Markov analysis

A Markov analysis is a state space analysis. These analyses enable the modelling of failure probabilities and probabilities of state changes as well as failure rates and repair rates. It is an analysis methodology which is primarily applied quantitatively using graphic models to represent possible states in a system under investigation, i.e. that a component exhibits faultless operation, limited operation or has failed, for example.
However, one of the prerequisites of using this deductive methodology is that the failure probabilities or the probabilities of individual system states are known beforehand.  

When using this analysis method it is typically assumed that a system has “no memory.” Hence the transitions between the individual states strictly depend on the current state and on time, but not on previous transitions between states. If a system exhibits different properties, i.e. a dependency on further states, appropriate modelling actions must be taken which in some cases significantly increase the complexity of the analysis.

The dependency on time which may be considered in such an analysis offers the possibility to consider failure and repair times. Hence the time that elapses between the detection of a fault or failure and the repair of the respective element may be represented in a Markov model.  
The Markov analysis is based on the Markov process, i.e. a stochastic process with a finite number of states. To calculate such an analysis, appropriate analysis tools are used.