One of the most significant Non-Boolean models is the Markov model. This will be applied, for instance, when

–          a binary allocation of the components’ failure behavior is not possible

–        the components are not independent from each other (e.g. due to the chronological order of failures)

The Markov-analysis is a state space analysis. A stochastic process is a Markov process when the likelihood for a transition of one state to another is only dependent on the present state and on the present point in time. In this sense, a Markov process is also called a “process without memory”.

Within a Markov analysis graphic models are created, which depict all possible states of a system, such as the states system functions faultlessly, system functions in a limited manner or system has failed.

Example of a state graph in a Markov analysis

Example of a state graph in a Markov analysis


Hereby, state transitions like failure or repair rates can be taken into account.

In the following, the simplified Markov-process of a brake system will be presented. Thereby, safe and dangerous failure states are given. With a repair one can reach state 1 from a former safe failure state. By this means the availability or the safety availability can be determined. This information provides the opportunity to optimize maintenance strategies or fail-safe strategies.