在研究鋰電池壽命的試驗中，常以電池完成一次充放電的過程為週期，觀察其電容、電壓或電流等品質特徵值隨週期變化的衰變試驗評估其壽命，而當品質特徵值下降到初始值的特定百分比之臨界值時判定電池性能終止(end of performance, EOP)，因此品質特徵值首次達性能終止之週期數可定義為電池使用壽命。將電池置於比正常環境應力(如溫度、壓力和放電率等) 更嚴苛環境下進行加速衰變試驗可以得到較完整的資訊，並經由外插得正常應力之壽命推論。本文以貝氏逆高斯(inverse Gaussian) 加速趨勢更新過程(accelerated trend-renewal process, ATRP) 模型，在參數與放電電流呈對數線性關係時配適電池在不同放電電流下之充放電電容資料，經外插推估於正常放電電流下的壽命。另一方面，由於製造成分和化學反應使得電池間存在差異性，一般以模型中參數具隨機效應分配來描述此差異，然而ATRP 模型不具共軛性，文獻上未見關於隨機效應的討論。本文嘗試利用階層貝氏(hierarchical Bayes) 方法，配合馬可夫鍊蒙地卡羅(Markov chain Monte-Carlo) 演算法，分別建構三種隨機效應ATRP 模 型，經由貝氏模型選擇(model selection) 準則決定最適合的衰變模型，據以推估電池在正常應力下的壽命分配，同時利用蒙地卡羅模擬驗證計算的合理性。最後應用一筆實際電池充放電資料，說明所提方法之可行性。;In studying the lifetime of Lithium-ion batteries, analysis is often performed using data collected from the cyclic charge-discharge tests such as capacity, current and voltage, so called the quality characteristic (QC). The evaluation of battery lifetime is defined by the first cycle of QC value dropping to a specific threshold, known as the end of performance (EOP). Accelerated degradation tests are conducted under severer stress conditions than the normal use condition, such as temperature, pressure, and discharge rate, to fasten the test and to collect more comprehensive information. Extrapolation is performed to estimate the lifetime under normal use condition. This study utilizes the inverse Gaussian accelerated trend-renewal process (ATRP) model in analyzing the discharge-capacity batteries data under different discharge currents, by assuming a log-linear relationship between model parameter and discharge current. Random-effect models are considered to describe the unit-to-unit variation among batteries by accommodating random parameter in the ATRP models. A hierarchical Bayesian approach incorporating with latent variables is adopted with the aid of the Markov chain Monte Carlo (MCMC) procedure to three ATRP random-effect models. Predictive lifetime inference is deduced under the most appropriate model through Bayesian model selection. Monte Carlo simulations are used to validate the calculation. The proposed method is applied to a real Lithium-ion battery data set and it demonstrates the feasibility of the methodology.
