A product consists of four components with reliability of 0.85,0.87,0.89,and 0.91,respectively.The first and third components each have a backup with reliability of 0.95 and 0.90,respectively.Calculate and indicate product reliability.
A)77.71%
B)62.80%
C)39.40%
D)89.10%

Question

Quizplus · Accepted Answer

The reliability of a system with backup components can be calculated by combining the reliabilities of the primary and backup components, and then multiplying the reliabilities of all components in the system. For the first component with a reliability of 0.85 and a backup of 0.95, the combined reliability is 1 - (1 - 0.85) * (1 - 0.95) = 0.9925. For the third component with a reliability of 0.89 and a backup of 0.90, the combined reliability is 1 - (1 - 0.89) * (1 - 0.90) = 0.989. The second and fourth components' reliabilities are 0.87 and 0.91, respectively. Multiplying these together gives the overall system reliability: 0.9925 * 0.87 * 0.989 * 0.91 ≈ 0.7771 or 77.71%.

A Product Consists of Four Components with Reliability of 0