Degradation data are considered for assessing reliability in highly reliable systems. The usual assumption is that degradation units come from a homogeneous population. But in presence of high variability in the manufacturing process, this assumption is not true in general; that is different sub-populations are involved in the study. Predicting residual lifetime of a functioning unit is a major challenge in the degradation modeling especially in heterogeneous environment. To account for heterogeneous degradation data, we have proposed a Bayesian semi-parametric approach to relax the conventional modeling assumptions. We model the degradation path using Dirichlet process mixture of normal distributions. Based on the samples obtained from posterior distribution of model parameters we obtain residual lifetime distribution for individual unit. Transformation based MCMC technique is used for simulating values from the derived residual lifetime distribution for prediction of residual lifetime. A simulation study is undertaken to check performance of the proposed semi-parametric model compared with parametric model. Fatigue Crack Size data is analyzed to illustrate the proposed methodology.

翻译：在评估高可靠性系统的可靠性时，常采用退化数据进行分析。通常的假设是退化单元来自同质总体。然而，当制造过程存在高度变异性时，这一假设通常不成立；即研究中涉及不同的子总体。预测运行中单元的剩余寿命是退化建模中的一个主要挑战，尤其在异质环境下。为处理异质退化数据，我们提出了一种贝叶斯半参数方法，以放宽传统的建模假设。我们使用正态分布的狄利克雷过程混合来建模退化路径。基于从模型参数后验分布中获得的样本，我们得到个体单元的剩余寿命分布。采用基于变换的MCMC技术从推导出的剩余寿命分布中模拟数值，以进行剩余寿命预测。通过模拟研究来检验所提出的半参数模型与参数模型相比的性能。文中分析了疲劳裂纹尺寸数据以说明所提出的方法。