ITEM TOOLKIT
ITEM Toolkit Manual
ITEM Toolkit Manual
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204 <strong>ITEM</strong> ToolKit Getting Started Guide<br />
1. Introduction<br />
Why Use a Markov Analysis?<br />
Markov models allow for a detailed representation of failure and repair processes, particularly when dependencies are<br />
involved, and therefore result in more realistic assessments of system reliability measures than simple time-to failure and<br />
time-to-repair models. Markov Analysis is well suited to handle rare events, unlike simulation-based analyses, and therefore<br />
allows such events to be analyzed within a reasonable amount of time.<br />
When is Markov Model Used?<br />
Markov Analysis is a technique used to obtain numerical measures related to the reliability and availability of a system or<br />
part of a system. Markov Analysis is performed when dependencies between the failure of multiple components as well as<br />
dependencies between component failures and failure rates cannot be easily represented using a combination of fault trees<br />
and standard time-to-failure and time-to-repair distributions. Specific examples of application areas are standby redundancy<br />
configurations as well as common cause failures.<br />
Markov Construction<br />
A Markov Analysis consists of three major steps:<br />
1. Specification of the states the system can be in<br />
2. Specification of the rates at which transitions between states take place<br />
3. Computation of the solutions to the model<br />
Steps 1 and 2 take place in the graphical Markov model editor. In this editor, drawing circles and arrows between the<br />
circles, respectively, can create states and transitions between them. The construction of larger Markov models is facilitated<br />
by the editor's ability to hierarchically construct Markov models, i.e. break down a higher-level state into lower-level states<br />
on a separate 'page', similar to the use of transfer gates in Fault Tree modeling.<br />
Both continuous and discrete transitions can be introduced into the model. Continuous transitions are those representing<br />
events that can take place at any time within a given time interval, whereas discrete transitions take place at a specified<br />
point in time. For this purpose, individual transitions belong to a transition group, consisting of all the transitions applicable<br />
to a given time interval, or taking place at a given point in time. Between intervals, the rate at which given transitions take<br />
place may be changed, providing a powerful scheme for phased-mission Markov Models.<br />
Another strong feature of ToolKit’s Markov Module is its capability to define state groups. State groups are groups of states<br />
within the model for which the user wants to obtain combined statistics, such as total time spent in any of the states, or<br />
number of transitions in or our out of the group. One group that is defined by default is the 'Unavailable' group. Any time<br />
spent in a state that is marked by the user as belonging to this group is considered to be system downtime, which is taken<br />
into account when computing reliability and availability measures.<br />
Once the definition of the model is complete, the user indicates which statistics should be computed, beyond the reliability<br />
measures that are computed by default. Available measures include state probabilities, time spent in a given state or state<br />
group, as well as transition rate and number of transitions in and out of a given state or state group.<br />
After computation of the solution, Step 3, these results can be observed in the various tabular and graphical formats.