ITEM TOOLKIT

2. ITEM ToolKit & Markov Analysis
Chapter 9 Markov 205
Markov Analysis is one of the many modules within the ITEM ToolKit application, which includes ITEM ToolKit’s
standard features and integration. Item Software’s Markov Module provides a powerful Markov modeling and analysis
technique with strong applications in time-based reliability and availability analysis.
The reliability behavior of a system is represented using a state-transition diagram, which consists of a set of discrete states
that the system can be in, and defines the speed at which transitions between those states take place. As such, Markov
models consist of comprehensive representations of possible chains of events, i.e., transitions, within systems, which in the
case of reliability and availability analysis correspond to sequences of failures and repair.
The Markov model is analyzed in order to determine such measures as the probability of being in a given state at a given
point in time, the amount of time a system is expected to spend in a given state, as well as the expected number of
transitions between states, for instance representing the number of failures and repairs.
Markov models provide great flexibility in modeling the timing of events. They can be applied when simple parametric
time-based models, such as Exponential or Weibull Time-to-Failure models are not sufficient to describe the dynamic
aspects of a system’s reliability or availability behavior, as may be the case for systems incorporating standby redundancy.
Computing the solution of a Markov model is equivalent to computing the solution of a large system of ordinary differential
equations, which is done by integration. For this purpose, the Markov Analysis module relies on a state-of the- art
computational engine that has seen many academic and commercial applications.
The engine is started by a simple click of a button within the ITEM ToolKit.
Highlights of the module’s features are:
• Phased-mission models
• Powerful graphical Markov model editor
• Discrete and continuous-time transition models
• Flexible definition of states and groups of states.
Markov Module provides the following measures and results:
• Expected up and down time
• Number of expected failures and repairs
• Failure and repair frequencies (at given point in time)
• Availability / Reliability (at given point in time, average over mission time interval)
• Probability of being in a particular state (at given point in time, average over mission time interval)
• Customizable Report Generator
• Extensive Import / Export facility from or to Jet Database, Excel or Text.
The Markov workspace area features a Multiple Document Interface (MDI), which allows you to:
• Choose which windows to display, and move and resize all open windows
• Open and create multiple Markov projects at the same time in order to compare analysis results
• Drag and drop State and Group components between projects. This feature allows you to quickly create a new
project by reusing components from other projects.