A Review of Reliability Theory: Advances, Challenges, and Future Directions

Abstract

Reliability theory is a crucial field of applied probability and statistics that focuses on analyzing system performance, durability, and failure prediction. Over the years, it has evolved from its early applications in military and aerospace engineering to becoming a fundamental aspect of manufacturing, healthcare, software engineering, and risk management. Traditional reliability estimation methods, such as failure rate analysis and probability distributions, have been significantly enhanced with the integration of Bayesian inference, machine learning, and real-time monitoring systems. Additionally, modern reliability engineering leverages fault tree analysis (FTA), failure mode and effects analysis (FMEA), and Markov processes to improve failure prediction and system robustness. This review chapter explores the key advancements in reliability modeling, stress-strength analysis, system redundancy, and predictive maintenance. It also provides a comprehensive review of the literature, summarizing existing models, recent developments, and emerging research directions in reliability theory. It examines key methodologies, including probabilistic models, stress-strength analysis, and redundancy techniques, highlighting their evolution and impact on modern reliability assessment. Additionally, the review explores the role of artificial intelligence, Bayesian inference, and copula-based modeling in enhancing system reliability and failure prediction.