Markov analysis

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Markov analysis (MA) is an analysis technique for modeling system state transitions
and calculating the probability of reaching various system states from the model.
MA is a tool for modeling complex system designs involving timing, sequencing,
repair, redundancy, and fault tolerance. MA is accomplished by drawing system
state transition diagrams and examining these diagrams for understanding how certain
undesired states are reached and their relative probability. MA can be used to
model system performance, dependability, availability, reliability, and safety. MA
describes failed states and degraded states of operation where the system is either
partially failed or in a degraded mode where some functions are performed while
others are not

Markov chains are random processes in which changes occur only at fixed times.
However, many of the physical phenomena observed in everyday life are based on
changes that occur continuously over time. Examples of these continuous processes
are equipment breakdowns, arrival of telephone calls, and radioactive decay.
Markov processes are random processes in which changes occur continuously
over time, where the future depends only on the present state and is independent
of history. This property provides the basic framework for investigations of system
reliability, dependability, and safety. There are several different types of Markov
processes. In a semi-Markov process, time between transitions is a random variable
that depends on the transition