Speed-up simulation for reliability analysis of Wiener degradation process with random failure threshold

This paper proposes an alternative approach to the analysis and modeling of the reliability of degradation systems with rare failures. We assume that the degradation measure of the multiphase system is described by the Wiener process and instantaneous failure occurs when the process reaches a given level. Let us consider a model of a multiphase system, where the degree of degradation is described by a Wiener process and an instantaneous failure occurs when the process reaches a given level. The failure threshold value can be either a constant or a random variable that takes values ​​on the positive semiaxis or on the fixed interval. Evaluation of the failure probability and other characteristics of the system is crucial for optimal control, however, for complex multi-phase systems with multiple failure thresholds, it is often impossible to find an analytical solution. For the process of regenerative degradation, instead of the standard Monte-Carlo procedure, it is proposed to use an accelerated version of the construction of regeneration cycles. The splitting of the Wiener process trajectory occurs at the moment of transition to the next phase of the degradation. This approach is useful when failures are rare.