Markov Chain Modeling – Just the Basics
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.
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?
- 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!
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