Abstract

Chris and Fred discuss Markov Chain modeling. Where we model transitioning from one state to another – which is often used for availability. How and when do I use it? Does it work in today’s reliability applications? Listen here to learn more.

Key Points

Join Chris and Fred as they discuss Markov Chain modeling – which is often taught in universities but may not be as practically useful. A Markov Chain is a series of ‘states’ that could (for example) represent a system fully functional (state 1), degraded (state 2) and failed (state 3). You can have as many states as you like. Then there are transition rates between each state – which must remain constant. This starts to become useful when you want to model failure AND things like repair – where you transition from a failed state to a functional state. Does this work?

Topics include:

• How are Reliability Block Diagrams (RBDs) and fault trees different? These traditional modeling mechanisms tend to focus on failure – and not going back to a functional state, degraded state, or any other state you define.
• … but Markov Chains are ‘memoryless’ or ‘ageless.’ This means that the transition rates are constant. They don’t change with respect to time – or system age. Nor do they change based on how long your system has been in each state.
• So Markov Chains are primarily used for steady-state availability. Trying to work out the likely long term probabilities of your system being in any one of the states you defined.
• Are they like Petri nets? No. Petri nets may look like Markov Chains, but instead, the model is based on tokens moving through the chain to understand system behavior.
• Other ways? Try Agent-Based Models. Relatively simple rules can then treat your system as an ‘agent’ … and then you can control the way your systems behave in much greater detail.
• What about Markov Chain Monte Carlo (MCMC) simulations? If you have heard of this – don’t worry! MCMC is a simulation technique based IN PART on Markov chains to help create a representative sample of random variable values from a given function (like a probability density function). This is useful for solving some complex calculations – including reliability engineering complex calculations – but is not what we are talking about here!

Enjoy an episode of Speaking of Reliability. Where you can join friends as they discuss reliability topics. Join us as we discuss topics ranging from design for reliability techniques to field data analysis approaches.

SOR 495 Markov Chain Modeling – Just the BasicsChristopher Jackson

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