For the overall reliability of the following system to be 0.975 or greater the reliability of the backup component, Rb, must be

A)at least 1.00
B)at least 0.896
C)at least 0.736
D)at least 0.534

Question

For the overall reliability of the following system to be 0.975 or greater the reliability of the backup component, Rb, must be

A)at least 1.00 
B)at least 0.896 
C)at least 0.736 
D)at least 0.534

Quizplus · Accepted Answer

To find the overall reliability of the system, we can use the formula:

Rs = Rp x Rb

where Rs is the overall reliability, Rp is the reliability of the primary component, and Rb is the reliability of the backup component.

We want Rs to be 0.975 or greater, so we can write:

0.975 ≤ Rp x Rb

To solve for Rb, we need to divide both sides by Rp:

0.975/Rp ≤ Rb

Since we don't have any information about Rp, we can assume it to be 1.0 (i.e., perfect reliability). This gives us:

0.975 ≤ Rb

The only choice that satisfies this condition is B: at least 0.896. Therefore, the answer is B.

For the Overall Reliability of the Following System to Be