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 a .80 reliable backup at K. This backup will change the system reliability from __________ to __________.
A) 0.9762 to 0.9605
B) 0.9605 to 0.9762
C) 0.9605 to some smaller value
D) cannot be determined
E) none of the above

Question

Quizplus · Accepted Answer

First, we need to find the current system reliability by multiplying the reliabilities of all four components:

0.99 x 0.98 x 0.992 x 0.998 = 0.9762

If we add the backup at K, the system will only fail if both K and at least one of the other components fail. Therefore, the new system reliability can be calculated as:

(0.80 x (1-0.99)) + (0.20 x 0.99 x 0.98 x 0.992 x 0.998) = 0.9605

This represents a decrease in system reliability from 0.9762 to 0.9605. Therefore, the answer is B.

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