Reliability Block Diagram Fundamentals

Basic Definitions

• Reliability: Ability to provide continuous and stable system/component function under defined operating conditions without failure(s).
• Mean Time Between Failures (MTBF): Average expected time interval between failures. Often a measure of reliability.
  • Failure Rate is the expected no. of failures over a period of time. MTBF is the inverse of failure rate.
• Availability: Percentage of time a system or component can perform its intended function without failure.   
  • Key aspects involve individual component reliability, system architecture, redundancy, and implementation of control strategies to ensure uninterrupted service. 
  • Availability = Uptime/(Total Operation Time) = MTBF/(MTBF+MTTR), MTTR is a measure of time to repair the system/component
  • For example, 99.999% (5-9’s of availability) -> 5 min downtime in one year
• Reliability Block Diagram: Reliability Block Diagram (RBD) is a graphical representation used to model reliability in complex systems. Illustrates interconnections between various components or subsystems within a system.

Fundamentals of Reliability Block Diagram Model

• In an RBD, different blocks represent individual components or subsystems of the system.
• These blocks are connected by lines representing the flow of reliability from one component to another.
• Used to analyze and optimize system reliability by identifying critical components, assess the impact of redundancy and evaluate overall system reliability under different failure scenarios.

Reliability of Complex Systems

For systems without redundancy (margin), the reliability of a system is equal to the product of the individual component’s reliability.

• To achieve system reliability (NO system failure), there must be NO failure of Components 1 AND 2 AND 3, AND 4 AND …
• System Reliability, Rs = R1 x R2 x R3 x R4 x …
• If all components have the same reliability the system reliability simplifies to Rs = Rc^N    where:
  • Rs = System Reliability, 
  • Rc = Component Reliability and 
  • N = Number of Components

Series and Parallel RBD

Series RBD 

• Any one component failure leads to system failure

• Rs = (0.95) (0.95) (0.95) = 0.857 = 85.7%

Parallel RBD

• System continues to operate if any component or subsystem is operational 
• 3 parallel subsystems with reliability levels of 90%
• Rs = 1 – (1-0.90) (1-0.90) (1-0.90)

            = 1 – (0.1) (0.1) (0.1) = 0.999  (3-9’s)

• k out of N is similar to parallel design where system some built in redundancy to tolerate system failure  

Reliability Metrics to monitor from RBD Models

• System reliability, availability, mean time between failures and failure rate are all critical metrics we can monitor from RBD models.

Source: Reliawiki