Markov State Analysis

Why Use a Markov Analysis?

Markov models allow for a detailed representation of failure and repair processes, particularly when dependencies are involved, and therefore result in more realistic assessments of system reliability measures than simple time-to failure and time-to-repair models. Markov Analysis is well suited to handle rare events, unlike simulation-based analyses, and therefore allows such events to be analyzed within a reasonable amount of time.

When is Markov Model Used?

Markov Analysis is a technique used to obtain numerical measures related to the reliability and availability of a system or part of a system. Markov Analysis is performed when dependencies between the failure of multiple components as well as dependencies between component failures and failure rates can not be easily represented using a combination of fault trees and standard time-to-failure and time-to-repair distributions. Specific examples of application areas are standby redundancy configurations as well as common cause failures.

Markov Construction

A Markov Analysis consists of three major steps:

1. Specification of the states the system can be in
2. Specification of the rates at which transitions between states take place
3. Computation of the solutions to the model

Steps 1 and 2 take place in a graphical Markov model editor. In this editor, drawing circles and arrows between the circles, respectively, can create states and transitions between them. The construction of larger Markov models is facilitated by the editor's ability to hierarchically construct Markov models, i.e. break down a higher-level state into lower-level states on a separate 'page', similar to the use of transfer gates in Fault Tree modeling.

Both continuous and discrete transitions can be introduced into the model. Continuous transitions are those representing events that can take place at any time within a given time interval, whereas discrete transitions take place at a specified point in time. For this purpose, individual transitions belong to a transition group, consisting of all the transitions applicable to a given time interval, or taking place at a given point in time. Between intervals, the rate at which given transitions take place may be changed, providing a powerful scheme for phased-mission Markov Models.

Another strong feature of Markov Analysis is its capability to define state groups. State groups are groups of states within the model for which the user wants to obtain combined statistics, such as total time spent in any of the states, or number of transitions in or our out of the group. One group that is defined by default is the "Unavailable" group. Any time spent in a state that is marked by the user as belonging to this group is considered to be system downtime, which is taken into account when computing reliability and availability measures.

Once the definition of the model is complete, the user indicates which statistics should be computed, beyond the reliability measures that are computed by default. Available measures include state probabilities, time spent in a given state or state group, as well as transition rate and number of transitions in and out of a given state or state group.

After computation of the solution, Step 3, these results can be observed in the various tabular and graphical formats.