Reliability of linear systems under Poisson white noise

A method is developed for calculating the failure probability of a linear dynamic system subjected to Poisson white noise assumed to function satisfactorily if its state X(t) does not leave a safe set DD during a specified time interval [0,τ][0,τ]. The method (1) is based on properties of Poisson white noise, features of system response to Poisson white noise, and conditional Monte Carlo simulation, and (2) delivers upper bounds on system failure probability, up to estimation errors. Numerical results illustrating the application and the accuracy of the proposed method include the largest value distribution of a generalized Ornstein–Uhlenbeck process and the reliability of a simple linear oscillator subjected to Poisson white noise. It is also shown that the proposed method can be applied to assess the performance of multidegree of freedom linear systems and nonlinear systems subjected to Poisson white noise.