A product consists of four components with reliability of 0.89,0.90,0.91,and 0.92,respectively.Each component has a backup with the same reliability.Calculate and indicate product reliability.
A)96.40%
B)86.31%
C)94.11%
D)79.32%

Question

Quizplus · Accepted Answer

The reliability of each component with a backup can be calculated using the formula for parallel systems: $R = 1 - (1 - r_1)(1 - r_2)$, where $r_1$ and $r_2$ are the reliabilities of the primary component and its backup, respectively. Since each backup has the same reliability as its primary component, the formula simplifies to $R = 1 - (1 - r)^2$. Calculating this for each component:- For the component with 0.89 reliability: $R = 1 - (1 - 0.89)^2 = 0.9801$ or 98.01%- For the component with 0.90 reliability: $R = 1 - (1 - 0.90)^2 = 0.99$ or 99%- For the component with 0.91 reliability: $R = 1 - (1 - 0.91)^2 = 0.9919$ or 99.19%- For the component with 0.92 reliability: $R = 1 - (1 - 0.92)^2 = 0.9936$ or 99.36%The overall product reliability, assuming the components are in series (since the product requires all components to function), is the product of the individual reliabilities: $R_{total} = 0.9801 \times 0.99 \times 0.9919 \times 0.9936 = 0.9640$ or 96.40%.

A Product Consists of Four Components with Reliability of 0