What Is Fault Tree Analysis (FTA) and How Does It Improve Reliability?

Fault Tree Analysis (FTA) is a top-down, deductive reliability engineering method used to determine the root causes of an undesired system state—called the "top event." Whether you're designing a new product or investigating a field failure, FTA helps you model how component failures and human errors combine to produce system-level failures. This article explains the method, its steps, and a simple worked example, based on the IEC 61025 standard for Fault Tree Analysis.

What It Is

FTA is a graphical and logical technique that begins with a single top event (e.g., "system fails to start") and breaks it down into lower-level causes using Boolean logic gates—primarily AND and OR gates. The result is a tree-like diagram that shows all combinations of basic events (component failures, human errors, or external conditions) that can lead to the top event. These combinations are called cut sets; a minimal cut set is the smallest set of basic events that, if all occur, will cause the top event. FTA is widely used in aerospace, nuclear, automotive, and medical device industries to quantify failure probability and guide design improvements.

How It Works / Steps

The IEC 61025 standard defines a systematic procedure:

1. Define the top event – State clearly what system failure you are analyzing (e.g., "loss of braking function").
2. Set the boundaries – Define the system scope, environment, and assumptions (e.g., "only one component fails at a time" unless otherwise modeled).
3. Construct the fault tree – Use symbols:

- OR gate: output occurs if any one input occurs.
- AND gate: output occurs only if all inputs occur.
- Basic event: a leaf cause with a known failure probability.
- Intermediate event: a result of lower-level gates.

1. Assign probabilities – Use component failure rates (e.g., from MIL-HDBK-217 or field data) to assign a probability to each basic event.
2. Evaluate the tree – Compute the top event probability using Boolean algebra or cut-set analysis. For independent events:

- OR gate probability: \( P(A \cup B) = P(A) + P(B) - P(A)P(B) \)
- AND gate probability: \( P(A \cap B) = P(A) \times P(B) \)

1. Identify minimal cut sets – These highlight the weakest links and guide where to add redundancy or improve components.

A Worked Illustrative Example

Example data (illustrative only) – Suppose a simple system has a top event "system fails" caused by either a power supply failure (Event A) or a control board failure (Event B). The two are connected by an OR gate. Assume the failure probabilities are:

• P(A) = 0.01 (power supply)
• P(B) = 0.02 (control board)

Using the OR formula:
\( P(\text{top}) = 0.01 + 0.02 - (0.01 \times 0.02) = 0.03 - 0.0002 = 0.0298 \)

So the system failure probability is approximately 0.03, or 3%. The minimal cut sets are {A} and {B}, meaning either event alone can cause the top event. To improve reliability, you might add redundancy so that two power supplies must both fail (AND gate) before losing power—reducing that branch's probability to \( 0.01 \times 0.01 = 0.0001 \).

Common Pitfalls

• Incomplete tree – Missing a credible failure mode leads to underestimated top-event probability.
• Incorrect gate logic – Using an OR gate where an AND gate is needed (or vice versa) changes results dramatically.
• Ignoring dependencies – Common-cause failures (e.g., same batch of components) violate independence assumptions; use special modeling or add a common-cause basic event.
• Using stale data – Failure rates change with environment and time; always document the data source and date.

FTA is a powerful tool, but it requires discipline and clear assumptions. For quick calculations and tree visualization, using a dedicated tool saves time and reduces arithmetic errors. Try the free Fault Tree Analysis tool at https://www.6sq.com/tools/reliability_fta/ to build and evaluate your own fault trees.