Templates  

About Fault Tree Analysis

Fault tree analysis serves to quantify (predict) the reliability / availability of a system.

Identify the real causes of a problem and narrow down the search space for rare errors.

Potential mechanisms of action that lead to errors. Focus on probable causes.

Basic Fault Tree Analysis. You can create fault trees using AND and OR gates. The module can calculate minimal cut sets as well as probabilities for main events.

The fault tree component in Qualica Software is derived from the tree diagram.

Learn how to create the logical structure of a fault tree, add gates and probabilities for leaf events, and evaluate the fault tree.

• 1

  Sample System

  We want to create the fault tree for the following system.

  The pumping system as described here, fills a storage tank within 10 minutes. After that, the storage tank empties within 50 minutes. A full cycle therefore lasts exactly 1 hour.

  
  

  Once the switch is closed, the timer will open the contacts after 10 minutes.

  
  

  If this mechanism fails, an alarm signal sounds (triggered by the filling level of the storage tank). When the alarm sounds, the operator opens the switch to prevent the tank from failing due to overfilling.

  
• 2

  Creating the Structure

  After you have started a new project using the fault tree component or added the component to your project, there is a new worksheet fault tree with some default items on the first level.

  

  • Click onto Failure Mode 1. This will become our top event for the fault tree.
  • Type the description for the top event: System Failure
  • Now change Failure Mode 2 to Filling
  • Use the mouse to drag Filling and drop it onto System Failure
  • Rename the third placeholder into Tank Failure and move it into the Filling event

  The fault tree should look like this:

  

  Now we have to add more events and gates:

  • Click Filling
  • Choose Insert Sub Item from the main ribbon and a new event will be added.
  • Rename the new event into Pump Failure

  Use Insert Item Before and Insert Item After to create new events on the same level. You may also try to use keyboard shortcuts:

  RETURN: adds a new element after the selected item

  SHIFT + RETURN: adds a new sub element

  Now add more elements until you get the following structure:

  

• 3

  Define logical operators

  In the next step logical operators have to be defined for all gates / groups of events. There are AND gates, OR gates, and "k out of n" for groups with more than 2 subordered events.

  All groups / gates have a small rectangular box at the right hand side. Clicking onto this box will show a menu to select the operator for this gate:

  • ≥ : OR operator
  • & : AND operator

  

  The two events under Control have to fail simultaneously to make the gate fail. Control is an AND gate. All other gates are OR gates, which is the default. Change the operator for Control into AND by clicking on the operator box.

  

• 4

  Edit Probabilities

  After defining the logical gates we have to enter probability values for all leaf events. To enter probabilities, select a leaf event in the fault tree and use the Probability menu from the Home ribbon.

  The Probability menu contains a set of predefined probability values. There are two different sets to choose from:

  • MIL Std 882 D: defines a range of 5 probabilities
  • FMEA 2019: offers the probability values corresponding to the 10 occurrence ratings for FMEAs

  Click one of the two set names in the menu to activate a specific set.

  

  Of course it is also possible to enter probability values individually. Use the Edit... item in the Probability menu:

  1. Enter the probability value

  2. If activated, probability is calculated from a best value in field 1 and a worst value in field 3

  3. Enter the worst probability value if calculation as log mean is activated

  4. Switch between values from 0.0 (never) to 1.0 (always) and PPM (parts per million)

  

  Logarithmic mean:

  
  

  $$ p=10^{\frac{log(best)+log(worst)}{2}} $$

  
  

  If you use individual values the probability menu will show the most recently used probabilities. This makes it possible to re-use the probability values for other primary events.

  Example

  Now it is time to set the probabilities for the example fault tree. Please use the edit feature to enter individual values for all primary events. The following table defines three categories of primary events with their probabilities:

  Category	Example	Probability
  Electromechanical Parts	Switch, Timer, Horn, Contacts	p=5e-4
  Active Elements	Pump	p=1e-4
  Human	-	p=2.7e-3

  After editing, our fault tree should look like this:

  

• 5

  Calculation

  After probability values have been assigned to all primary events, probabilities for the main events can be calculated. Calculation can be started by clicking Refresh.Calculate Now from the Home ribbon. Results are shown by the Minimal Cut Sets worksheet: Expand the Fault Tree worksheet in the project tree, then double click on Minimal Cut Sets.

  

  The system uses the MOCUS algorithm to create minimal cut sets for the fault tree. Using the minimal cut sets, probabilities for the main events can be calculated effectively and correctly.

  
  

  With minimal cut sets only main events can be calculated. In order to get the probability of a group or gate, you can set the focus on this gate by using the drop down button in the first line. Now the cut sets get created for the selected event and its probability can be evaluated.

  
  

  The rank of a minimal cut sets is the number of primary events that have to occure at one time in order to fire the main event. A low rank is an indicator for important primary events.

Besides the basic fault tree functions, Qualica Software offers features to prioritize, mark, or hilite events, and assign tasks to events.

Prioritize

On the Home ribbon you can find a button named Priority. Clicking it will show a drop down menu offering priorities from 1 (very high) to 5 (very low). Selecting a priority will show a small box on the marked element:

Knowledge State

On the Home ribbon you can find a button named Knowledge. Clicking it will show a drop down menu offering the available knowledge states. Selecting a knowledge state will show a small box on the marked element:

Categories

On the Home ribbon you can find a button named Categories. Clicking it will show a drop down menu offering 14 different categories. Each category has a label and a associated color. Selecting a category will change the background of an element to the color assigned to this category.

Defining Categories

Click into an edit line and type the label for the category. Right of the edit line you can find buttons for color and pattern selection. Click OK to commit the dialog. Next time you use the Categories menu, you can see the new labels and colors.

Hiliting Elements

You can choose to show background colors instead of the state boxes using the options in the Conditional Formatting section of the Home ribbon. There are 3 options to toggle highlighting priorities, knowledge states, and conditional formats. Categories are treated as conditional formats.

Tasks

There is a button Task on the Home ribbon. Select a failure event in the fault tree, click that button and you will get a dialog to define a task on this failure event.

• Use the central edit field to enter the description of your task
• Enter the due date below Due Date. You can type a date or select a milestone or relative timespan, e.g. "next week". Use the [...] button on the right to open a calendar control for selecting a date.
• Use the drop down box Responsible to assign a team member to the task. There is also a [...] button for advanced editing options for team members.

Worksheets

fault_tree

More Worksheets

• Minimal Cut Sets
• FTA Calculation