Reliability Block Diagrams: An Overview

What is a Reliability Block Diagram (RDB)

An RBD is a graphical diagram to qualitatively and quantitatively determine the overall reliability of a system. This helps identify the overall success or failure rate of a system in deployment. The RBD shows the essential components that contribute the success of the system.

How to create one?

Let's build an example!

Consider a simple lightbulb circuit (Fig 1). There is a battery powering a lightbulb through a switch and a current limiting resistor.

Fig 1: Simple lightbulb circuit

A failure in any of the component will lead to the light bulb not functioning

• Battery fails - > no power to the lightbulb

• Switch fails -> circuit remains open

• Resistor open - > circuit remains open

• Light bulb filament broken -> light off

With the assumption that the purpose of the circuit is to make the lightbulb glow, the RBD will look like the diagram below (Fig 2).

Fig 2: RBD for simple lightbulb circuit

All the components are in series. This means that if any of the components fail, the light bulb will stop being operational.

Now, let's quantify the results. Let's assume that we know the failure rate of components. We can now determine which of the components are critical. In order to do so, we need the MTTF (Mean Time to Failure) of components.

Fig. 3 shows the failure rates (λ) and MTTF of each of the components of the lightbulb circuit. The failure rates can be estimated based on standards such as IEC 61709, Siemens SN29500, NIL-HDBK-217F, or similar standards. They can also be determined based on historical failure data. Based on the failure rates of each component, the criticality of each component can be determined. Fig. 4 shows the criticality of each component. Since the light bulb has the highest failure rate (100 FIT) and smallest MTTF (1.1k years), it is the most critical component.

Fig 3: Failure rates and MTTF for each component

Fig 4: Component criticality based on RBD

The overall system reliability of the system is expressed by a reliability function

The mathematics behind the reliability function is explained in this blog.

Fig.5 shows the overall reliability of the system as a function of time.

Fig.5 : Overall system reliability

Based on the graph and the data to the right of the graph, the following conclusions can be made

• From the graph,

  • Reliability at the beginning is 1 => 100% of components are functioning

  • The reliability is exponentially decreasing as time increases

  • The MTTF is 815 years. i.e. MTTF = 815 years means the total expected operating time before one failure is 815 system-years.

  • Also, note that MTTF is the "mean" time to failure and not the "median" time

  
  

• From the data on the right of the graph

  • After 1 year, 99.88% of the products will still be operational

  • If the warranty period is 2 years, 99.76% of the products will be still operational at the end of the warranty period

  • At MTTF (815 years), 36.79% of the components are still operational

  • B10 life (when 10% of the components fail) can be estimated from the graph = 85.9 years

  • Similarly, B50 can be estimated from the graph

The warranty information based on reliability can also be determined, as shown in Fig. 6.

• Assuming the product is continuously working for 24 hrs./day, and the warranty is 2 years.

• We know that reliability at the end of 2 years is 99.76% (see Fig 5).

• If 10,000 of these products are sold, we can expect ~25 (24.5) to be returned before the warranty period, due to failures.

Fig 6: Warranty Information

Summary

Reliability Block Diagrams give engineers a simple yet powerful lens for seeing exactly how a system's architecture, whether series, parallel, or a mix of both, shapes its overall reliability. Whether designing for redundancy or identifying a single point of failure, RBD is a powerful toolbox for engineers to design reliable systems.