presenting a new method for calculating the reliability of active systems with Weibull-based time-dependent failure rates

Due to the high sensitivity in applying of electronic and mechanical equipment, creating any conditions to increase the reliability of a system is always one of the important issues for system designers. Hence, making academic models much closer to the real word applications is very attractive. In the most studies in the reliability area, it is assumed that the failure rates of the system components are constant and have exponential distributions. This distribution and its attractive memory less property provide simple mathematical relationships in order to obtain the system reliability. But in real word problems, considering time-dependent failure rates is more realistic to model processes. It means that, the system components do not fail with a constant rate during the time horizon; but this failure rate changes over the time. One of the most useful statistical distributions in order to model the time-dependent failure rates is the Weibull distribution. This distribution is not a memory less one, so it was impossible to apply simple and explicit mathematical relationships as the same as exponential distributions for the reliability of a system. Therefore, researchers in this field have used simulation technique in these circumstances which is not an exact method to get near-optimum solutions. In this paper, for the first time, it is tried to obtain a mathematical equation to calculate the reliability function of a system with time-dependent components based on Weibull distribution. Also, in order to validate the proposed method, the results compared with exact solution that exists in literature.