Application of the interacting particle system method to piecewise deterministic Markov processes used in reliability

Area of Science:

• Reliability Engineering
• Stochastic Processes
• Computational Statistics

Background:

• Reliability assessment of complex industrial systems often requires variance reduction techniques.
• Piecewise deterministic Markov processes (PDMPs) offer high modeling capacity for Markovian phenomena without diffusion.
• Concentrated PDMPs, common in industrial reliability, feature low jump rates and favor safe arrivals, posing challenges for standard methods.

Purpose of the Study:

• To address the inefficiency of the interacting particle system (IPS) method on concentrated PDMPs.
• To propose and validate a novel adaptation of the IPS method for improved reliability assessment.
• To demonstrate enhanced variance reduction in reliability analysis of industrial systems.

Main Methods:

• Introduced the interacting particle system (IPS) method for reliability assessment using PDMPs.
• Identified limitations of the standard IPS method with concentrated PDMPs due to repetitive deterministic trajectories.
• Developed the IPS+M method, modifying IPS propagation steps to avoid redundant trajectory generation.

Main Results:

• The standard IPS method is inefficient for concentrated PDMPs, often failing to achieve variance reduction.
• The proposed IPS+M method effectively reduces the generation of identical trajectories during simulation.
• Mathematical proofs demonstrate that IPS+M consistently yields estimators with lower variance compared to the standard IPS.
• Simulations on two-component systems empirically validate the superior performance of IPS+M.

Conclusions:

• The IPS+M method offers a significant improvement over the standard IPS for reliability assessment of concentrated PDMPs.
• This enhanced method provides a more efficient and reliable approach to estimating system reliability.
• IPS+M is a valuable tool for analyzing complex industrial systems where traditional methods fall short.