在電池的可靠度試驗中，以電池完成充放電的過程為一週期，重複觀察其電容、電壓或電流等特徵值，定義電池壽命為特徵值變化第一次超過給定臨界值的週期數。然而，這類週期資料雖然具有常返性 (recurrent property)，其性能卻隨每次充放電而遞減，每個充放電週期資料不符合更新過程的條件。本文考慮融合先驗資訊於模型中的貝氏模型，以趨勢更新過程 (trend renewal process)，將週期資料經對數線性函數 (log-linear function) 的趨勢函數 (trend function) 轉換為具獨立同分配特性的逆高斯 (inverse Gaussian) 更新過程，並以尺度參數具伽瑪分配的隨機效應模型來描述電池之間可能存在的個別差異。在隨機效應模型中，個別差異性視為隱藏變數 (latent variable)，建構階層貝氏 (hierarchical Bayes) 模型，分析鋰電池置於固定放電電流下電容之加速衰變資料。應用適應馬可夫鍊蒙地卡羅 (Markov chain Monte-Carlo) 演算法，並根據參數與應力之間的關係，推估正常使用狀態下電池壽命的貝氏預測推論 (predictive inference)。最後以一組鋰電池電容衰變的實際資料驗證貝氏方法的可行性，並與傳統最大概似方法做比較。;In the reliability test of the batteries, the process of charging and discharging is taken as a cycle for each battery, and the changes in its characteristics such as capacitance, voltage, or current are repeatedly observed to assess its lifetime inference which is defined as the first cycle of its change passing a given threshold. However, the performance of a battery decreases in testing cycles, so it is unable to meet the completely recovery conditions of the renewal process. In this thesis, the trend renewal process with a log-linear trend function is used to convert the periodic data into an inverse Gaussian renewal process to analyze the degradation data of lithium batteries that are placed at different discharge currents. In addition, a random effect model of the degradation process is considered to address the unit-to-unit variation among the batteries. A Bayesian approach incorporated with the prior information is used where a hierarchical model is constructed for the random-effect model by treating individual random-effect as latent variables. With the aid of the Markov chain Monte-Carlo procedure, predictive lifetime inference is deduced under normal conditions according to the relationship between the parameters and the stress levels. The proposed method provides reasonable results through the empirical study of a real data set compared to the classical maximum likelihood approach.
