Reliability of repairable reserved systems with failure aftereffect

We propose new models for analyzing the reliability of repairable systems with failure aftereffect, when the probability distribution of an element's time to failure changes only during the time when another element is being repaired. The key idea here is the so-called coupling principle for various probability distributions when the system's operation conditions or the “residual lifetime preservation condition” change. We show a method for constructing a system of integral equations as a universal tool for modeling the reliability of systems under the assumption that time to failure of each element obeys the Weibull distribution.