Verification of Calculations of Non-Homogeneous Markov Chains Using Monte Carlo Simulation

Dependability models allow calculating the rate of events leading to a hazard state - a situation, where the safety of the modeled dependable system is violated, thus the system may cause material loss, serious injuries, or casualties. The calculation of the hazard rate of the complex non-homogeneous Markov chains is time-consuming and the accuracy of the results is questionable. We have presented two methods able to calculate the hazard rate of the complex non-homogeneous Markov chains in previous papers. Both methods achieved very accurate results, thus we compare four Monte-Carlo based simulation methods (both accuracy and time-consumption) with our methods in this paper. A simple Triple Modular Redundancy (TMR) model is used in this paper since its hazard rate can be calculated analytically.