In a two-component parallel system, the overall reliability is 0.9994. If the reliability of the first component is 0.9890, determine the reliability of the second component.
A) Equal to or greater than 0.60 but less than 0.70
B) Equal to or greater than 0.70 but less than 0.80
C) Equal to or greater than 0.80 but less than 0.90
D) Greater than 0.90

Question

Quizplus · Accepted Answer

In a parallel system, the overall reliability $R_{system}$ is given by $1 - (1 - R_1)(1 - R_2)$, where $R_1$ and $R_2$ are the reliabilities of the two components. Given $R_{system} = 0.9994$ and $R_1 = 0.9890$, we can solve for $R_2$. Rearranging the formula gives $R_2 = 1 - \frac{1 - R_{system}}{1 - R_1}$. Substituting the given values, $R_2 = 1 - \frac{1 - 0.9994}{1 - 0.9890} = 1 - \frac{0.0006}{0.011} = 1 - 0.0545$, which is greater than 0.90.

In a Two-Component Parallel System, the Overall Reliability Is 0