Mathematical Foundations of Reliability Theory with Applications in Engineering and Applied Statistics

Dear Colleagues,

Reliability theory has become a cornerstone of modern engineering, applied statistics, and risk analysis. The growing complexity of technological systems—ranging from aerospace and energy infrastructure to biomedical devices and information networks—demands mathematical tools that are both rigorous and applicable to real-world decision-making. This Special Issue aims to bring together cutting-edge contributions that deepen the mathematical foundations of reliability while highlighting their impact on engineering practice and applied statistics.

The scope of the Issue spans both theoretical advances and methodological innovations, with emphasis on problems that bridge pure mathematics and practical applications. We invite papers that address fundamental challenges such as renewal and renewal–reward processes, asymptotic methods for distribution functions in reliability, and optimal maintenance policies under short- and long-horizon planning. Contributions that integrate advanced probability, stochastic processes, asymptotic analysis, and computational methods are particularly welcome.

Applications are expected to cover a broad spectrum: maintenance optimization in complex systems, reliability assessment of renewable energy technologies, survival analysis in biomedical contexts, and reliability-inspired statistical models for emerging data-rich environments. By uniting mathematical challenges with engineering and statistical applications, this Special Issue will showcase the interdisciplinary vitality of reliability theory.

Topics of interest include, but are not limited to, the following:

• Foundations of reliability mathematics:
  • Renewal and renewal–reward theory;
  • Stochastic processes in reliability analysis;
  • Distributional methods: survival, hazard, and cumulative failure models;
  • Asymptotic expansions, Laplace-type methods, and error bounds.
• Maintenance and optimization policies:
  • Short- and long-horizon maintenance strategies;
  • Cost-per-unit-time and replacement policies;
  • Block and group maintenance for modular systems;
  • Age-dependent and state-dependent policies.
• Statistical modeling and inference:
  • Parametric and nonparametric methods in reliability data analysis;
  • Goodness-of-fit and model selection for lifetime distributions;
  • Bayesian approaches to reliability and failure prediction;
  • Reliability in the presence of censored and grouped data.
• Applications in engineering and applied sciences:
  • Reliability of energy systems and renewable technologies;
  • Reliability in electrical and electronic engineering;
  • Survival and reliability models in biostatistics;
  • Reliability under uncertainty, risk analysis, and decision theory.
• Stochastic maintenance.
• Renewal and renewal–reward models.
• Bayesian reliability.
• Degradation models.
• Survival analysis..
• Reliability in power systems.
• Statistical inference under censoring.
• Machine learning for reliability and predictive maintenance.
• Risk and decision models.

Prof. Dr. Serguei Maximov
Dr. Francisco Rivas-Dávalos
Guest Editors

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