How does component arrangement affect system reliability?

System reliability depends on what service requires, not just on the number of components. Here reliability means the probability of surviving one stated interval without failure. Components A and B have survival probabilities measured over that same interval, and their outcomes are explicitly independent.

In a series arrangement, both components must survive for service to continue. Independence allows their survival probabilities to be multiplied: Rseries = RA × RB. With RA = 0.9 and RB = 0.8, system reliability is 0.72, or 72 percent. Requiring both makes the system less reliable than either component considered alone.

In a parallel arrangement, either component alone is sufficient for the complete service. System failure requires both to fail. Their failure probabilities are 1 − RA and 1 − RB, so Rparallel = 1 − (1 − RA)(1 − RB). The same component values give 1 − 0.1 × 0.2 = 0.98, or 98 percent.

The difference comes from combining events under different service requirements. It is not an improvement in either component's own survival probability. Parallel redundancy means an alternative can sustain service after the other fails; it does not make failure impossible.

Independence is essential to these products. A shared power loss or environment can make outcomes dependent and invalidate the calculation. The illustration also assumes perfect connections, no repair and no capacity shortfall when only one parallel component survives. These supplied probabilities explain a bounded model rather than certify a real system.