All courses › Statistics and Risk Analysis › Series and parallel systems

Series and parallel systems

In a series system all components must work for the system to work, so the reliability is the product of each component's reliability. In a parallel system it is enough that at least one works, so the system only fails if all fail together.

Rseries=∏iRiR_{\text{series}} = \prod_i R_iall components must work
Rparallel=1−∏i(1−Ri)R_{\text{parallel}} = 1 - \prod_i (1 - R_i)at least one component must work

Symbols

RiR_ireliability (probability that component ii works)

Example

Two components with R=0.9R = 0.9 each:

In series: 0.92=0.810.9^2 = 0.81. In parallel: 1−0.12=0.991 - 0.1^2 = 0.99.

A parallel connection always increases reliability compared to one component — series always lowers it.
Practise probability for free →

← Union, intersection and complement · Bayes' theorem →

Part of Statistics and Risk Analysis: Probability.