Question

A system consists of n identical components in parallel with each component having a reliability of p. The failure events of the components can be assumed to be independent. Compute the reliability of the system as functions of p and n. Plot system reliability as functions of p and n for the ranges of p = [0.9, 0.99, 0.999] and n = [3, 5, 10, 100, 1000].

Answer 1

The reliability of a system with n identical components in parallel with each component having a reliability of p is

The reliabilities for p = [0.9, 0.99, 0.999] and n = 3 are plotted below.

The reliabilities for p = [0.9, 0.99, 0.999] and n = 5 are plotted below.

The reliabilities for p = [0.9, 0.99, 0.999] and n = 10 are plotted below.

The remaining reliabilities have the same graph as above for n = 100, 1000.