Accurate Inexact Calculations of Non-Homogeneous Markov Chains

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. Hierarchical dependability models allow expressing multiple redundancies made at multiple levels of a system consisting of multiple cooperating blocks. The hazard rates of the blocks are calculated independently and, when combined, they are used to calculate the hazard rate of the whole system. The independent calculations are significantly faster than the calculation of a single model composed of all models of the blocks. The paper shows a method of calculating the hazard rate of the non-homogeneous Markov chains using different homogeneous probability matrices for several hundreds small time intervals. 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.