The Markov Reward Model for a Multi-State System Reliability Assessment with Variable Demand

This paper considers reliability measures for a multi-state system where the system and its components can have different performance levels ranging from perfect functioning to complete failure. The suggested approach presents a generalized reliability measure as a functional of trajectories of two stochastic processes — output performance of the entire multi-state system and the corresponding demand. It shows how the commonly used reliability measures 120 can be derived from this functional and how they can be computed by using the developed Markov reward model. Corresponding procedures for rewards definition are suggested for different reliability measures. A numerical example is presented in order to illustrate the approach.