 25
3.1壽命分布 25
3.2平均失效時間及q-分位數 28
3.3壽命分布之Birnbaum-Saunders近似 30
3.4壽命分布之診斷 32
3.5序列預測分析 33
3.5.1先驗分布之序列更新 34
3.5.2序列預測之試驗終止時間 37
第四章實例與序列分析 38
4.1 LED資料-1 39
4.2 LED資料-2 44
4.3電器連接器資料 48
4.4模擬分析 52
4.4.1參數估計 52
4.4.2序列分析 55
第五章結論 58
參考文獻 59

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指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2024-11-28

推文