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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題名:	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
作者:	陳稚蕙;Chen, Chih-Hui
貢獻者:	統計研究所
關鍵詞:	伽馬隨機過程;隨機效應;DIC 準則;後驗預測 p-值;階層貝氏;Gamma process;random effect;DIC criterion;posterior predictive p-value;hierarchical Bayesian
日期:	2024-11-28
上傳時間:	2025-04-09 17:30:16 (UTC+8)
出版者:	國立中央大學
摘要:	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。;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.
顯示於類別:	[統計研究所] 博碩士論文

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