Time-Dependent Reliability Analysis of a Multicomponent System Subject to Multiple Dependent Competing Failure Processes Using Phase-Type Distribution

This paper develops a method for the time-dependent reliability analysis of a multicomponent system subject to multiple dependent competing failure processes (MDCFPs) using phase-type (PH) distribution. Unlike existing methods that are limited to convolution-closed distributions, the PH distribution method can also handle those that lack this property or are statistically undefined due to limited data. In MDCFPs, the gamma process is utilized to model the degradation process in soft failure, whereas the mixed shock model that combines the extreme shock model and the cumulative shock model is utilized to model random shocks in soft and hard failures. The reliability functions for series and parallel systems can be represented in matrix form using the PH distribution, enabling efficient computation. Monte Carlo simulation, numerical integration, and PH distribution methods are all employed for comprehensive performance comparison. Four examples are used to validate the proposed method, and comparative results demonstrate that the PH distribution method achieves significantly superior performance in terms of accuracy, efficiency, and applicability.