Reliability block diagram
A reliability block diagram (RBD) is a diagrammatic method for showing how component reliability contributes to the success or failure of a redundant. RBD is also known as a dependence diagram (DD).
An RBD is drawn as a series of blocks connected in parallel or series configuration. Parallel blocks indicate redundant subsystems or components that contribute to a lower failure rate. Each block represents a component of the system with a failure rate. RBDs will indicate the type of redundancy in the parallel path.[1] For example, a group of parallel blocks could require two out of three components to succeed for the system to succeed. By contrast, any failure along a series path causes the entire series path to fail.[2]Cite error: Closing </ref> missing for <ref> tag
Calculating an RBD
The first thing one must determine when calculating an RBD is whether to use probability or rate. Failure rates are often used in RBDs to determine system failure rates. Use probabilities or rates in an RBD but not both.
Series probabilities are calculated by multiplying the reliability (a probability) of the series components:
- [math]\displaystyle{ R_\text{SYS} = R_1(t)\times R_2(t)\times\cdots\times R_n(t) }[/math]
Parallel probabilities are calculated by multiplying the unreliability (Q) of the series components where Q = 1 – R if only one unit needs to function for system success:
- [math]\displaystyle{ Q_\text{SYS} = Q_1(t) \times Q_2(t) \times \cdots \times Q_n(t) }[/math]
For constant failure rates, series rates are calculated by superimposing the Poisson point processes of the series components:
- [math]\displaystyle{ \lambda_\text{SYS} = \lambda_1 + \lambda_2 + \cdots + \lambda_n }[/math]
Parallel rates can be evaluated using a number of formulas including this formula[3] for all units active with equal component failure rates. n − q out of n redundant units are required for success. μ >> λ
- [math]\displaystyle{ \lambda_\text{SYS}=\frac{n!\lambda^{q+1}}{(n - q - 1)!\mu^q} }[/math]
If the components in a parallel system have n different failure rates a more general formula can be used as follows. For the repairable model Q = λ/μ as long as [math]\displaystyle{ \mu\gg\lambda }[/math].
- [math]\displaystyle{ \lambda_\text{SYS}=\sum_{i=1}^n \left( \lambda_i \prod_{j=1; j\neq i}^n Q_j \right) }[/math]
See also
References
- ↑ Electronic Design Handbook, MIL-HDBK-338B, October 1, 1998
- ↑ "4". Reliability Engineering and Risk Analysis: A Practical Guide. Ney York, NY: Marcel Decker, Inc.. 1999. p. 198. ISBN 978-0-8247-2000-1. https://books.google.com/books?id=IZ5VKc-Y4_4C&pg=PA198. Retrieved 2010-03-16.
- ↑ Electronic Design Handbook, MIL-HDBK-338B, October 1, 1998
External links
- http://www.reliabilityeducation.com/rbd.pdf (commercial website)
- Institut pour la Maîtrise des Risques, method sheets, english version[yes|permanent dead link|dead link}}]
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