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: : 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: : 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: : \lambda_\text{SYS} = \lambda_1 + \lambda_2 + \cdots + \lambda_n Parallel rates can be evaluated using a number of formulas including this formula for all units active with equal component failure rates.
n −
q out of
n redundant units are required for success.
μ >>
λ : \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 \mu\gg\lambda. : \lambda_\text{SYS}=\sum_{i=1}^n \left( \lambda_i \prod_{j=1; j\neq i}^n Q_j \right) ==See also==