Reliability block diagram

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:

${\displaystyle R_{\text{SYS}}=R_{1}(t)\times R_{2}(t)\times \cdots \times R_{n}(t)}$

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:

${\displaystyle Q_{\text{SYS}}=Q_{1}(t)\times Q_{2}(t)\times \cdots \times Q_{n}(t)}$

For constant failure rates, series rates are calculated by superimposing the Poisson point processes of the series components:

${\displaystyle \lambda _{\text{SYS}}=\lambda _{1}+\lambda _{2}+\cdots +\lambda _{n}}$

Parallel rates can be evaluated using a number of formulas including this formula^[5] for all units active with equal component failure rates. n − q out of n redundant units are required for success. μ >> λ

${\displaystyle \lambda _{\text{SYS}}={\frac {n!\lambda ^{q+1}}{(n-q-1)!\mu ^{q}}}}$

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 ${\textstyle \mu \gg \lambda }$.

${\displaystyle \lambda _{\text{SYS}}=\sum _{i=1}^{n}\left(\lambda _{i}\prod _{j=1;j\neq i}^{n}Q_{j}\right)}$

• ARP4761
• Block diagram
• Reliability engineering
• System safety
• Fault tree analysis