## What is Fault Tree Analysis

Fault tree analysis (FTA) is a graphical tool to explore the causes of system level failures. It uses boolean logic to combine a series of lower level events and it is basically a top-down approach to identify the component level failures (basic event) that cause the system level failure (top event) to occur. Fault tree analysis consists of two elements “events” and “logic gates” which connect the events to identify the cause of the top undesired event.

Fault tree analysis is an easier method than the Failure Mode and Effects Analysis (FMEA) as it focuses on all possible system failures of an undesired top event. Whereas FMEA conducts analysis to find all possible system failure modes irrespective of their severity.

**History of Fault Tree Analysis**

Fault tree analysis is a top down approach that was originally developed in Bell laboratories by H Waston and A Mearns for the air force in the year 1962. This concept later adopted by Boeing and today it is widely used in aerospace, automobile, chemical, nuclear and software industries especially reliability and safety related events.

## When Would You Use FTA

Fault tree analysis can be used to perform for all types of system level risk assessment process. The purpose of FTA is to effectively identify cause(s) of system failure and mitigate the risks before it occurs. This is an invaluable tool for complex systems that visually displays the logical way of identifying the problem. Moreover system efficiency can be attained by this analysis. It can be implemented alone or complement to Failure Mode and Effects Analysis (FMEA).

## FTA** Symbols**

Fault tree uses logical gates to perform the analysis. There are numerous FTA symbols exists, but these are broadly divided in to two categories, Event symbols and Gate symbols.

#### Event Symbols in FTA

#### Gate Symbols in FTA

## How do you do Fault Tree Analysis

- Define the primary failure to be analyzed in other words identify the undesirable top event
- Identify first level contributors which are just below the top level using the available technical information
- Link these contributors to top level event by using logical gates (AND, OR gates), and also see the relationship, so that it will help to identify the appropriate logical gate
- Identify the second level contributors and link to top by using logical gates.
- Identify minimal cut set
- Repeat the same steps till the basic causes
- Finally complete and evaluate the FTA
- Calculate probability of lowest level elements occurrence and also measure the probabilities from bottom up

**Minimal Cut Sets**

One of the important factors in qualitative analysis of fault tree is to identify minimal cut set. For instance complex and large fault tress have to use superior tools (algorithms for extraction) to get the minimal cut sets.

**Cut set:** A set of
basic events that together cause the TOP undesirable event.

Ex: X, Y and Z (from the below picture)

**Minimal cut set:** A cut set with minimal number of events that can still cause the TOP
undesirable event. In other words the TOP undesirable event occurs if one or
more minimal cut set occurs.

Ex: (X and Y); (X and Z) from the below picture

## Practical Example of FTA

A fire broke out at unit 1 of XYZ cable manufacturing company despite safety system in-place. General Manager was very concern about the accident and requests safety in-charge to evaluate the system. However as part of initial analysis of the existing system, safety team using FTA to identify the different causes for accident.

**Quantitative Fault Tree Analysis**

Top undesirable event occurs if one or more of the minimal cut set occurs, hence the main target is to identify minimal cut sets. Moreover if all the minimal cuts are independent to each other, then we could compute the probability of top undesirable event by:

Where P_{j} is the failure
probability of minimal cut set

**Example: **Find the
probability of water pump failure from the below example

The water pump will fail because of value failure and value closed or fault indicator or light fail or control command fail or operator unable to open valve. Since OR gates add and AND gates multiply the probability of pump failure

μ_{pumpfail }=1-(0.05*0.05)*(1-0.003)*(1-0.002)*(1-0.018)*(1-0.02)
= 0.0448

Hence, the probability of water pump failure = 4.48%

**Advantages of Fault tree** analysis

- Fault tree visually depict the analysis that will help team to work on cause of event in logical way that leads to failure
- Highlights the critical components related to system failure
- Provides an efficient method to analyze the system
- Unlike other analysis methods, human errors are also include in the analysis
- It helps to prioritize the action items to solve the problem
- Provides qualitative and quantitative analysis

**Disadvantages of Fault tree** analysis

- Too many gates and events to be consider for large system analysis
- The basic disadvantage is that it examine only one top event
- Common cause failures are not always obvious
- Difficult to capture time related and other delay factors
- Needs experienced individuals to understand the logical gates

## Comments (8)

Thank you very much Sir for your explanation of FTA. God Bless you!

I am an Afghanistani Student in France doing my MSc. thesis on quantitative risk management techniques. This lectures helped me to understand the technique more wisely.

I’m glad it helped, Yama! You’re very welcome.

Thanks for this wonderful Work done. Helped me lot for my current Capstone Project.

Warm Regards

ROHIT 🙂

That’s great to hear, Rohit! You’re very welcome.

I’d love to learn more about your capstone project!

Hi Ted,

The steps above list to ‘Calculate probability of lowest level elements occurrence and also measure the probabilities from bottom up’.

Just wondering how you go about this or have missed a step already stated?

Thanks.

Hi Paul,

Does the example below the instructions help make it more clear?

Best, Ted.

What is the difference between WHY-WHY Analysis & Fault tree analysis.

Hi Kanak,

A Why-why analysis is commonly referred to as a 5 whys analysis.

They are completely different. So much so that this sounds like a homework question, which we do not solve for students.

If not and you’re genuinely curious I’d ask you to look at our 5 whys article here. The methods and desired outcomes are completely different. If you have a specific question, I’m happy to help.

Best, Ted.