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Markov Analysis Software - MKV Version 3.0

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markov analysis software, markov chain Overview

MKV is a Markov Analysis program for analysing state transition diagrams (markov chain) using numerical integration techniques. MKV provides facilities for defining multiple phases representing continuous or discrete transitions. The program also analyses non-homogeneous processes by allowing time-dependent transition rates to be defined. Systems with time-dependent transition rates are strictly non-Markovian, however the addition of this facility in the MKV program allows certain types of ageing processes to be modeled.

MKV runs under Microsoft Windows 95, 98, NT, Me and XP and program control is achieved via standard dialogs, pull-down menus and accelerator keys. MKV is accessed via a sophisticated graphical user interface (GUI) which allows the user to construct state transition diagrams with a minimum of effort.

Facilities provided by the program are summarised below :

  • Graphically constructed transition diagram
  • Division of analysis into separate phases
  • State attribute editing via easy-to-use dialogs
  • Data verification for consistency checks
  • Time-dependent transition rates modelled
  • Global parameter facility for repetitive data
  • Calculation of a wide range of probabilities and frequencies
  • Comprehensive reports interfacing with Microsoft Word, Excel etc.
  • Graphs and plots showing time-dependent results

markov numerical integration Numerical Integration

MKV uses 4th order Runge-Kutta numerical integration techniques to analyse the Markov diagram. The system logic is represented by a state transition diagram which may be easily constructed using the program's interactive graphics facilities. The system lifetime may be split into phases with different transition rates.

markov analysis method Markov Analysis Methods

Markov analysis provides a means of analysing the reliability and availability of systems whose components exhibit strong dependencies. Other systems analysis methods (such as the Kinetic Tree Theory method generally employed in fault tree analysis) often assume component independence which may lead to optimistic predictions for the system availability and reliability parameters. Some typical dependencies which can be handled using Markov models are :

  • Components in cold or warm standby
  • Common maintenance personnel
  • Common spares with a limited on-site stock

    The major drawback of Markov methods is that Markov diagrams for large systems are generally exceedingly large and complicated and difficult to construct. However, Markov models may be used to analyse smaller systems with strong dependencies requiring accurate evaluation. Other analysis techniques, such as fault tree analysis, may be used to evaluate large systems using simpler probabilistic calculation techniques. Large systems which exhibit strong component dependencies in isolated and critical parts of the system may be analysed using a combination of Markov analysis and simpler quantitative models.

markov time discrete transition phase Continuous Time and Discrete Transition Phases

MKV allows the user to split the system lifetime into discrete fixed-interval phases. Each phase may be represented by a set of transitions unique to that particular phase. States may not vary between phases. Phases may be specified as continuous time phases or discrete transition phases. Continuous time phases have transitions which are quantified with transition rates. Transition rates are generally failure and repair rates. Continuous time phases have finite phase durations. Discrete phases do not have a phase duration associated with them as they represent fixed probability transitions between states. They may be used to represent fixed interval inspections and preventive maintenance actions. The transitions in a discrete phase must be identified with fixed probabilities.

For continuous time phases the user may specify transition rates which vary with absolute system time or absolute phase time. The time-varying transition rates are specified in the form of a Weibull distribution which is superimposed on the base failure rate.

markov parameter Calculated Parameters

MKV calculates a wide range of system parameters during the integration process. These parameters are

  • Unavailability
  • Availability
  • Unreliability
  • Reliability
  • Failure frequency (unconditional failure intensity)
  • Repair frequency (unconditional repair intensity)
  • Conditional failure intensity
  • Conditional repair intensity
  • Number of expected failures
  • Number of expected repairs
  • Mean unavailability over lifetime
  • Mean availability over lifetime
  • Expected total downtime over lifetime
  • Expected total uptime over lifetime

    MKV also calculates mean and lifetime probabilities for states in the transition diagram.

report graph Reports and Graphs

MKV provides comprehensive printed reports which include the state transition diagram. Reports may be directed to a printer or may be sent to a comma-delimited or fixed-field format file. In addition reports may be directed to the clipboard for pasting into other applications such as Microsoft Word.

MKV also provides a facility to display and print time-dependent data in the form of graphs.

markov and fault tree Integrating Markov and Fault Tree Analysis

The FaultTree+ program now contains an integrated Markov facility which is compatible with the MKV program. This will allow users to model strong dependencies in small sub-systems using Markov analysis and use the results in a full fault tree analysis study.