Non-Homogeneous Continuous Time Markov Chains Calculations

Abstract

Dependability models allow calculating the rate of events leading to a hazard state – a situation, where safety of the modeled dependable system is violated, thus the system may cause material loss, serious injuries or casualties. This paper shows a method of calculating the hazard rate of the non-homogeneous Markov chains using different sets of homogeneous differential equations for several hundreds small time intervals (using default parameters settings – the number of the intervals can be adjusted to balance accuracy/time-consumption ratio). The method is compared to a previous version based on probability matrices and used to calculate the hazard rate of the hierarchical Markov chain. The hierarchical Markov chain allows us to calculate the hazard rates of the blocks independently and the non-homogeneous approach allows us to use them to calculate the hazard rate of the whole system. This method will allow us to calculate the hazard rate of the non-homogeneous Markov chain very accurately compared to methods based on homogeneous Markov chains.