The time-dependent reliability models of series,parallel and k-out-of-n systems with dependent failure were developed,and the relationship between reliability of system and time and that between failure rate of system and time were studied.Using the load-strength interference model in system level,the reliability models of systems with dependent failure were developed.Based on the analyses of reliability models,
the cumulative distribution function and probability density function of system strength were built.Then,the cumulative distribution function and probability density function of equivalent load were derived with the order statistic theory when random load acted for multiple times.Further,the reliability models of systems under random repeated load and the time-dependent reliability models of systems without strength degeneration were derived respectively.With the probability differential equation,the time-dependent reliability models of systems were built when strength degenerates.Finally,for series,parallel and k-out-of-n systems,the relationship between reliability and time and that between failure rate and time were studied.The results show that system has the similar characteristic as component.Reliability of system decreases gradually with time, and the reliability of k-out-of-n system is between that of series system and parallel system.When strength does not degenerate the failure rate of system decreases gradually;and when strength degenerates the failure rate of system has the whole feature of the bathtub curve.The reliability models proposed herein are useful for determining the time of trial run and reliable life of system and making the maintenance project for system rationally.
