可修復系統之特徵為產品故障後經修復可以重複使用，收集到的資料具有循環性，然某些可修復系統之使用性能隨修復次數增加而有遞減的現象，如電池經充放電後之電容量等，因此傳統的更新過程不適合分析此類型資料。此時可將每次修復後的循環資料經趨勢函數轉換，建構趨勢更新過程配適之。然而，當樣本間存在個別差異時，囿於趨勢更新過程模型複雜的概似函數，致使參數不存在共軛結構，使得以隨機效應模型描述樣本差異性的最大概似推論產生困難。本文探討趨勢更新過程模型中參數的可辨別性，經重新參數化提出通用趨勢更新過程，並發現了通用趨勢更新過程模型中的共軛結構，進而發展出通用趨勢更新過程隨機效應模型，不僅可以應用在任一具共軛性的更新分布所衍伸出的通用趨勢更新過程模型，也可以推廣到加速通用更新過程之隨機效應模型。另一方面，本文推導出評估循環性資料壽命之性能終止時間的近似式，使可修復資料之可靠度分析更臻完備與彈性。除經由模擬資料驗證通用趨勢更新過程模型壽命推論的準確性，並將模型應用到飛機空調系統及鋰電池之衰變資料外，更進一步分析一筆鋰電池加速衰變資料，用以評估正常使用條件下的產品壽命，成功的詮釋具差異性的可修復產品之可靠度推論。;A repairable system can be reused after repairs, but data from such systems often exhibit cyclic patterns. For instance, in the charge-discharge cycles of a battery, capacity decreases with each cycle, and the system′s performance may not fully recover after each repair. To address this issue, the trend renewal process (TRP) transforms periodic data using a trend function to ensure the transformed data satisfy independent and stationary increments. This study explores random-effects models with a conjugate structure, achieved by reparameterizing the TRP models, called generic TRP (GTRP). These random-effects GTRP models, adaptable to any GTRP model with a renewal distribution possessing a conjugate structure, provide enhanced convenience and flexibility in describing sample heterogeneity. An approximate formula for the end of performance is derived to make life inferences about recurrent systems, with a simulation study confirming the validity of these inferences for GTRP models. Moreover, the proposed random-effects models are extended to accelerated GTRP (AGTRP) for assessing the reliability of lithium-ion battery data, in addition to analyzing aircraft cooling system data and NASA battery data.
