Reading a Markov diagram
How a Markov diagram is laid out and ordered, the two notation profiles, the state symbol, rates and probabilities on the diagram, the summary strip, the Node Inspector and focus.
How it is laid out
- States run from working order on the left to failure on the right.
- A failure out and a repair back between neighbouring states are drawn as a pair of arrows side by side.
- A longer way back, such as a repair from the far end to the start, is routed around the outside of the row.
- A label on an arrow is moved off other lines, labels and states, so each rate stays beside its own arrow.
To work out which way the model runs, the visual treats every transition typed Repair, and every transition towards a healthier state, as running back. To judge which state is healthier, it uses the first of these that every state has: Failed Element Count, then State Class, then Node Type.
A table with neither Node Type nor Transition Type leaves it guessing. It starts from a state nothing leads into or, when every state has something leading into it, from the first State ID in sort order. A plain table of states UP, DEG and DOWN therefore starts at DEG, with UP and DOWN side by side after it. Give the states a Node Type or the transitions a Transition Type, and it starts at UP.
Nodes cannot be dragged. Change the result with orientation, density and spacing. Every orientation is available under both profiles.
Notation profiles
| Profile | How it draws |
|---|---|
| IEC 61165:2006 (default) | Every state as the same plain circle with its identifier inside and its description and probability beneath. Every transition as the same plain arrow, repairs included. |
| Custom | The identifier and the description together inside a larger circle, coloured by state type. Failures red, repairs green and dashed, other transitions grey. An absorbing state has a heavier border. |
Choose the profile under Diagram → Notation → Profile. Neither profile locks a setting: colour, line weight, connector routing, label position and the state symbol can be changed under both. Move the label inside under IEC 61165:2006 and the identifier moves in with it, above the description.
State symbol
Under Diagram → State symbol → States drawn as, choose Circle, Rectangle or Rounded rectangle. The choice applies under both profiles. A rectangle is drawn wider and shorter than the circle it replaces.
Rates and probabilities on the diagram
These settings are in the Rates and probabilities group on the Labels tab.
| Connector shows | On the arrow from S0 in the example, with a Transition Label of Failure |
|---|---|
| Its label, or the rate if it has none (default) | Failure |
| Label and rate | Failure · 0.0002 |
| Rate only | 0.0002 |
| Nothing | No text |
State probability is Show on state or Hide. When shown, the probability is written beneath the state's description, unless the state already has a secondary label of its own.
Both use the Power BI format of their column. A probability of 0.9978 in a column formatted as a percentage is drawn as a percentage; with no format, the number is written as stored, so a rate of 0.00001 is not rounded to 0.
Summary strip
Turn on Labels → Summary strip → Show summary. A Markov diagram counts all its states by Status. For the example it shows 4 states: 2 Failed, 1 Degraded and 1 Healthy.
Node Inspector
The Analysis section lists the state's probability, Status, identifier, and the absorbing, initial, state class and failed element values, wherever they are mapped and filled in. A transition's rate belongs to the transition: hover the arrow to see it in the tooltip.
There is no Relationships section, except on a state that more than one transition arrives at. That shows Used in with the number of transitions arriving, followed by the states they come from. In the example, One pump failed reads Used in 2 branches, from Both pumps available and Both pumps failed.
Focus branch
Focus branch keeps the state, every state it can reach and every state that can reach it. A repairable model loops, so that is usually every state: in the example, focusing any state keeps all four.