Fault Tree Example

Fault Tree Example

Problem Statement

Create a fault tree diagram for why a car driver would hit an object while driving. Consider the following elements shown in the table below.

a

Driver could be drunk

 

 

 

 

 

b

Maybe he did not see the object

 

 

 

 

c

Maybe he was going too fast

 

 

 

 

d

Maybe he fell asleep on the wheel

 

 

 

e

Maybe the object just appeared around the corner and he did not have time to react

 

f

Maybe the brakes did not work since they were worn out

 

How to perform analysis

Step 1: Open Sigma Magic
  1. Click on the Sigma Magic button on the Excel toolbar.
  2. Click on the New button to create a new project.
Step 2: Add the analysis template
  1. Click on the Tool Wizard to add the analysis template.
  2. Click on Project and then Fault Tree.


Step 3: Specify analysis options
A new worksheet will be added to your workbook. Analysis Setup will be automatically opened, in the setup tab specify the following details.



If you need to make changes to the charts, specify the optional settings in the Charts tab.

 Labels:

  • Add a title for the chart.
  • Label the X-axis and Y-axis appropriately.

Appearance:

  • Adjust colors, font sizes, or other visual elements as needed.
  • Enable/disable gridlines or background shading.


Step 4: Enter the details in worksheet
Click Create, the worksheet will created and then enter all the details. A sample is provided below:





 Click on Verify tab to ensure all the inputs are okay and shown in a green checkmark.



Step 5: Generate analysis results
Click OK and then click Compute Outputs to get the final results



Interpretating Results

The probability of the top event, "Car hits object," is 0.36. This suggests a moderate likelihood of the accident occurring based on the contributing factors.

The fault tree identifies two main contributing events (E1 and E2) leading to the top event:

    • E1: Driver does not see object (0.6 probability)
    • E2: Car fails to brake (0.6 probability)

Since an AND gate connects these events, both must occur simultaneously for the top event to happen, significantly influencing the accident probability.

E1 is influenced by three sub-events connected through an OR gate:

    • B1: Object just around corner (0.1 probability)
    • B2: Driver drunk (0.2 probability)
    • B3: Driver asleep (0.3 probability)

The highest contributor here is driver asleep (0.3), followed by driver drunk (0.2), making these human-related factors crucial in visibility-related accidents.

E2 is influenced by two sub-events connected through an OR gate:

    • B4: Car going too fast (0.4 probability)
    • B5: Brakes are weak (0.2 probability)

Speeding (0.4 probability) is a significant factor leading to brake failure, making it a primary focus area for accident prevention.

The most significant contributors to the top event are:

    • Driver does not see object (0.6 probability)
    • Car fails to brake (0.6 probability)
    • Car going too fast (0.4 probability)
    • Driver asleep (0.3 probability)

These indicate that driver behaviour (fatigue, speeding, impairment) and vehicle conditions (braking performance) are key risk areas.

The bar chart visualizes that E1 and E2 have the highest probabilities, followed by speeding (B4) and driver fatigue (B3).

This suggests that reducing speeding and driver fatigue can significantly lower the likelihood of accidents.

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