在如 IC 產品的一些電子零件中，由於製程或其他因素產生瑕疵，導致產品前期早衰（infant mortality）失效，而非瑕疵品則最終會因磨耗（wear-out）而失效。廣義有限失效母體（Generalized Limited Failure Population，GLFP）模型，可用於分析同時受因製程產生的瑕疵導致產品前期早衰，與後期終因長期磨損失效的產品或電子零件之失效時間數據。另一方面，自 E-M 演算法後，資料增補 (data augmentaion) 在統計學中的應用極為廣泛。本研究於對數常態分布 GLFP 模型，以貝氏方法結合資料增補建構完整概似函數，在各參數具共軛先驗分布下，以吉布斯抽樣（Gibbs sampling）加速馬可夫鍊蒙地卡羅（Markov chain Monte Carlo，MCMC）演算法的計算過程，從而提升計算效率。同時藉由資料增補的隱藏變數之後驗抽樣過程中，為每筆失效資料之失效模式和其是否為瑕疵品進行預測，並針對 Backblaze 公司所提供的硬碟資料，考慮不同的先驗資訊，進行壽命之可靠度相關分析。;Some electronic components such as integrated circuits contain latent defects introduced during manufacturing or other processes, causing a subset of units to fail prematurely (infant mortality), while non-defective units eventually fail due to wear-out. The generalized limited failure population (GLFP) model captures this dual behavior by jointly modeling early failures arising from manufacturing defects and later failures driven by long-term degradation. Based on the widely used data augmentation technique in statistics, this study develops a Bayesian GLFP framework with log-normal lifetime distributions. By augmenting the latent data, we construct the complete likelihood, assign conjugate priors to all parameters, and employ Gibbs sampling to accelerate Markov chain Monte Carlo (MCMC). The posterior draws of the latent augmentation variables simultaneously yield predictive classifications of each observed failure mode and defect status. Finally, using hard-drive failure data released by Backblaze, we perform reliability analysis under various prior assumptions to illustrate the practical utility of the proposed method.
