A stochastic hybrid systems based framework for modeling dependent failure processes.

Area of Science:

• Reliability Engineering
• Stochastic Systems Analysis
• System Dynamics

Background:

• Complex systems often face multiple, interacting degradation processes and unpredictable random shocks.
• Accurate modeling of such systems is crucial for predicting failures and ensuring operational integrity.
• Existing methods may struggle with the computational demands of dependent failure processes.

Purpose of the Study:

• To develop a robust framework for modeling and analyzing systems with dependent, competing degradation processes and random shocks.
• To provide accurate reliability estimations with improved computational efficiency.
• To validate the framework against established methods and real-world scenarios.

Main Methods:

• Utilizing Stochastic Hybrid Systems (SHS) to integrate continuous degradation (stochastic differential equations) and discrete state transitions (random shocks).
• Deriving differential equations to characterize conditional moments of state variables.
• Employing the First Order Second Moment (FOSM) method and Markov inequality for reliability and lower bound estimation.

Main Results:

• The developed SHS framework successfully models dependent failure processes.
• Reliability estimations derived from conditional moments show high accuracy.
• The framework significantly reduces computational costs compared to Monte Carlo simulations.

Conclusions:

• The proposed SHS framework offers an effective and computationally efficient approach for reliability analysis of complex systems.
• This method provides a valuable alternative to traditional simulation techniques for systems with dependent degradation and shocks.
• The framework demonstrates practical applicability and accuracy in modeling real-world failure scenarios.