Reliability analysis and anomaly detection are crucial to the Prognostics and Health Management (PHM) of modern complex systems. Recently, with the advancement of measurement technology, a Long-Range Dependence/Long-Term Memory (LRD/LTM) effect has recently been detected in reliability and quality monitoring fields. The LRD effect is a type of non- Markovian property and refers to the high dependence between two measurements across a longtime interval or a long-distance range. In mathematics, the LRD effect indicates that the autocorrelation of the metrics is non-summable. In reliability and anomaly detection fields, most studies have been conducted ignoring the LRD effect, which could incur some serious issues, such as biased lifetime prediction or inaccurate anomaly detection. To overcome these challenges, we propose novel reliability analysis and anomaly detection approaches to integrate the LRD effect. Specifically, in Chapter 2 we propose a reliability analysis considering the LRD effect and random errors simultaneously under normal operating conditions. In Chapter 3, we develop a reliability analysis integrating the LRD effect under accelerated conditions. In Chapter 4, we propose a quality control analysis on surface anomaly detection considering LRD. In Chapter 5, we develop an LRD-integrated anomaly detection using 3D composite structure information. Results show that the proposed LRD-integrated approaches, by considering the LRD effect, significantly outperforms the conventional models that ignore the LRD effect.