In industrial statistics, degradation models constitute a fundamental class of methodologies for analyzing performance deterioration in engineering systems. These models find broad applications in characterizing various industrial reliability metrics, such as engine crack lengths or battery capacity. The present investigation focuses on a particular degradation mechanism - the lifetime delayed heterogeneous degradation process - which exhibits two distinctive features: (1) the initiation of performance deterioration occurs stochastically after an operational period, and (2) the subsequent degradation rate demonstrates dependence on the initial degradation onset time. First, we establish the theoretical framework for the lifetime delayed heterogeneous degradation process model and derive the corresponding reliability statistical inference procedures. Subsequently, we implement variational inference techniques for efficient parameter estimation and conduct comprehensive simulation studies to evaluate the performance of the statistical inference methodology.

Dr. Zan Li is currently a Lecturer at Nankai University. She obtained her Ph.D. in Science from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (AMSS, CAS) in 2022 and earned her B.S. in Mathematics from the University of Science and Technology of China (USTC). Her primary research interests include industrial statistics, reliability mathematics, deep learning, and subsampling methods. She has published papers in high-impact journals such as IEEE Transactions on Reliability and Reliability Engineering & System Safety.