對於高可靠度產品而言，若僅依賴傳統失效時間資料進行壽命分析，往往需耗費較長試驗時間，且可能面臨失效樣本不足的問題。相較之下，衰變資料分析可利用產品品質特徵隨時間之變化資訊，在尚未觀察到足夠失效時，即提供較豐富的可靠度推論依據。實務上，衰變資料除存在個體間的隨機差異外，亦常呈現潛在群體間衰變速率不同的情形，因此本研究目的在於衰變模型同時刻劃個體與群體層級的異質性。本研究以 Tweedie 過程為基礎，提出混合隨機效應 Tweedie 過程（mixture random effect Tweedie process, mRETP）模型，用以分析具有潛在分群結構之單調衰變資料。Tweedie 過程具備較一般化的建模彈性，常見之 Wiener 過程、Gamma 過程與 Inverse Gaussian 過程皆可視為其特例，因此相較於僅依賴單一隨機過程模型之作法，所提模型能以更統一且彈性的架構描述不同型態之衰變行為。模型中以隨機效應刻劃試驗單位間的個體差異，並以混合模型捕捉潛在群體間之結構差異，使模型同時兼顧個體間與群體間之異質性。參數估計方面採用 EM 演算法，進一步建立壽命分配，並使用有母數 bootstrap 與 Fractional-Random-Weight bootstrap 方法求得參數估計值與壽命分配累積分配函數之信賴區間。在實例分析中，本研究使用裂縫成長資料進行模型比較，並將所提 mRETP 模型與混合隨機效應 Gamma 過程和混合隨機效應 Inverse Gaussian 以及不含混合結構之模型進行配適比較。結果顯示，所提 mRETP 模型具有最佳的整體表現，顯示其更能有效描述裂縫成長資料中同時存在的個體差異與群體差異。綜合而言，本研究所提出之 mRETP 模型，不僅在理論上提供一個涵蓋多種常見隨機過程的統一建模架構，也在實際裂縫成長資料分析中展現較佳的模型適配能力與壽命推論表現，可作為處理具異質性單調衰變資料之有效方法。

Failure-time studies of highly reliable products are often lengthy and yield few failures. Degradation data provide earlier lifetime information, but their paths may contain both continuous unit-to-unit variation and discrete latent groups. This study proposes a mixture random effect Tweedie process (mRETP) model to represent both sources of heterogeneity. An Inverse Gamma random effect describes individual mean-rate variation, while a finite mixture allows groups to differ in their time-accumulation pattern, population mean rate, or both. The Tweedie family also includes the Gamma and Inverse Gaussian processes as special cases. Parameters are estimated using an EM algorithm. Gauss–Laguerre quadrature evaluates the random-effect integral. Parametric and fractional-random-weight bootstrap procedures provide confidence intervals. Simulations show that incorporating a genuine latent mixture generally reduces the bias and root mean squared error of lifetime quantile estimates. Uncertainty is greatest when the target probability is near the mixing proportion, where the component lifetime distributions meet. In the fatigue crack-growth application, the 𝛾-mixture mRETP model has the smallest Akaike information criterion and closely follows both the degradation paths and mpirical lifetime distribution. The main group difference lies in the temporal accumulation pattern. The proposed model therefore provides a flexible approach to lifetime inference for monotone degradation data with individual and latent-group heterogeneity.

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