Hierarchical Dependability Models Based on Markov Chains

Abstract:
A dependability model allows calculating the rate of an event leading to a hazard state – a situation, where safety of the modeled system is violated, thus the system may cause material loss, serious injuries or casualties. A hierarchical dependability model allows expressing multiple redundancies made at multiple levels of a system decomposed to multiple cooperating blocks. A hierarchical dependability model based on Markov chains allows each block and its relation to the other blocks to be expressed independently by a Markov chain. This allows a decomposition of a complex dependability model into multiple small models to be made. The decomposed model is easier to read, understand and modify. A hazard rate is calculated significantly faster using hierarchical model, because the decomposition allows exponential calculation-time explosion to be avoided. The hazard rate of the system is the key value to specify the Safety Integrity Level (SIL).