A Simulation Method to Estimate Two Types of Time-Varying Failure Rate of Dynamic Systems

Abstract

The failure rate of dynamic systems with random parameters is time-varying even for linear systems excited by a stationary random input. In this paper, we propose a simulation-based method to estimate two types (type I and type II) of time-varying failure rate of dynamic systems. The input stochastic processes are discretized in time and the trajectories of the output stochastic process are calculated. The time of interest is partitioned into a series of time intervals and the saddlepoint approximation (SPA) is employed to estimate the probability of failure in each interval. Type I follows the commonly used definition of failure rate. It is estimated at discrete time intervals using SPA and the correlation information from a properly selected time-dependent copula function. Type II is a proposed new concept of time-varying failure rate. It provides a way to predict the failure rate considering a virtual “good-as-old” repair action of repairable dynamic systems. The effectiveness of the proposed method is illustrated with a vehicle vibration example.