Degradation and reliability of multi-function systems using the hazard rate matrix and Markovian approximation

The study presents a new method to model the degradation and reliability of multi-function complex systems using the hazard rate matrix and Markovian approximation. The system is hierarchically decomposed into a set of states according to the states of its functions, and the hazard rate matrix is proposed to describe the failure rates of the functions. By using Markovian approximation, the elements of the hazard rate matrix can be expressed as a set of dynamical equations involving the failure information about the functions. Consequently, the dynamical behavior of the degradation for the whole system and its functions can be determined using the observed failure data of those functions instead of the lifetime data of the whole system, eliminating the need for lifetime testing data of the whole system in statistical-based reliability assessment. The overall method is illustrated using an example problem, and is further applied to a power system degradation problem to demonstrate its usage in realistic engineering applications.