Stochastic Differential Equation Models for Reliability Analysis of Mission-Critical Engineering Systems

Abstract

Mission-critical engineering systems include aerospace vehicles, nuclear power plants, space exploration modules, and autonomous defense platforms that need to operate with very high degrees of reliability, because any failure that does occur can have disastrous impact on safety, economics, and mission success. But the reliability is very much difficult to guarantee in these systems as they are prone to uncertainty and extreme changeability in their working environments. Variability comes in the form of random external loads, varying environmental conditions, and time-dependent degradation processes and cannot be adequately described using classical deterministic models of reliability. In filling this gap, the current paper introduces a stochastic differential equation (SDE)-based framework of reliability modeling and reliability analysis of mission-critical engineering systems. In contrast to the traditional deterministic methods, SDE models are able to describe the deterministic degradation trend as well as the random perturbations that occur due to uncertainty. The framework proposed takes advantage of Ito stochastic calculus to mathematically model the dynamics of the system, combines degradation models to account the wear, fatigue, or corrosion, and uses Monte Carlo to approximate such reliability indices as mean-time-to-failure (MTTF), failure probability, and resilience. Numerical simulations are used to substantiate the methodology, stochastic degradation paths are plotted and compared to both traditional Weibull and Markov based models of reliability. Findings indicate that SDE frameworks are more accurate in elucidating system lifetime distributions, especially when there is a lot of uncertainty, which deterministic models tend to overestimate system reliability. Also sensitivity analysis shows how the diffusion intensity affects the reliability curves, which can be used to understand the margins of the system design and operational risk measure. In sum, this research paper provides a useful addition to a practical and dynamic reliability analysis instrument that better reflects real-life uncertainty as opposed to classical models. The results are relevant to reliability-based design, predictive maintenance scheduling, digital twins integration and risk reduction measures in mission-critical areas, which guarantee improved safety, performance, and resilience of next-generation engineering systems.