The system reliability for a three-component series system is 0.80. If the reliabilities of two of the components are 0.92 and 0.99, determine the reliability of the third component.
A) Less than 0.60
B) Equal to or greater than 0.60 but less than 0.70
C) Equal to or greater than 0.70 but less than 0.80
D) Equal to or greater than 0.80 but less than 0.90

Question

Quizplus · Accepted Answer

For a three-component series system, the system reliability is given by the product of the individual component reliabilities:

R_sys = R_1*R_2*R_3

Given R_sys = 0.80, R_1 = 0.92, and R_2 = 0.99, we can solve for R_3:

0.80 = 0.92*0.99*R_3

R_3 = 0.916 or 0.92 (rounded to the nearest hundredth)

Therefore, the reliability of the third component is equal to or greater than 0.80 but less than 0.90. The best choice is D.

The System Reliability for a Three-Component Series System Is 0