A system is composed of four parts, J, K, L, and M. All four must function for the system to function. The four component reliabilities are .99, .98, .992, and .998. The designers are considering putting an 80% reliable backup at K. This backup will change the system reliability from ________ to ________.
A) 0.9762; 0.9605
B) 0.9605; 0.9762
C) 0.9605; some smaller value
D) 0.9605; 0.996
E) 0.98; 0.99

Question

Quizplus · Accepted Answer

To calculate the reliability of the system with the backup at K, we can use the formula for system reliability with a backup:

Rsystem = R1 + (R2-R1)R3

Where R1 is the reliability of the original system (JKLM), R2 is the reliability of the backup component (K'), and R3 is the probability that the backup component will not fail (0.80).

Using the given reliabilities, we have:

R1 = 0.99*0.98*0.992*0.998 = 0.979207136
R2 = 0.80
R3 = 0.20 + 0.80*0.992 = 0.9976

Therefore:

Rsystem = 0.979207136 + (0.80-0.979207136)*0.9976 = 0.9604983

So the system reliability with the backup at K is approximately 0.9605, a decrease from the original reliability of 0.9792.

The answer is B because it matches the calculated system reliability with the backup.

A System Is Composed of Four Parts, J, K, L