Markov Chains and State Transition Diagrams in Power BI
A Power BI Markov chain visual that shows how a system moves between states, straight from the rows in your report: from working to degraded to failed and back again, or between any states you define. States are laid out as a progression, with a transition and its return drawn as a pair, and any rates and state probabilities you have are written on the diagram.
Part of Ataytis Assurance, with all six analysis modes in one visual. 30-day free trial, licensed and billed through Microsoft Marketplace.
Failures, repairs and returns
Failures and degradation run forward, and repairs and other returns run back to earlier states, with the layout routing them around the row so the progression stays readable.
Rates and probabilities on the diagram
Each transition shows its label, its rate or both, and each state the probability you give it, in the format set on the column in Power BI.
IEC 61165:2006 profile or your own look
Plain circles with identifiers inside under the IEC 61165:2006 profile, or states coloured by type under Custom, drawn as circles or boxes under either.
About the method
What is a Markov state diagram?
A Markov state diagram is the state transition diagram of a Markov chain: the states a system or process can be in and the rates or probabilities of moving between them. What makes it a Markov model is that the next transition depends only on the current state, not on the path taken to reach it. In dependability work it models repairable systems, standby redundancy and availability over time, and the same diagram serves any process described as states and transitions. Markov analysis is also one of the risk assessment techniques in IEC 31010:2019.
Also known as
- Markov state diagram
- Markov model
Common uses include
- Availability modelling
- Repairable systems
- Standby redundancy
- Condition and degradation modelling
- Customer and process journeys
- Any state transition model
Markov models can be used across industries wherever something moves between defined states at known or estimated rates or probabilities, from equipment and services to customers and processes.
States and transitions, row by row
Each row names the state a transition leaves, the state it reaches and, if you have it, its rate. A state nothing leaves, such as an absorbing state, has a row of its own with no state to reach. States are ordered by their type, their class or the number of failed elements, or from the transitions themselves when a table has none of those. States can be drawn as circles, rectangles or rounded rectangles.
Click a state for everything behind it
Select a state and the Node Inspector opens beside the model with whatever your table holds for it, such as its probability, status, owner or last review date, and the states it connects to. Hover a state for a tooltip with its key values. You choose which columns appear and what each heading is called.
Plain circles, or states coloured by type
By default a model is drawn with a profile designed with reference to IEC 61165:2006: plain circles with the state's identifier inside, its description and probability beneath, and a plain arrow for every transition, repairs included. Switch Profile to Custom and each state is coloured by its type with its description inside, failures are drawn red and repairs green and dashed. The data stays the same, and switching back keeps the settings you made.
Your data
Two pumps, six rows
Both pumps available, one failed, both failed, and a casing rupture the system cannot recover from. Transition Rate and, when you have them, the State Probability values from your Markov analysis go in Values, set to Don't summarize. Add a Diagram ID and one table holds several models, so a slicer or the diagram picker can switch between systems, populations or scenarios.
| State ID | Connected State ID | Node Type | State Label | Transition Type | Transition Rate | State Probability |
|---|---|---|---|---|---|---|
| S0 | S1 | Initial State | Both pumps available | Failure | 0.0002 | 0.9978 |
| S1 | S0 | Degraded State | One pump failed | Repair | 0.125 | 0.0016 |
| S1 | S2 | Degraded State | One pump failed | Failure | 0.0001 | 0.0016 |
| S2 | S1 | Failed State | Both pumps failed | Repair | 0.0625 | 0.0005 |
| S2 | S3 | Failed State | Both pumps failed | Failure | 0.00001 | 0.0005 |
| S3 | Absorbing State | Pump casing ruptured | 0.0001 |
What it draws
Every state and transition
Drawn by default with a profile designed with reference to IEC 61165:2006, Application of Markov techniques. A Custom look colours states by type, and states can be circles, rectangles or rounded rectangles under either.
States
- State
- Initial state
- Degraded state
- Failed state
- Absorbing state
Transitions
- Failure transition
- Repair transition
- Transition
State symbols
- Circle
- Rectangle
- Rounded rectangle
Validation
Checked against the rules of the method as you build
The Validation tab lists anything that breaks these rules and where it is, so the diagram is right before it reaches a review.
- Transition rates are numbers of 0 or more
- Every transition leads to a state with a row of its own
- Nothing leaves an absorbing state
- Every state has a transition into it, once an initial state is set
- One transition per pair of states in each direction
- Every transition has a rate, or none does
Getting started
From your table to Markov models in a report
Install from Marketplace
In Power BI Desktop, open Get more visuals, search for Ataytis Assurance, and add it.
Add your table
Put State ID, Connected State ID and Node Type in Data fields, and Transition Rate in Values if you have rates.
Choose Markov State Diagram
Select the visual, open More options (…) and choose Edit, then pick Markov State Diagram in the Diagram type list on the left.
Licence it to publish
Power BI Desktop needs no licence. Readers in the Power BI Service do, with the first 30 days free.
Pricing
One licence includes all six analysis modes
Markov State Diagram is included alongside Fault Tree Analysis, Bow-Tie Risk Analysis, Event Tree Analysis, Reliability Block Diagram and Goal Structuring Notation. Ataytis Assurance is licensed per user: $4.99 per user per month for small teams, dropping to $2.49 for 500 users or more. The first month is free on every plan, billed by Microsoft.
Licensing a large team or a whole organisation? Request an enterprise quote
Also in Ataytis Assurance
The other analysis modes in the same visual
Every licence includes all six. Switch mode in the editor, and each one keeps its own mapping, layout and look.
Fault Tree Analysis
How could this top event happen?
Explore fault treesBow-Tie Risk Analysis
What can go wrong, what prevents it, and what limits the consequences?
Explore bow-tiesEvent Tree Analysis
What follows an initiating event, and how often?
Explore event treesReliability Block Diagram
Does the system keep working when parts of it fail?
Explore reliability block diagramsGoal Structuring Notation
Does the argument for a claim hold together?
Explore goal structuresQuestions
Markov State Diagram questions
Your next Markov model, in Power BI
Build it in Power BI Desktop with no licence and nothing to sign up for. A licence only comes into it when the report is published for others to open.