Main Menu

See All Acoustic End-of-Line Test Systems See All DAQ and instruments See All Electroacoustics See All Software See All Transducers See All Vibration Testing Equipment See All Academy See All Resource Center See All Applications See All Industries See All Insights See All Services See All Support See All Our Business See All Our History See All Our Sustainability Commitment See All Global Presence

Main Menu

See All Actuators See All Combustion Engines See All Durability See All eDrive See All Production Testing Sensors See All Transmission & Gearboxes See All Turbo Charger See All Industrial electronics See All S&V Signal conditioner See All DAQ Systems See All Power Analyser See All S&V Hand-held devices See All High Precision and Calibration Systems See All Test Solutions See All nCode - Durability and Fatigue Analysis See All ReliaSoft - Reliability Analysis and Management See All Test Data Management See All DAQ Software See All Drivers & API See All Utility See All Vibration Control See All Acoustic See All Current / voltage See All Displacement See All Load Cells See All Pressure See All Strain Gauges See All Vibration See All Torque See All LDS Shaker Systems See All Vibration Controllers See All Power Amplifiers See All Accessories for Vibration Testing Equipment See All Training Courses See All Acoustics See All Asset & Process Monitoring See All Custom Sensors See All Data Acquisition & Analysis See All Durability & Fatigue See All Electric Power Testing See All NVH See All Reliability See All Smart Sensors See All Vibration See All Weighing See All Automotive & Ground Transportation See All Calibration See All Installation, Maintenance & Repair See All Support Brüel & Kjær See All Release Notes See All Compliance See All Our People

Main Menu

See All QuantumX See All LAN-XI See All SomatXR See All MGCplus See All CANHEAD See All Optical Interrogators See All GenHS See All API See All Microphone Cartridges See All Microphone Sets See All Microphone Pre-amplifiers See All Sound Sources See All Acoustic Calibrators See All Special Microphones See All Accessories for acoustic transducers See All Experimental testing See All Transducer Manufacturing (OEM) See All CCLD (IEPE) accelerometers See All Charge Accelerometers See All Rotating See All Non-rotating (calibration) See All Electroacoustics See All Noise Source Identification See All Environmental Noise See All Sound Power and Sound Pressure See All Noise Certification See All Industrial Process Control See All Structural Health Monitoring See All Electrical Devices Testing See All Electrical Systems Testing See All Grid Testing See All High-Voltage Testing See All Vibration Testing with Electrodynamic Shakers See All Structural Dynamics See All Machine Analysis and Diagnostics See All Dynamic Weighing See All Calibration Services for Transducers See All Calibration Services for Handheld Instruments See All Calibration Services for Instruments & DAQ See All On-Site Calibration See All Resources See All Software License Management

Markov Diagrams

What are Markov diagrams?


Markov diagrams allow you to model the behavior of a system in various states using a memoryless process, where the next state of the system is only dependent on the transition values and the current state of the system. This gives you the ability to look at partial or degraded working states, and to start analysis in varying states. Markov diagrams are available in ReliaSoft BlockSim software. If you have access to the Event Analysis module in BlockSim, you can analyze a Markov diagram during a simulation and use the analysis result in your RENO flowchart.

Using Markov Diagrams in ReliaSoft BlockSim for Reliability Analysis


With BlockSim, we will demonstrate an initial estimation analysis on the life cycle of a complex drilling system that starts off as brand new (100% initial probability in the full capacity state). The system has a probability to degrade into various states of capacity with time and can eventually enter a salvage state. There is also a probability of being returned to the as-good-as-new condition from each degraded state, except from the salvage state. The salvage state is considered to be a "sink," a state from which there are no transitions to any other state and therefore we have zero probability of leaving. We want to determine, on average, what percent of the time will be spent in each state over a 10-year period. To perform this type of analysis, we will use a discrete Markov diagram. Our initial setup looks like this:

We estimate the following probabilities per month to move between states:

  • 1% chance to degrade from 100% to 80% capacity
  • 10% chance to be restored from 80% to 100% capacity
  • 3% chance to degrade from 80% to 60% capacity
  • 8% chance to be restored from 60% to 100% capacity
  • 6% chance to degrade from 60% to 40% capacity
  • 5% chance to be restored from 40% to 100% capacity
  • 8% chance to degrade from 40% capacity to salvage

Based on these percentages, the final diagram that is ready for analysis looks like this:

Since our estimated probabilities are on a month scale, we will take each step of the analysis to be the equivalent of one month. This means that we will run our calculation for 120 steps. After we calculate the diagram, we can see that the transition probability matrix between the states looks like this (which we can easily use to verify our inputs):

Full Diagram
FROM -> TO 100% capacity 80% capacity 60% capacity 40% capacity Salvage
100% capacity 0.99 0.01 0 0 0
80% capacity 0.1 0.87 0.03 0 0
60% capacity 0.08 0 0.86 0.06 0
40% capacity 0.05 0 0 0.87 0.08
Salvage 0 0 0 0 1
We can use the state point probability plot to see if our system has reached steady state within our time frame.

In this case study example, because we have a "sink" state, we do not reach steady state, where all the probabilities have reached a constant value, but rather a pseudo-steady state where the probabilities are changing at a roughly constant rate.


Afterwards, we can check the results summary to determine the mean probabilities in each state and the point probabilities after 120 steps (10 years).

Results After 120 Steps
State name Initial probability Mean probability Point probability Steps spent in state
100% capacity 1 0.894127 0.859252 107.295203
80% capacity 0 0.064845 0.066382 7.781451
60% capacity 0 0.013046 0.014282 1.565469
40% capacity 0 0.005597 0.00662 0.671615
Salvage 0 0.022386 0.053464 2.686261



From the results we can conclude that the majority of the time (89.4%) our system should be running at 100% capacity and that after the 10-year period there is about a 5.3% chance that the system will degrade to a point from which it cannot be restored (the salvage state).