MADE Training > Session 4 > 4.5 Markov Analysis

Session 4.5: Markov Analysis

Session 4.5 Outline

ARP4761 Standard: Guidelines & methods of performing safety assessment for certification of civilian aircraft
Markov Analysis (MA) Definition: A Markov Model (chain) represents various system states & the relationships among them.
- States: Operational, Degraded, Non-Operational (Failed)
- Transition rate between states is a function of failure/repair rate
- State probabilities derived from differential equations derived from Markov chain
Used to model complex, fault-tolerant systems with condition monitoring & reconfiguration
Performed during Concept and Preliminary Design Stages
Unlike Fault Trees, MA covers complex system behaviours of repairable systems or systems where failure/repair rate are state dependent
Disadvantage: Markov model size grows exponentially with number of components
- In MADE, MA is conducted on each individual item for simplicity

To create a Markov Analysis:

Select Analyses > Markov Analysis from the main menu
Alternatively, right-click an item in the Project Explorer/System Model and select Markov Analysis
Select the new Markov Analysis icon
From the dialog, select Primary Fuel Filter
Select OK

Canvas: Displays states, transitions and transition durations in hours
Palette: Contains a selection tool, list of state categories and transition connection
Markov Analysis Results: Shows states & corresponding availability, reliability & duration of operation

Note: Properties Viewer edits canvas details: transitions, durations, state details.

There are 4 types of states used in the Markov Analysis:

Initial State: Item state at time t = 0. Indicated by a blue circle. Default numerical label (indicating state) is 0 but can be a larger value.
Operational State: Item state in which the item is capable of performing the required function. Indicated by a green circle. Default numerical label is ≥ 0.
Degraded State: Item state in which the item is capable of partially performing the required function. Indicated by a yellow circle. Default numerical label is ≥ 0.
Failure State: Item state in which the item is not capable of performing the required function. Indicated by a red circle. Default numerical label is ≥ 0.

The user can modify Markov states from the Properties viewer:

State Name: Updates individual state names in the canvas
Initial State (check box)
(State) Type:
- Normal Operation
- Degraded Operation
- Total System/Component Failure
- Dangerous Failure: Failure which has the potential to put the safety related system into a hazardous state or fail-to-function state
- Safe Failure: Failure that does not have the potential to put the system into a hazardous state or fail-to-function state
Description Field: Used to describe the condition of the item during a specific Markov state

Create the following states: Operational State, Degraded State
- Step 1: Select states in Markov Analysis palette
- Step 2: Select canvas to create state
Change Total System/Component failure type to Dangerous Failure
Delete the existing connection between Normal Operation and Dangerous Failure

Markov Analysis Transitions represent the change from one state to another
Indicated by a single or double-sided arrow connecting two states in the canvas
- Single arrow indicates transition in only one direction/only one state
- Double-headed arrow indicates transition is possible between both states
Transition connection displays time in hours to transition between states
- Double-headed arrows show 2 transition times
- Set from the Properties viewer
Transition placement is manipulated by selecting the square on the line

Note: numbering may differ due to the order each state was created.

Select Transition between Normal Operation 0 and 2
- Normal Operation (0): Set Transition state 0 to state 2 (Hours) to 1.5
- Normal Operation (2): Deselect "Allow transition from state 2: Normal Operation to state 0: Normal Operation"

Complete remaining Markov State transitions:

Normal Operation to Degraded State
- Degraded Operation: 56.55
- Normal Operation (2): 2.5
Degraded Operation to Dangerous Failure
- Degraded Operation: Deselect Transition
- Dangerous Failure: 10.6
Normal Operation to Dangerous Failure
- Normal Operation: Deselect Transition
- Dangerous Failure: 79.75

Markov Analysis — Results collapsible canvas is refreshed to generate updated results
Results are displayed in table or line chart format
Export of table in .csv format available

To generate results for all Markov states:

To apply the current Markov Analysis to multiple items in the system:

Navigate to Overview/Management page
Select the Markov Analysis
Select the icon to open the Target Items dialog
From the target item dialog select item check boxes that apply: Apply to Primary Fuel Filter (default), Secondary Fuel Filter & Air Filter
Select Apply
Verify Markov Analysis application in table