Question

Consider a product with three components in​ series, with reliabilities of​ 0.90, 0.80, and 0.99 for components​ A, B, and​ C, respectively.​ Furthermore, component B uses a backup that also has a reliability of 0.80. What is the reliability of the​ system?

Answer 1

Answer:0.853

Explanation:

Given

Reliability of A is 0.90

Reliability of B is 0.80

Reliability of C is 0.99

B has a backup with reliability of 0.8

i.e. B has a component in parallel to it.

A,B& C is series.

B actual reliability is

$R_b=1-\left ( 1-0.8\right )\left ( 1-0.8\right )$

$R_b=0.96$

Thus $R_{net}$ is given by

$R_{net}=R_A\times R_B\times R_C$

$R_{net}=0.9\times 0.96\times 0.99$

$R_{net}=0.8553$